Model-Based Framework for Real-Time Dynamic Structural Performance Evaluation

Transcription

1 NSL Report Sere Report No. NSL- Augut Model-Bed Frmewor for Rel-Tme Dynmc Structurl Performnce vluton Brn M. Phllp nd Blle F. Spencer, Jr. NWMARK STRUCTURAL NGINRING LABORATORY Deprtment of Cvl nd nvronmentl ngneerng Unverty of Illno t Urbn-Chmpgn

2 UILU-NG--8 ISSN:

3 The Newmr Structurl ngneerng Lbortory (NSL) of the Deprtment of Cvl nd nvronmentl ngneerng t the Unverty of Illno t Urbn-Chmpgn h long htory of ecellence n reerch nd educton tht h contrbuted gretly to the tte-of-the-rt n cvl engneerng. Completed n 967 nd etended n 97, the tructurl tetng re of the lbortory h vertle trong-floor/wll nd three-tory cler heght tht cn be ued to crry out wde rnge of tet of buldng mterl, model, nd tructurl ytem. The lbortory nmed for Dr. Nthn M. Newmr, n nterntonlly nown eductor nd engneer, who w the Hed of the Deprtment of Cvl ngneerng t the Unverty of Illno [956-7] nd the Chr of the Dgtl Computng Lbortory [947-57]. He developed mple, yet powerful nd wdely ued, method for nlyzng comple tructure nd emblge ubjected to vrety of ttc, dynmc, blt, nd erthque lodng. Dr. Newmr receved numerou honor nd wrd for h chevement, ncludng the pretgou Ntonl Medl of Scence wrded n 968 by Predent Lyndon B. Johnon. He w lo one of the foundng member of the Ntonl Acdemy of ngneerng. Contct: Prof. B.F. Spencer, Jr. Drector, Newmr Structurl ngneerng Lbortory NCL, MC-5 5 North Mthew Ave. Urbn, IL 68 Telephone (7) -86 -ml: bf@llno.edu Th techncl report bed on the frt uthor doctorl dertton of the me ttle, whch w completed n Aprl. The econd uthor erved the dertton dvor for th wor. The uthor would le to cnowledge the upport of the Ntonl Scence Foundton under wrd CMMI-54 led by Shrley J. Dye, well Rchrd. Chrtenon for the ue of the N MR dmper nd the upport of Jm M. Rcle nd the NS@Lehgh tff wth the tetng t Lehgh Unverty. The frt uthor would lo le to cnowledge the upport of Sylv Cho durng the coure of th reerch. The cover photogrph re ued wth permon. The Trn-Al Ppelne photogrph w provded by Terr Gller Photogrphy (

4 ABSTRACT treme dynmc event contnue to demontrte the frglty of cvl nfrtructure worldwde. Over the yer, degn code nd computtonl tool hve come to reflect n mproved undertndng of dynmc lod nd effect. However, epermentl tetng often drve thee chnge. permentl tetng vtl to undertndng the behvor of tructure ubjected to thee dynmc lod nd evlutng new oluton for hzrd mtgton. Common epermentl frmewor nclude qu-ttc tetng, he tble tetng, nd hybrd multon. The trdeoff n lodng protocol me ech epermentl frmewor ttrctve n dfferent tuton. Hybrd multon powerful, cot-effectve frmewor for tetng tructurl ytem, cloely couplng numercl multon nd epermentl tetng to obtn the complete repone of tructure. Through ubtructurng, the well-undertood component of the tructure re modeled numerclly, whle the component of nteret re teted phyclly. Generlly, n rbtrry mount of tme my be ued to clculte nd pply dplcement t ech tep of the hybrd multon. However, when the rte-dependent behvor of the phycl pecmen mportnt, rel-tme hybrd multon (RTHS) mut be employed. In RTHS, computton, communcton, nd ctutor lmtton cue dely nd lg whch led to nccurce nd potentl ntblte. At the me tme, the phenomenon of control-tructure ntercton (CSI) led to couplng of the dynmc behvor of the ctutor nd the tructure. Trdtonl ctutor control pproche for RTHS compente for n pprent tme dely or tme lg rther thn ddre the ctutor dynmc drectly. Furthermore, mot ctutor control pproche focu on ngle-ctutor ytem. The model-bed ctutor control pproch propoed heren drectly ddree ctutor dynmc ncludng CSI nd ctutor couplng through model-bed feedforwrd-feedbc control. The feedbc controller fleble to nclude mult-metrc meurement for mproved trcng of hgher-order dervtve, movng beyond the trdtonl focu olely on dplcement trcng. The propoed pproch llutrted for predefned trjectore well RTHS of both ngle nd mult-ctutor ytem. The mlrte between ctutor control for RTHS nd he tble re leverged to pply the propoed model-bed control pproch to ccelerton trcng. She tble provde drect men by whch to evlute tructurl performnce under erthque ectton. entlly, n ctutor ecte be plte on whch tructurl model mounted wth predefned ccelerton record. Improvement to ccelerton trcng eplored n the preence of lrge nonlnerte n he tble behvor well chnge n he tble dynmc through CSI. The reerch preented n th report provde n dvnced frmewor for the dynmc performnce evluton of tructurl ytem. A brod cl of tructure condered for RTHS, ncludng mult-degree-of-freedom (MDOF) tructure through ccurte control cro brod frequency rnge, mult-ctutor ytem through the modelng of ctutor couplng, nd mproved trcng of hgher-order dervtve through mult-metrc feedbc control. Applcton to he tble control demontrte the vertlty of the propoed ctutor control cheme for generl rel-tme ctutor control.

5 CONTNTS CHAPTR : INTRODUCTION.... Motvton.... permentl Tetng Frmewor.... Rel-tme Hybrd Smulton....4 Overvew of Report... 5 CHAPTR : LITRATUR RVIW Hybrd Smulton Frmewor Rel-Tme Hybrd Smulton quton of Moton Numercl Integrton....5 permentl rror Rel-Tme Actutor Control Strtege Control-Structure Intercton....8 Mult-Actutor Sytem....9 She Tble Control.... Summry... 4 CHAPTR : BACKGROUND Clc Control Theory Modern Control Theory.... Dcrete Tme Servo-Hydrulc Sytem Modelng Summry CHAPTR 4: MR DAMPR MODLING AND CONTROL MR Dmper Specmen Chrcterzton Tet... 48

6 4. Hgh-Fdelty MR Dmper Model Advnced Sem-Actve Control Algorthm Force Trcng erce MR Dmper Flud Settlng Summry CHAPTR 5: MODL-BASD ACTUATOR CONTROL FOR RTHS Problem Formulton Regultor Redegn Model-Bed Controller SISO mple MIMO Sytem wth Actutor Couplng Mult-Metrc Feedbc Control Summry CHAPTR 6: SINGL ACTUATOR CONTROL permentl Setup Chrcterzton of the Servo-Hydrulc Sytem Controller Degn Trcng Performnce n the Frequency Domn Trcng Performnce n the Tme Domn Prelmnry Rel-Tme Hybrd Smulton Study Rel-Tme Hybrd Smulton of Sem-Actvely Controlled Structure Summry... CHAPTR 7: MULTI-ACTUATOR CONTROL Mult-Actutor Nonlner Numercl Study Lrge-Scle Mult-Actutor permentl Frmewor Summry... CHAPTR 8: ACTUATOR CONTROL FOR SHAK TABLS... 4

7 8. Model-Bed Control for She Tble Tetng permentl Setup Bre She Tble Two-Story Lner Buldng Nonlner Structure Summry CHAPTR 9: CONCLUSIONS AND FUTUR STUDIS Concluon Future Stude... 6 RFRNCS... 6

8 Chpter. Motvton INTRODUCTION treme dynmc event contnue to demontrte the frglty of cvl nfrtructure. Unle ttc lod, for whch humn hve hd n ntutve undertndng for mny mllenn, thee dynmc lod cue unpredctble nd wdepred dmge worldwde. rthque re one of the mot detructve nturl hzrd; recent emple nclude mgntude 8. erthque n Wenchun, Chn n 8, mgntude 7. erthque n Ht n, nd mgntude 9. erthque off the cot of Tōhou, Jpn n. very new cttrophc event provde the nfluentl combnton of publc nteret nd rch et dt tht ued to develop emc retnt devce nd ytem, mprove degn code, nd chnge publc polcy. To fnd n event comprble n mgntude nd detructon n the US, one mut loo bc to the mgntude 7.9 erthque n Sn Frncco, Clforn n 96. Snce 96, Clforn h been ht by erthque n Sn Fernndo n 97, Lom Pret n 989, nd Northrdge n 994. However, n ech ce, the erthque were le thn 7. n mgntude, the mpcted re were lmted n ze, nd the communte rebounded wthn wee (NAS, ). Loong bc even further, ere of three erthque, ech wth n etmted mgntude of 8. followed by everl hundred of fterhoc, ht the New Mdrd emc zone n the Mdwet of the US from 8 to 8. At the tme, the Mdwet w prely populted nd dmge to cvl nfrtructure w very lmted. If mlr event were to tre tody, the cte of Memph nd St. Lou re epected to utn evere dmge. It etmted tht mgntude 7.7 erthque n the New Mdrd emc zone would reult n 86, culte nd $ bllon dollr n drect economc loe (lnh et l., 9). Depte lc of recent cttrophc emc event wthn the US, the nevtblty of future event hould eep US from ene of complcency. Nturl hzrd re n unfortunte rectve men by whch to ffect chnge n undertndng nd polcy. Conderng humn nd economc loe, t the downtme between event when engneer hould be mot vglnt, ctng n preventtve mnner through etenve reerch progrm. Over the yer, degn code hve een conderble mprovement nd computtonl method for the nly of dynmc tructure repone hve become more dvnced. However, epermentl tetng often drvng thee chnge. When the repone of tructurl component or ytem unnown or dffcult to model numerclly, epermentl tetng provde the only wy to ccurtely e the dynmc repone.. permentl Tetng Frmewor ngneer hve number of epermentl tetng frmewor wth whch to e the behvor of tructurl ytem under dynmc lod. The trdeoff n lodng protocol me ech frmewor ttrctve n dfferent tuton. The mot trghtforwrd method of epermentl tetng qu-ttc tetng, whereby tructure or tructurl component loded n predefned mnner t low rte. Becue of the low rte of lodng, very lrge force cn be

9 generted by hydrulc ctutor, nd thu full-cle pecmen re ely ccommodted. Typclly qu-ttc tetng ued to nvetgte the cpcty or hyteretc behvor of mterl, tructurl component, or tructurl ytem. Th nformton prtculrly ueful for clbrtng numercl model tht cn be ued etend the reult of the qu-ttc tet. Alo, qu-ttc tetng pproprte for prmetrc tude where the nfluence of ncrementl chnge n tructurl degn or mterl cn be objectvely eed. Such prmetrc tude re eentl n developng nd mprovng degn code provon. However, qu-ttc tet re lmted by ther predefned lodng protocol n tht the behvor of the pecmen wll not ffect the future lod tep. In hort, qu-ttc tet provde cpcty nformton rther thn performnce nformton. Another well-etblhed epermentl tetng frmewor ue hng tble. In he tble tetng, the entre tructurl ytem modeled phyclly nd ground moton ppled n rel-tme. Nturlly, th type of tetng mpoe the lmtton tht dynmc lod uch wnd or blt cnnot be condered drectly. For ground moton multon, the dynmc effect of the tructure re completely cptured, mng th tetng method ttrctve for erthque tude. Conderng the pylod of mot he tble, reduced-cle tructurl model re typclly requred. Mntnng mltude reltonhp eentl to ure tht the cled model re provdng ccurte repreentton of ther full-cle counterprt. However, there re mny phenomenon, uch ftgue, frcture, frcton, locl buclng n teel, nd crc propgton nd her n concrete tht hve ze effect lmtng the ccurcy of cle model. Alo, t dffcult to cpture ol-tructure ntercton unle the foundton ytem ncluded n the phycl model. Some lrge-cle hng tble et tht re cpble of tetng full-cle tructurl model ncludng the foundton ytem; however, the cot of ther ue nd mntennce retrctve. Hybrd multon combne epermentl tetng nd numercl multon to provde n effcent nd cot-effectve frmewor to tet lrge, comple tructure (e.g., Huno et l., 969; Tnh et l., 975; Mhn nd Shng, 985; Tnh nd Nhm, 987; Mhn et l., 989; Shng et l., 996). In hybrd multon, the dynmc effect from lod uch erthque, trong wnd, or tunm re clculted through numercl ntegrton nd ued for determnng the lodng protocol of the epermentl component. The repone of the epermentl component meured nd ued to updte the numercl ntegrton n loop of cton nd recton to multe the dynmc repone of the totl tructure. Becue the tructurl dynmc re epreed numerclly nd the rte-dependent effect of the epermentl component re umed neglgble, hybrd multon typclly employ n etended tme cle. Th lowng of the eperment plce le trngent retrcton on epermentl component. For emple, becue lrge velocte re not requred, the repone lg of ctutor re not concern. Therefore, ctutor re not lmted by ther flow rtng, nd lrge, prece force cn be ely mpoed on the phycl pecmen. Lewe, the etended tme cle llow for more fleblty durng tetng. The pecmen my be under contnul obervton nd ny problem ddreed mmedtely wthout dvncng to the net lod tep. The eperment my be pued nd retrted t ny tme wth neglgble effect on the reult. Thu, hybrd multon my lt hour or even dy. A drect reult of the etended tme cle n nblty to pply pecfed velocty tme htory, whch cn be problemtc when tetng rte-dependent pecmen (e.g.,

10 upplementl energy dpton devce) or mply when rte-dependent behvor not neglgble. When ubtructurng ued, tructurl component for whch the repone well undertood cn be modeled numerclly, gretly reducng the requred lbortory pce nd equpment. Becue only the crtcl tructurl component re phyclly teted, they cn be lrge or even full-cle repreentton of the ctul component, reducng ze effect. In th wy, even mll lbortore cn crete nd conduct ccurte tetng of comple tructure. Severl fctor mut be condered n choong the crtcl tructurl component. Becue dmge ntrnclly locl phenomenon, the component my be elected bed on flure mechnm; flure hghly nonlner nd nherently dffcult to model numerclly. Alo, when tetng tructurl ytem wth new devce or mterl for whch numercl model re ndequte or mply do not et, uch component hould be teted epermentlly. Hybrd multon nerly dentcl to qu-ttc tetng n regrd to the type of pecmen tht cn be teted nd the equpment requred. Qu-ttc tetng, he tble tetng, nd hybrd multon provde dfferent pproche for eng the dynmc performnce of tructure. Hybrd multon, often condered the mot vertle of the three, h evolved nto fmly of dtnct tetng method to erve pecfc need of the engneerng communty. Of the mny vrton of hybrd multon, rel-tme hybrd multon wll be the focu of th reerch the rte-dependent behvor of the phycl pecmen cn be cptured drectly.. Rel-tme Hybrd Smulton Advnce n upplementl energy dpton devce, uch be olton, flud dmper, nd frcton devce, provde promng oluton for mtgtng dmge reultng from dynmc lod (Soong nd Spencer, ). The repone of thee devce re rte-dependent, requrng rel-tme epermentl evluton. When thee devce re ued prt of hybrd multon, rel-tme eecuton of the eperment necery to obtn ccurte nd tble reult (.e., reltme hybrd multon (RTHS)). A rel-tme hybrd multon chllengng epermentl frmewor due to nterdcplnry requrement ncludng hgh-peed ctutor control, number of uneplored re tll remn before the frmewor cn rech t full potentl. A detled undertndng of the RTHS dynmc nd ntercton of the epermentl equpment requred... Rel-Tme Actutor Control RTHS requre ccurte trcng of dered trjectory n rel-tme, typclly ung ervohydrulc ctutor. Cloe emnton of the ytem repone how tht epermentl equpment ntroduce both tme dely nd frequency-dependent tme lg nto the RTHS loop. Tme dely re not functon of frequency, generlly beng cued by the communcton of dt, nlog to dgtl (A/D) nd dgtl to nlog (D/A) dt converon, nd computton tme. Thee dely cn be reduced by ung fter hrdwre, mller numercl ntegrton tme tep, nd more effcent oftwre. In contrt, tme lg re reult of the phycl dynmc nd lmtton of the ervo-hydrulc ctutor nd vry wth both the frequency of ectton nd pecmen condton (Dye et l., 995). Tme dely nd lg re n ntrnc prt of epermentl tetng, nd mtgton of ther effect n eentl prt of RTHS.

11 Horuch et l. (996) demontrted tht for lner-eltc, ngle-degree-of-freedom (SDOF) ytem, the effect of the energy ntroduced by tme dely equvlent to negtve dmpng. The negtve dmpng w hown to be lrge for eperment wth lrge tffne or lrge tme dely. If the negtve dmpng eceed the nherent tructurl dmpng n the ytem, the eperment wll become untble. Moreover, even f the ytem remn tble, the reult wll be nccurte. A ngle pprent tme dely, lumpng together ll of the ctul tme dely nd lg preent n the RTHS loop, the b for erly effort t ctutor control for RTHS. For th reon, erly pproche re referred to mply dely compenton. Note tht pure tme dely h contnt, unt gn; thu, thee pproche lo gnored the frequency-dependent mpltude vrton of the ervo-hydrulc ctutor repone. One of the mot wdely ued pproche for dely compenton the polynoml etrpolton method (Horuch et l., 996). In th pproch, nown dplcement re ft n tme wth polynoml, nd the dplcement fter contnt tme dely etrpolted n tme (predcted). The etrpolted dplcement ent to the ervo-hydrulc ytem the commnded dplcement. trpolton method hve be mproved by ddng dptve onlne etmton of the tme dely. One of the frt ttempt to meure the tme dely onlne w propoed by Drby et l. (). Th reerch lo demontrted tht the pprent tme dely depend on the tffne of the phycl pecmen, whch cn chnge the pecmen undergoe dmge. Becue tme lg re not contnt, but rther frequency nd pecmen dependent, umng ngle tme dely not dequte to chrcterze the dynmc behvor of ervohydrulc ctutor. At the me tme, etrpolton pproche hve lmted frequency bndwdth for ccurte compenton, whch dmnhe the pprent tme dely ncree. Th problem prtculrly cute when tructurl repone gnfcnt t multple frequence (e.g., mult-degree-of-freedom (MDOF) tructure). Recently, reercher hve begun to ddre the ervo-hydrulc ytem dynmc ytem, cretng low-order trnfer functon to repreent the dynmc (Jung et l., 7; Wllce et l., 7; Chen nd Rcle, 9). Invere of thee model cn provde ccurte compenton over the frequency rnge for whch the model ccurte. Wth tff or MDOF tructure, there potentl for ntblte to mnfet due to unmodeled hgh frequency ervo-hydrulc dynmc. Thee pproche re generlly heurtc, degned to compente for n oberved tme dely or tme lg n the ytem... Actutor Couplng A rel-tme hybrd multon gn trcton n cceptble tetng method for cvl tructure, puhe re beng mde towrd tetng ncrengly comple phycl pecmen. Multple ctutor my be requred to ecte the pecmen nd meure correpondng retorng force. A couplng of the dynmc between ctutor nd pecmen w oberved nd eplned by Dye et l., (995) nd dentfed the phenomenon of control-tructure ntercton (CSI). CSI h been well tuded for ngle-ctutor ytem, nd RTHS ctutor control pproche conderng pecmen dependency through CSI hve been propoed (Crron nd Spencer, 7; Crron et l., 9; Phllp nd Spencer, ). For mult-ctutor ytem, CSI led to comple ctutor control chllenge. Becue the dynmc of ngle ctutor re coupled to pecmen, 4

12 when multple ctutor re connected to the me pecmen, the dynmc of ll of the ctutor become coupled to ech other through the pecmen. Stude nvolvng multple ctutor for rel-tme control hve been lmted..4 Overvew of Report Th report develop new model-bed ctutor control trtege tht provde hgh-fdelty trcng of dered trjectory necery for ccurte nd tble RTHS. Trcng over brod frequency rnge condered to ccommodte tff epermentl tructure where much of the m my be multed numerclly, MDOF ytem wth lghtly dmped hgher mode, nd pecmen tht my dd hgh-frequency dynmc to the tet through chnge or dmge. Wth the propoed model-bed pproch, rther thn compentng for n pprent tme dely or tme lg n the ytem repone, focu wll be plced on ytem modelng nd control theory bed trjectory trcng. The term model-bed refer to the model of the ervohydrulc ytem. To ccommodte both ngle nd mult-ctutor ytem, the dynmc behvor of the ctutor nd the dynmc couplng between ctutor re condered, urng ccurte control n the preence of CSI. At the me tme, model-bed mult-metrc feedbc control lgorthm re propoed tht repreent new prdgm n RTHS, provdng more ccurte trcng of hgher-order dervtve ncludng velocty nd ccelerton. Th reerch h fve mjor component: () chrcterzton nd modelng of rte-dependent em-ctve control devce (b) development of model-bed ctutor control, (c) pplcton to nglectutor ytem, (d) pplcton to mult-ctutor ytem, nd (e) pplcton to he tble control. A decrpton of the content of ech chpter provded below. Chpter contn detled revew of prevou tude n hybrd multon nd reltme hybrd multon wth focu on numercl ntegrton cheme nd ctutor control trtege. A revew of he tble control trtege lo preented to jutpoe the etenon of propoed model-bed control trtegy to tte-of-the-rt he tble control. Chpter provde techncl bcground necery for th report tht outde of trdtonl cvl engneerng reerch. The bc of both clcl nd modern control re preented, both of whch form the b of the propoed ctutor control trtegy. Model of the ervo-hydrulc ytem re dcued for whch the ctutor control trtegy wll be derved. Chpter 4 nvetgte the behvor of lrge-cle mgnetorheologcl (MR) dmper devce. Chrcterzton tet of the MR dmper re provded, followed by the development of hgh-fdelty numercl model. Sem-ctve control trtege re developed to mprove the repone tme of the MR dmper. The unque behvor of the MR dmper lo dcued, ncludng the effect of dle tme on dmper performnce. Chpter 5 detl the formulton of the model-bed ctutor controller for generl mult-ctutor ytem, trtng wth eprton nto feedforwrd nd feedbc control ln. Implementton of the feedforwrd controller dcued, ncludng the relzton of mproper ytem nd ther dcrete tme equvlent for ue n dgtl gnl proceor. The feedbc controller bed on the ervo-hydrulc ytem model wth hpng flter to retrct the frequency rnge the feedbc control effort. Mult-metrc feedbc control lo propoed, recognzng tht rte-dependent pecmen re entve to velocte nd ccelerton. 5

13 Chpter 6 pple the model-bed controller to ngle-ctutor ytem. An dvnced hrdwre nd oftwre ytem embled for lrge-cle RTHS nd ued the prmry men to evlute the propoed ctutor control trtege. The effect of control-tructure ntercton re demontrted ung MR dmper pecmen, whoe properte depend on n ppled electrc current. The propoed model-bed controller, ncludng mult-metrc feedbc, ued to control th hghly nonlner pecmen, whch cn undergo gnfcnt chnge durng tetng n RTHS. The uccee of Chpter 6 for ngle-ctutor ytem re etended n Chpter 7 to mult-ctutor ytem. A mple numercl model ued to demontrte mult-ctutor control whch followed by proof-of-concept tet on phycl three-tory teel frme tructure. Chpter 8 etend the model-bed control frmewor to he tble tetng. Accelerton nd mult-metrc feedbc propoed prt of the outer-loop controller to enure ccurte trcng of the dered ccelerton. Accelerton trcng eplored n the preence of trong he tble nonlnerte well chnge n he tble dynmc through CSI for pecmen undergong dmge. Chpter 9 ummrze the reerch preented n th report. Recommendton for future wor re propoed n regrd to ctutor control well RTHS nd he tble tetng. 6

14 Chpter LITRATUR RVIW Th chpter provde revew of the lterture on hybrd multon, wth focu on the numercl ntegrton cheme nd ctutor control trtege tht hve uccefully been ued n RTHS. A bref revew of he tble control trtege lo ncluded.. Hybrd Smulton Frmewor Hybrd multon the currently fvored term for wht lo nown peudodynmc tetng (Shng nd Mhn, 984), hrdwre-n-the-loop multon (Hnelmnn, 99), nd vrtul prototypng (Wng, ). The concept of hybrd multon w frt propoed by Huno et l. (969) to tet ngle degree of freedom ytem under emc lod. The equton of moton were olved ung n nlog computer whle n electromgnetc ctutor w ued to ecte the phycl pecmen n rel-tme. Dynmc repone w obtned for the frt tme wthout the ue of hng tble, lthough the nlog computer lmted the ccurcy of the reult. Hybrd multon w etblhed n t current recognzble form through the ntroducton of dcrete tme ytem nd dgtl controller (Tnh et l., 974, 975). Ung dgtl controller to olve the equton of moton, the rel-tme lodng contrnt could be reled to rmp nd hold procedure over n etended tme cle. Typcl qu-ttc tetng equpment could be ued whle numercl ntegrton could be performed t lower rte pproprte for the computer t the tme. ffort to vldte nd epnd the hybrd multon frmewor were purued n prllel both n Jpn nd the US (Tnh nd Nhm, 987; Mhn nd Shng, 985; Mhn et l., 989; nd Shng et l., 996). Reercher hve nce etended the orgnl hybrd multon frmewor nto vertle fmly of technque vlble tody. Thee nclude () ubtructure hybrd multon (Dermtz nd Mhn, 985), (b) contnuou hybrd multon (Tnh nd Oh, 98), (c) rel-tme hybrd multon (Nhm et l., 99), (d) effectve force tetng (Dmg et l., 999), (e) dtrbuted ubtructure hybrd multon (Wtnbe et l., ), (f) dtrbuted contnuou hybrd multon (Moqued et l., 4), nd (g) dtrbuted rel-tme hybrd multon (Km et l., ). Note tht when ome of the erler technque were publhed, the term peudodynmc tetng w more wdely ccepted. A detled revew of thee tet method cn be found n Crron nd Spencer (7). Fgure. llutrte the evoluton of the fmly of hybrd multon technque, dpted from Crron nd Spencer (7). 7

15 Hybrd Smulton (Huno et l., 969; Tnh et l., 975) Contnuou Hybrd Smulton (Tnh nd Oh, 98) Subtructure Hybrd Smulton (Dermtz nd Mhn, 985) Rel-Tme Hybrd Smulton (Nhm et l., 99) ffectve Force Tetng (Dmg et l., 999) Dtrbuted Contnuou Hybrd Smulton (Moqued et l., 4) Dtrbuted Subtructure Hybrd Smulton (Wtnbe et l., ) Dtrbuted Rel-Tme Hybrd Smulton (Km et l., ) Fgure.. Fmly of hybrd multon technque When ubtructurng employed to hybrd multon, the component of nteret cn be modeled epermentlly whle the ret of the tructure cn be modeled numerclly. Throughout hybrd tet, communcton between the epermentl nd numercl component mntned n loop of cton nd recton preented n Fg... Hybrd Smulton Loop M N N C M N N N R R F C N, K N g Servo-Hydrulc Loop Computer u D/A u PID Servo-vlve y R A/D Servo-Controller y LVDT Actutor Phycl Subtructure Lod Cell R Fgure.. Hybrd multon loop wth ubtructurng 8

16 The equton of moton governng the dynmc repone of the ytem re olved by tme-teppng numercl ntegrton cheme ung the numerclly mpoed ectton F N, meured dplcement y, nd meured retorng force R. Bed on the oluton of the numercl ntegrton, the commnd dplcement u ent to the ervo-hydrulc ytem to mpoe on the phycl pecmen. Through dplcement feedbc, the ervo-controller enure tht the commnded dplcement relzed by the pecmen. Then, the new meured dplcement y nd meured retorng force R re ent bc to the computer to be ued n the net tep of numercl ntegrton. The proce repeted untl the complete repone of the tructure clculted.. Rel-Tme Hybrd Smulton The frt hybrd multon, due to the lmtton of ung n nlog computer, w nturlly conducted n rel-tme (Huno et l., 969). Hrdwre lmtton lo compromed the ccurcy of the eperment by ddng phe lg tht w recognzed but uncompented. The development of rte-dependent tructurl control devce uch be olton berng nd flud dmper h purred nteret n epndng hybrd multon to nclude more rgorouly verfed rel-tme frmewor. The frt modern rel-tme hybrd multon ung dgtl computer w conducted by Nhm et l. (99) on SDOF ytem. In th ytem, ccurte velocty control w ought by ntroducng dgtl ervo-mechnm between the computer performng the numercl ntegrton nd the ervo-controller. Th dgtl ervomechnm cted rmp genertor between numercl ntegrton tme tep nd lo ncluded feedbc loop to mprove the dplcement performnce t ubtep of the numercl ntegrton. Horuch et l. (996) tuded the effect of tme dely on RTHS n detl nd propoed the polynoml etrpolton dely compenton cheme. In th ytem, uper rel-tme controller (Umet et l., 995) ung prllel computng nd pecl progrmmng lnguge w ued to perform ll clculton wthn the requred tme tep. Nhm nd Mo (999) propoed eprtng the t of gnl generton nd repone nly to llow RTHS to be performed on commerclly vlble proceor. The repone nly t, ncludng numercl ntegrton, could be performed t low rte (e.g., t = mec). In order to ure ccurte velocty trcng, the gnl generton t could be performed t fter rte (e.g., t = mec). Mny RTHS tude hve been conducted nce thee poneerng tude. Focu typclly plced on developng or pplyng new numercl ntegrton cheme, chevng more ccurte rel-tme ctutor control, developng new hrdwre nd oftwre for mproved computtonl power, or combnng RTHS wth other hybrd multon technque uch geogrphclly dtrbuted tetng.. quton of Moton For hybrd multon, the equton of moton, whch re econd-order ordnry dfferentl equton, mut be epreed n dcrete tme form (qn.. nd.). Durng numercl ntegrton, equlbrum mut be tfed t ech tme tep. t t t (.) 9

17 M N N, F N N C R R, (.) N N where M the m mtr of the numercl ubtructure, C the lner dmpng mtr of N the numercl ubtructure, R the retorng force vector of the numercl ubtructure, R N the retorng force vector of the epermentl ubtructure, F the vector of ectton force,,, nd vector of dplcement, velocty, nd ccelerton t tme t, nd t the numercl ntegrton tme tep. Note tht the retorng force of the epermentl ubtructure nturlly nclude contrbuton from ttc, dmpng, nd nertl force. When dmpng nd nertl force n the epermentl ubtructure re neglgble, then the phycl pecmen cn be loded t low rte wthout compromng ccurcy..4 Numercl Integrton Numercl ntegrton requred to olve the equton of moton repreentng the complete behvor of the tructure n qn. (.). Numercl ntegrton cheme typclly fll nto two brod ctegore: eplct nd mplct. Scheme olely bed on prevou nd current tme tep to determne future repone re referred to eplct. plct cheme re preferred for reltme hybrd tetng they re generlly le computtonlly ntenve nd requre no terton on the oluton. The mn drwbc tht eplct cheme re often condtonlly tble, plcng lmt on the mmum nturl frequency of the tructure or the mmum ntegrton tme tep ze. Scheme tht me ue of future tme tep to determne future repone re clfed mplct. Thee cheme re generlly uncondtonlly tble, regrdle of the tme tep choen. However, terton requred to converge on the oluton whch led to lrge computtonl demnd nd potentl purou ectton of the phycl ubtructure. Numercl ntegrton cheme cn lo be dvded nto the cl of problem tht they re degned to olve. quton of moton for cvl engneerng pplcton re econd-order ordnry dfferentl equton nd cheme hve been degned pecfclly for uch problem. Thee econd-order ordnry dfferentl equton could lo be epnded nto ytem of frtorder ordnry dfferentl equton, openng the door to even more cheme. Frt-order pproche re ttrctve n tht they cn be drectly ppled to tte-pce formulton whch re populr n modern dynmc nd control theory. The numercl ntegrton cheme preented n the remnder of th ecton nclude lgorthm ether degned for or uccefully ued n RTHS..4. Centrl Dfference Method The centrl dfference method (CDM) one of the mot populr numercl ntegrton cheme for RTHS (Nhm et l., 99; Shng et l., 996; Drby 999; Horuch et. l., 999; Nhm nd Mo 999; Horuch nd Konno ; Wu et l., 5; Crron nd Spencer, 7; Phllp nd Spencer, ). Wth th method, the velocty nd ccelerton re clculted ung the followng centrl dfference equton: (.) t

18 (.4) The CDM computtonlly effcent, etenvely ued n reerch, nd ey to mplement. The mn beneft of the CDM tht t n eplct cheme n dplcement. The dplcement t tme tep t (to be mpoed on the phycl pecmen) cn be drectly clculted by ubttutng qn. (.) nd (.4) nto (.). t t M N C t N t M N t M N C t N R N R F N (.5) One drwbc of the CDM tht t condtonlly tble, wth the tblty crteron gven t, where the hghet nturl frequency of the ytem (n rdn/ec). Addtonlly, the velocty cnnot be eplctly clculted (lthough t not generlly needed)..4. Centrl Dfference Method Rel-Tme Subtructure Tetng Wu et l. (5) propoed modfcton to the CDM uch tht t eplct n velocty, dentfed the centrl dfference method rel-tme ubtructure tetng (CDM RST). The velocty clculted ung bcwrd dfference n Nhm et l. (99): (.6) t Wth th contrnt on the velocty, the tblty of the CDM become dependent upon the dmpng of the phycl ubtructure. Generlly n eplct formulton of the velocty not requred for RTHS; f the dplcement generted qucly nd ccurtely trced, then the correct velocty trjectory wll lo be cheved..4. Newmr-Bet Method The Newmr-Bet method (Newmr, 959) compre fmly of numercl ntegrton cheme for econd-order ordnry dfferentl equton. The Newmr-Bet method cn be ether eplct or mplct, dependng on the electon of prmeter nd Thee prmeter determne how the ccelerton wll vry over the tme tep t. t t (.7) t (.8) Wth, the Newmr-Bet method econd order ccurte nd ehbt no numercl dmpng. If, negtve numercl dmpng ntroduced whle f, potve numercl dmpng ntroduced. In thee ce, the ccurcy drop to frt order. Addng numercl dmpng to the tructure offer ome dvntge. Typclly, ccurtely repreentng

19 the hgher nturl frequence of tructure dffcult. At the me tme, thee hgher nturl frequence re entve to epermentl error (Mhn nd Shng, 985). In uch ce, ddng numercl dmpng cn reduce purou ectton of hgher mode. Th ecton dcue ome of the RTHS ntegrton cheme tht cn be creted ung the Newmr-Bet method. Newmr plct Scheme By electng from the Newmr-Bet method, the method become eplct n dplcement nd thu referred to the Newmr eplct cheme. When further electng, the Newmr eplct cheme become numerclly equvlent to the CDM nd thu poee the me order of ccurcy nd tblty crter. However, the Newmr eplct cheme ehbt ome dvntge over the CDM. Shng nd Mhn (98) demontrte the Newmr eplct cheme to hve better error-propgton thn the CDM. Alo, the ntlzton procedure more trghtforwrd thn the CDM nce no nformton requred before the frt tme tep t t =. Applcton of the Newmr eplct cheme for RTHS nclude Bleborough et l. () nd Bonnet et l. (8). Contnt Averge Accelerton Method The contnt verge ccelerton (trpezodl) method (CAAM) cheved from the Newmr-Bet method by electng 4 nd. Th method econd order ccurte nd dd no numercl dmpng, mlr to the CDM, whle ehbtng uncondtonl tblty. However, th method mplct, lmtng t pplcton to RTHS. Horuch et l. () ppled the contnt verge ccelerton method to RTHS. In th reerch, terton on the commnd w elmnted by ung the gnl t tme t rther thn t to generte the ctutor commnd. The dded dely of t w lumped nto the overll dely of the ytem for dely compenton. Chng Algorthm Chng () modfed the Newmr-Bet method to ume the followng reltonhp for dplcement nd velocty: t t (.9) βt βt (.) Smlr to the CDM, the Chng lgorthm eplct n dplcement. The prmeter β nd β re defned for lner SDOF ytem : 4 t n (.) 4 4 n t n t (.) 4 4 t t n n

20 where the dmpng rto nd n the nturl frequency of the tructure. The followng prmeter were propoed for lner MDOF tructure: β I t CM t KM I t CM 4 (.) β I CM t KM t (.4) 4 where M the m mtr of the tructure, C the lner dmpng mtr of the tructure, nd K the lner tffne of the tructure. The Chng lgorthm ehbt the me numercl properte for lner ytem the CAAM. Thu, for lner ytem the Chng lgorthm doe not ntroduce ny numercl dmpng nd uncondtonlly tble. For nonlner ytem, the ntl lner tffne w propoed for the clculton of β nd β, lthough complete tudy of ccurcy nd tblty for nonlner ytem w not performed. CR Algorthm Cheng nd Rcle (8) propoed the CR lgorthm bed on frequency domn nly of numercl ntegrton cheme, formultng n eplct cheme for both dplcement nd velocty. t α (.5) t t α (.6) The prmeter α nd α re derved by emnng the dcrete tme trnfer functon of lner SDOF oclltor. By equtng the SDOF oclltor trnfer functon to the dcrete tme repreentton of the CR lgorthm n qn. (.5) nd (.6), the prmeter re determned to be the followng: Smlr reult re obtned for lner MDOF tructure: 4 (.7) 4 4 t t α α 4 n n 4M C t K M t (.8) The CR Algorthm doe not ntroduce ny numercl dmpng nd ehbt the me perod elongton the CAAM nd the Chng lgorthm. Modfcton to qn. (.7) nd (.8) hve been propoed for nonlner tructure (Chen nd Rcle, 9b). Wth thee modfcton, the lgorthm w hown to be uncondtonlly tble for oftenng behvor.

21 HHT-α A modfcton to the Newmr method w propoed by Hbler et l. (977) to llow for the ntroducton of numercl dmpng wthout reducng the order of ccurcy. The prmeter dded to the equton of moton to control the numercl dmpng: M N N N N N N N C C R R R R F F (.9) The equton for the Newmr-Bet method tll pply, wth prmeter determned ung the followng equton: 4 (.) (.) (.) Wth, the HHT-α method ntroduce no numercl dmpng nd equvlent to the CAAM. The HHT-α method mplct, uncondtonlly tble, nd ntroduce numercl dmpng n the hgh mode whle not ffectng lower mode pprecbly. The numercl dmpng ncree wth the qure of the frequency. Jung et l. (7) mplemented th tertve numercl ntegrton cheme n RTHS for nonlner tructure ung modfed Newton pproch..4.4 quvlent Force Control quvlent force control (FC) n pproch to mplct numercl ntegrton where the terton procedure replced by tunble feedbc loop (Wu et l., 7). Ung the CAAM, the equton of moton re wrtten n the followng form: K PD R, FQ, N R, (.) where K PD the peudodynmc tffne nd F Q n equvlent ppled force tht contn the eternlly ppled force nd peudodynmc effect dependng only on the prevou tme tep. K PD nd F Q re gven below: N N 4M C K PD (.4) t t 4

22 F Q, F N M N N N N 4M N 4M C C t t t (.5) entlly, F Q, cn be computed eplctly t t ung qn. (.5). Then, over the tme tep from t to t, F Q, wll be computed t fter rte ung qn. (.) whle ectng the epermentl ubtructure to reduce the error between qn. (.5) nd (.). The clculton of qn. (.) llutrted n Fg... A PID loop ued to reduce the error n the dered equvlent force F Q,, nd the ' meured equvlent force FQ,. Th loop run t fter rte thn t uch tht the error mll by the end of ech tme tep. A trnformton mtr necery to convert the PID control effort e Q to dplcement commnd u. Wu et l. (7) propoe the followng mtr to convert from force to dplcement: N K K K C F PD (.6) N where K nd K re the ntl lner tffne mtrce octed wth the numercl nd epermentl ubtructure, repectvely. In the ce of nonlner tet tructure, the bove ppromton my be nccurte. Therefore, nonlner control lgorthm my be developed n plce of the PID loop nd C F ppromton. Suggeted pproche n Wu et l. (7) nclude dptve or ldng mode control; however nether pproch were nvetgted n detl. F Q,+ + e Q u e n PID C F + Servo- Controller Actutor y permentl Subtructure Numercl Subtructure R N (u) + + R (y) + F' Q,+ K PD K PD u Fgure.. quvlent force control epermentl loop At the end of ech tme tep t, the dplcement needed to clculte nd ung the CAAM. Rther thn ung the commnded dplcement u or meured dplcement y from Fg.., Wu et l. (7) recommend to clculte from qn. (.) uch tht equlbrum tfed..4.5 Integrl Form of quton of Moton Chng et l. (998) propoed ung n ntegrl form of the equton of moton for hybrd multon. The tudy condered n ntegrl form of the Newmr eplct method. The tblty, ccurcy, perod elongton, nd other bc properte were found dentcl between the orgnl 5

23 equton of moton nd ntegrl form. However, ung the ntegrl of eternlly meured force dd moothng effect to the numercl ntegrton cheme, reducng noe nd llowng lrge tme tep to be ccommodted. Drby et l. (999) nd Bleborough et l. () me ue of ntegrl form of the equton of moton for RTHS ung frt-order numercl ntegrton cheme..4.6 Runge-Kutt One of the mot wdely ued numercl ntegrton cheme outde of hybrd multon the Runge-Kutt cheme, developed to olve frt-order ordnry dfferentl equton. Runge-Kutt cheme cn be ether eplct or mplct nd cn hve hgh order of ccurcy. The frt-order equton of moton re wrtten for n ntl-vlue problem below: f t, (.7) t (.8) where vector of the tte of the ytem, the tme dervtve of the tte, nd vector of ntl condton. The oluton t tme t gven the oluton t tme t plu lner combnton of ntermedte tge # tht ppromte qn. (.7). # tbn n n (.9) One of the mot common Runge-Kutt cheme fourth-order eplct cheme. quton (.9) cn be rewrtten qn. (.) whch contn the weghted verge of four lope clculted t ubntervl of t n qn. (.) through (.4). Th method fourthorder ccurte. 6 t 4 (.), f t (.) t t f, t (.) f, t (.) 4 f t, t (.4) The fourth-order Runge-Kutt cheme h been ued n RTHS by Crron nd Spencer (7), Crron et l. (9), Ln nd Chrtenon (9), Jng nd Chrtenon (), Fredmn et l. (), Phllp nd Spencer (), Phllp et l. (), nd Km et l. (). 6

24 .4.7 Frt-Order Hold Dcretzton Drby et l. () propoed ung frt-order hold ppromton of the contnuou equton of moton n tte-pce form for RTHS. In order to tep the method n tme, the tte t tme t were clculted ung frt-order etrpolton. Between numercl ntegrton tme tep, qudrtc nterpolton cheme w propoed to generte mooth dplcement commnd. In th reerch, the equton of moton were epreed n modl coordnte, retrctng nonlnerte to the phycl pecmen..4.8 Tutn Method Bleborough et l. () propoed mlr method to Drby et l. () ung Tutn method to develop the dcrete tme equton of moton. Tutn method cheved by equtng ntegrton n the -plne (contnuou) to the trpezodl rule between conecutve mple n the z-plne (dcrete). Tutn method w ued to crete dcrete tme-teppng form of the equton of moton; therefore, no etrpolton w needed to generte the tte t tme t. Becue modl coordnte were ued to epre the equton of moton, t w propoed tht hgher frequency mode could be drectly reduced or elmnted f necery..5 permentl rror Hybrd multon reltvely entve to epermentl error becue the meured retorng force nfluence future control effort. permentl error cn be ntroduced from fleblty n the recton frme, mlgnment of the pecmen, force relton, mbent noe, ntrumentton clbrton ue, ntrumentton precon lmtton, ntrumentton noe, A/D nd D/A converon, nd error n ctutor control. The net reult of thee error tht dplcement nd force my be ncorrectly ppled nd meured. In hybrd multon, epermentl feedbc error ccumulte through the numercl ntegrton cheme due to dplcement control error nd force meurement error. Thee error cont of both ytemtc nd rndom component (Shng nd Mhn, 98). Among the ytemtc feedbc error, both overhootng the dplcement or led n dplcement cn ncree the pprent dmpng n the ytem (removng energy), whle underhootng the dplcement or lg n the dplcement wll decree the pprent dmpng (ddng energy) (Shng nd Mhn, 98; Shng nd Mhn, 987). For MDOF tructure, hgher mode hve reltvely lttle contrbuton to the dynmc repone of tructure; however, they re more entve to ytemtc error thn lower mode. If energy dded to thee hgher mode, the cumultve error cn grow ndefntely n reonnce-le fhon (Shng nd Mhn, 987). Rndom error re typclly low mpltude, hgh frequency, nd zero men. Thee error, whch re fed bc to the numercl ntegrton, cn ecte hgher frequency mode, epeclly f they re underdmped. Reercher commonly dd numercl dmpng t hgher mode to reduce hgh frequency ectton (Hlbert et l., 977; Shng nd Mhn, 984). The equton of moton cn lo be converted to ntegrl form n Chng (998) to reduce noe. The mot gnfcnt epermentl error n RTHS poor phe trcng of the dered dplcement. For mple llutrton, the totl effect of both tme dely nd tme lg wll be ppromted ngle tme dely T d. Horuch et l. (996) demontrted tht for lnereltc SDOF ytem, tme dely T d ntroduce negtve dmpng nto the ytem equl to 7

25 Td, where the tffne of the pecmen. Fgure.4 llutrte the tme dely between the dered dplcement r nd the meured repone y. Fgure.4b how tht lthough the pecmen repone wll trc the lner-eltc blc lne, f the force R contently meured when y cheved yet octed wth r, then counter-clocwe hytere loop perceved. Th loop equvlent to negtve dmpng, whch wll ntroduce nccurce nto the RTHS. Furthermore, n ce when the negtve dmpng eceed the tructurl dmpng, the eperment cn become untble. Negtve dmpng cn be epeclly problemtc for teel frme whch ehbt hgh tffne nd low tructurl dmpng. Meured y Actul Repone f R t y r Dered r T d Meured Repone Fgure.4. () Tme dely (b) ffect of tme dely on hytere.6 Rel-Tme Actutor Control Strtege Accurte ctutor control eentl to the tblty nd ccurcy of RTHS nd h been the focu of numerou tude. rly pproche mount to tme dely compenton, umng contnt pprent tme dely n the ervo-hydrulc ytem nd etrpoltng the dplcement fter the tme dely. Improvement were dded to the tme dely pproch by ncludng onlne predcton of the tme dely. More recently, the ervo-hydrulc ytem h been modeled dynmc ytem nd low-order nvere model or led compentor hve been propoed for ctutor control. Some ctutor control trtege nclude feedbc controller to mnmze the trcng error nd dd robutne. Alterntvely, ome pproche ccept mll tme dely/lg nd nted djutment me djutment to the force meurement. Specfc emple of thee pproche to ctutor control wll be emned n th ecton. The controller preented re outer-loop controller, bult round the nner-loop control of ervo-controller whch provde tblty to the ervo-hydrulc ytem nd ome degree of trcng control. Thu, the gol of the outer-loop controller to mprove upon the performnce of the nner-loop control. Alterntvely, the nner-loop could be removed nd ngle controller degned for hgh-fdelty control of the ytem, however th pproch h not been the focu of reerch n RTHS to dte. 8

26 .6. Polynoml trpolton Pror to the wor of Horuch et l. (996), RTHS dd not conder dely compenton. Thee erly tude were conducted on tructure wth low nturl frequence or lrge tructurl dmpng, nd therefore the negtve effect of dely were condered neglgble. To me RTHS vlble to wder rnge of tructurl ytem, Horuch et l. (996) propoed the polynoml etrpolton method for dely compenton. In th pproch, prevou nd current dered dplcement re ft wth polynoml, nd the dplcement fter contnt etmted tme dely T d etrpolted. Th etrpolted dplcement then ent to the ervo-hydrulc ytem the commnded dplcement. A polynoml of ny order my be employed, wth hgher-order polynoml ledng to hgher ccurcy coupled wth more computtonl effort nd entvty to noe. The ccurcy nd tblty of th method become n ue when the tme dely T d lrge compred to the mllet perod of the tructure. For SDOF ytem, the tblty relted to the nondmenonl prmeter Td. Th contrnt cn be problemtc for lghtly-dmped, tff, or MDOF tructure, ll of whch would ehbt hgher nturl frequence nd thu lower perod..6. Lner Accelerton Horuch nd Konno () propoed nother pproch to dely compenton whch me ue of hgher-order dervtve for etrpolton. Wth the CDM, whch w ued for th tudy, only the dered dplcement nown eplctly. To crcumvent th ue, rther thn etrpoltng over the ntervl T d from the dered dplcement, etrpolton performed over the ntervl Td t ung the nown dplcement, velocty, nd ccelerton of the current tme tep. In th method, the ccelerton fter Td t lnerly etrpolted. Then, umng tht the ccelerton lnerly vryng between the current nd etrpolted ccelerton, the predcted dplcement fter the dely Td t clculted. Th method w hown to ehbt mproved tblty over the polynoml etrpolton method..6. Let Squre trpolton Wth the polynoml etrpolton method, the etrpolton bed on N + pont for n N th order polynoml. Wllce et l. (5) rele thee retrcton by fttng n N th order polynoml to greter number of dt pont ung let-qure bet ft. Increng the number of dt pont reduce the nfluence of noe on the etrpolton whle mng the compenton more computtonlly ntenve (.e., more dt mut be tored). Wth th method, the tme dely T d doe not hve to be n nteger multple of the numercl ntegrton mplng perod t, relng nother retrcton of the polynoml etrpolton method..6.4 Dervtve Feedforwrd Jung et l. (7) propoed modfcton to the ervo-hydrulc nner-loop control for RTHS. A feedforwrd term proportonl to the dervtve of the commnded dplcement dded to the etng PID loop. The feedforwrd term tuned to n ntcpted pprent tme dely n the RTHS loop. 9

27 .6.5 Dcrete Feedfowrd Compenton Jung et l. (7) lo propoed modfyng the dplcement commnd bed on the ntcpted trcng error. The trcng error for the net tme tep umed to be ppromtely the me the trcng error for the current tme tep. The current error multpled by proportonl gn nd dded to the commnd for the net tme tep to correct for the ntcpted error..6.6 Led Compentor Zho et l. () propoed ung phe-led compentor networ to elmnte the effect of mpltude nd phe error. A ngle-pole ngle-zero led compentor dded to the commnd gnl to compente for the frequency-dependent mpltude repone of the ervo-hydrulc ytem. Th compentor lo reduce ome of the tme dely n the RTHS loop. A econd ngle-pole ngle-zero led compentor dded to the meured retorng force. The gol of th econd compentor to remove ny remnng tme dely n the loop. Jung et l. (7) mplemented th de n RTHS ung ngle phe-led compentor for feedforwrd compenton..6.7 Force Correcton Method In RTHS, focu cn lo be plced on djutng the force meurement to compente for ny tme dely nd tme lg, n plce of or n ddton to dplcement compenton cheme. trpolton technque re dffcult to employ on force meurement nce they re generlly too noy for ccurte etrpolton over lrge tme dely. Ahmdzdeh et l. (8) propoed fttng the ltet force nd dplcement meurement ech to ther own econd order polynoml. The tme when the dplcement polynoml wll cro the dered dplcement clculted ung the qudrtc formul. After choong the pproprte root of the qudrtc formul (the cloet root to the current tme), the force t tht me tme clculte ung the force polynoml. The meured force nd the dered dplcement re thu lgned when they re epected to occur wthout hvng to eplctly clculte tme dely. Wth th pproch, the qudrtc formul could reult n comple tme root, ledng to comple force. If the mgnry component mll, then the bolute vlue of the comple force w hown to provde good etmte..6.8 CR Invere Chen nd Rcle (8) repreented the ctutor tme dely T d t multple of the tme tep t. Wth th mplfcton, dcrete tme reltonhp w etblhed ung the prmeter to relte the commnded dplcement to the meured dplcement. By tng the z-trnform, dcrete tme trnfer functon w creted, the nvere of whch w ued to provde feedforwrd compenton. The trnfer functon contn one pole nd one zero, both tble, therefore n nvere ely obtned..6.9 Model-Bed Invere Crron nd Spencer (7) propoed model-bed control method to ccount drectly for the frequency-dependent dynmc (both mpltude nd phe) of the ervo-hydrulc ytem over brod frequency rnge. Accurte trnfer functon model of the ervo-hydrulc ytem were

28 developed bed on epermentlly collected trnfer functon nd nvere of thee model were ued for feedforwrd control. A low-p flter w dded to the model nvere to crete proper ytem for mplementton..6. Schedulng Control Crron nd Spencer (7) lo propoed chedulng control method to ccount for chnge n the pecmen condton ffectng the dynmc of the ervo-hydrulc ytem. Feedforwrd controller were developed for the two etreme of epected pecmen condton. The trnton between the two feedforwrd controller w determned ung bumple trnfer. The bumple trnfer method h mert for pecmen wth behvor tht controlled by the uer (e.g., the nput current to MR dmper), however not generlly pplcble (e.g., degrdng tructure)..6. Adptve Scheme In the ce tht ngle tme dely T d ued to ppromte the dely cro ll frequence, dptve pproche tht etmte the dely onlne cn be ued. Thee pproche requre lernng gn whch mut be tuned to cheve good convergence nd vod ntblte. One of the frt ttempt to e the tme dely onlne w propoed by Drby et l. (). Drby demontrted tht the dely depend on the tffne of the pecmen. Thu, pecmen tht undergo dmge durng n eperment my requre n dptve compenton cheme. In th pproch, bet gue of the ntl tme dely ued for compenton. Then, bed on whether or not meured gnl ledng or lggng the dered gnl, the dely etmte updted. Th dely etmton technque nvolve determnng two lernng gn before the tet begn. Thee gn control blnce between the rte of convergence, overhoot, nd ocllton of the dely etmton. Although method for choong thee emprcl prmeter preented, ther clbrton remn drwbc to the method. Ahmdzdeh et l. (8) propoed n mprovement to onlne dely etmton ung the lope of the dered nd meured gnl, demontrtng fter convergence nd reducton n ocllton n the etmted dely. However, n th pproch, the preence of the dvon opertor n the lope clculton problemtc. If the denomntor quntty become very mll, the tme dely etmton cn jump conderbly. Th method lo contn lernng gn whch mut be clbrted pror to tetng. Cheng nd Rcle () propoed ung the trcng ndctor (Mercn, 7) to djut the ntl etmte of ctutor dely. The trcng ndctor tble meure of whether or not one gnl ledng or lggng nother, mng t utble for RTHS pplcton. Proportonlntegrl (PI) control ued to trnlte the trcng ndctor quntty nto n djutment of the etmted tme dely. The PI gn mut be clbrted pror to tetng..6. Feedbc Control Rel-tme ctutor control cheme cn be ugmented by feedbc control to further mnmze trcng error between the dered nd meured gnl. Crron nd Spencer (7) nd Cheng nd Rcle (9c) dded proportonl feedbc gn to the mn feedforwrd control cheme to ncree robutne. However, cuton mut be eerced, hgh feedbc gn for outer-

29 loop control cn lo led to ytem ntblte n RTHS (Crron nd Spencer, 7). Feedbc controller propoed thu fr employ proportonl gn, but do not te dvntge of the nown dynmc of the ytem (.e., re not model-bed)..6. Mnml Controller Synthe Modfed Demnd (MCSmd) Outer-Loop Scheme Lm et l. (7) propoed model-followng compenton cheme for RTHS. In th pproch, the ervo-hydrulc controller nd ctutor re treted together trnfer ytem. Th trnfer ytem not determned drectly; rther reference ytem wth dered cloed-loop performnce defned by the uer. The outer-loop controller compred of nvere of th reference ytem n conjuncton wth n dptve control cheme to ure tht the trnfer ytem trc the reference ytem. The performnce w found etremely entve to the ntl electon of the dptve gn prmeter. A fed-gn tudy w lo conducted to provde gudnce on ntl gn electon. Bonnet et l. (7) ued the MCSmd cheme n multple RTHS tude. The reference model n th tudy w creted by performng ytem dentfcton on the trnfer ytem nd fttng to frt order trnfer functon model. Th tudy lo dopted mult-tng trtegy whereby the outer-loop compenton w performed t fter rte thn the numercl ntegrton..7 Control-Structure Intercton When mechncl ctutor re ued to ecte pecmen, trong dynmc couplng uully preent between the ctutor nd pecmen, dentfed control-tructure ntercton (CSI). Th phenomenon w oberved nd eplned by Dye et l. (995). Pror to th tudy, mny reercher neglected CSI n epermentl tetng. Th overght w cceptble for low-peed tet ncludng conventonl hybrd multon, but uncceptble for the emergng frmewor of RTHS. When pecmen undergo chnge n behvor (e.g., through dmge), the dynmc of the ctutor wll chnge through CSI. Actutor control cheme tuned to one pecmen condton my no longer be effectve. CSI h been well tuded for ngle-ctutor ytem, nd RTHS ctutor control pproche conderng pecmen dependency through CSI hve been propoed (Crron nd Spencer, 7; Crron et l., 9; Phllp nd Spencer, ). However, RTHS beng ued for more complcted tet, control of multple ctutor wll be requred. For mult-ctutor ytem, CSI led to comple ctutor control chllenge. When multple ctutor re connected to the me pecmen, the dynmc of ll of the ctutor become coupled to ech other through the pecmen..8 Mult-Actutor Sytem To dte, mot tude n RTHS hve focued on ngle-ctutor ytem, overloong the ntcpted chllenge of ctutor couplng. When the multple ctutor re not phyclly coupled through the pecmen, ther dynmc cn be ndependently compented. Chen nd Rcle () nvetgted tructurl ytem wth two phyclly olted MR dmper connected through the numercl ubtructure prt of the me lterl retng ytem. Independently developed ctutor controller proved dequte for RTHS. In Km et l. (), ctutor controller for two geogrphclly dtrbuted MR dmper were ndependently

30 developed nd uccefully ppled. In thee tude, lthough the dynmc of the olted pecmen re ted together through the numercl ubtructure, there no phycl couplng n plce. A few tet wth phyclly coupled ctutor hve been nvetgted, however n ech ce the couplng of the ctutor w noted but not ccounted for n the ctutor control. Jung et l. (7) nvetgted both SDOF nd two-degree-of-freedom (DOF) her frme wth the tffne modeled by phycl column n ech ce. The column w cntlevered wth one ctutor ttched n the SDOF ce nd two ctutor ttched n the DOF ce. Reltve to the SDOF ytem, the DOF ytem ehbted lrger epermentl error when compred to numercl multon. The uthor ttrbute the dfference to ynchronzton error between the ctutor due to dfference n lod nd ervo-vlve cpcte. Both dcrete feedforwrd compenton nd led compenton were eplored for ctutor control n th tudy. Bonnet et l. (7) creted modulr ytem of nlne m, dmpng, nd tffne element. Two boundry condton for the phycl ubtructure were eplored: () ctutor t one end nd fed t the other nd (b) dentcl ctutor t ech end. Notcebly lrger control error were oberved for the two-ctutor ytem when compred to the ngle-ctutor ytem. To further nvetgte the phenomenon of ctutor couplng, the tffne of the phycl pecmen w ncreed. Wth the tffer pecmen, tble tet were only chevble when the ctutor moved n ynch. The MSCmd outer-loop control cheme w ued n th tudy. rly wor n mult-ctutor control llutrte the need for the conderton of phycl ctutor couplng n controller development. A more detled nvetgton of ctutor couplng requred uch tht RTHS cn be ppled to broder cl of tructure..9 She Tble Control Current dvnce n he tble control wll be eplored to nvetgte the potentl for pplyng RTHS ctutor control trtege to he tble tetng. She tble control h mny of the me chllenge of ctutor control for RTHS ncludng trcng of dered trjectory n rel-tme, nonlnerte n ctutor performnce, nd pecmen dependent dynmc through CSI. She tble provde drect men by whch to mprt dered ground moton on phycl pecmen. She tble tetng unque n tht the dered trjectory n ccelerton gnl; however, for tblty, ervo-hydrulc ctutor tll operte n dplcement feedbc. The ccelerton gnl nown pror nd not ffected by the repone of the tructure n hybrd multon. Becue the entre tructure mounted on the tble, dynmc effect cn be drectly cptured. She tble re nherently nonlner devce due to nonlnerte n ctutor behvor, frcton n the tble, nd CSI. Due to the nonlnerte, t dffcult to reproduce dered erthque record over wde rnge of frequence. A wth RTHS, mny he tble controller re outer-loop controller bult round n nner-loop dplcement feedbc controller. The mot bc pproch to chevng the dered ccelerton record to frt ntegrte twce to determne comptble dplcement record. Smov (98) preent th offlne method, whereby the reultng dplcement record trced by the he tble ung dplcement feedbc. The followng he tble control method provde mprovement upon th mple pproch.

31 .9. Trnfer Functon Iterton Fletcher (99) preent the trnfer functon terton method ued by mny commercl he tble, lter ppled to mll-cle he tble n Spencer nd Yng (998). Th pproch bed on lnerzed model of the he tble commnd to meured ccelerton. An nvere of th model ued to generte commnd gnl htory from the ccelerton record, tng nto ccount the modeled tble behvor. However, nonlnerte led to error between dered nd meured ccelerton. Thee error re ued offlne to tertvely modfy the commnd gnl. A mlr pproch ung tertve lernng control propoed by Dley et l. (4) whereby the reference trjectory tertvely modfed to reduce the trcng error..9. Feedforwrd-Feedbc Approche Newell et l. (995) propoed n offlne optmzton pproch to develop the reference gnl to trc dered ccelerton bed on tme-vryng nonlner model of the he tble dynmc. The nonlner model lo lnerzed bout the reference gnl to crete Klmn flter for feedbc control. Dplcement nd ccelerton meurement re compred to reference dplcement nd ccelerton to clculte dfferentl reference gnl correcton. The ue of ccelerton feedbc cn be problemtc becue ccelerton meurement re entve t hgh frequence; hgh frequency behvor pprent n the meured ccelerton. At the me tme, lnerzton of the tme-vryng nonlner model computtonlly burdenome. Another feedforwrd-feedbc pproch to he tble control w propoed by Kuehn et l. (999) bed on recedng horzon control. In th pproch, meurement of dplcement nd dfferentl preure were ued to ppromte the tte of the ytem model. The pproch w demontrted to be uperor to trdtonl LQR control n term of phe performnce. Nt () propoed n ccelerton trjectory trcng control n whch lnerzed model of the he tble ued feedfowrd controller, joned by dplcement feedbc controller bed on comptble dplcement record. In th pproch commnd re ent drectly to the ervo-vlve (no nner-loop controller ued). Thu, the dplcement feedbc controller necery to provde tblty to the he tble. An ntentonl dely dded to the feedbc controller to enure tht the more ggreve control effort provded by the feedforwrd controller nd the feedbc controller mply prevent eceve drft. Th method requre the embly of pecl equpment to byp the nner-loop ervo-controller (Nt, ).. Summry Th chpter preented n overvew of hybrd multon focung on etenon nto rel-tme hybrd multon. A revew of numercl ntegrton cheme nd ctutor control cheme re preented wth focu on rel-tme pplcton. Conderble room for mprovement n the re of ctutor control remn, trtng wth n ccurte undertndng of ctutor dynmc. Moreover, mot tude only conder ngle-ctutor ytem nd thoe tht do conder multctutor ytem neglect ctutor couplng. Alo, ctutor control trtege to dte focu on dplcement control nd dplcement trcng. Actutor control tnd to beneft from multmetrc feedbc to cheve ccurte trcng of hgher-order dervtve uch velocty nd 4

32 ccelerton, whch re mportnt to cpture rte-dependent behvor ccurtely. Advnce mde to ctutor control for RTHS cn be ppled to other re of epermentl tetng, ncludng he tble control. Mult-metrc feedbc control, ncludng ccelerton feedbc, h prtculr prome to mprove the trcng of dered ccelerton. 5

33 BACKGROUND Chpter Some bcground n control theory provded n th chpter to ly the groundwor for the development of dvnced ctutor control cheme for RTHS. A lnerzed model of the ervohydrulc ctutor ytem lo propoed the plnt to whch the control theory wll be ppled.. Clc Control Theory Clc control theory focue on frequency domn pproche to emnng tblty, noe, bndwdth, nd performnce. Trnfer functon re fundmentl to clc control theory, provdng frequency domn repreentton of the nput/output reltonhp of lner tmenvrnt ytem. Trnfer functon re typclly epreed n the Lplce plne. The Lplce trnform of functon f t defned : F L t f t e f t dt (.) Where L repreent the Lplce trnform nd comple number n the -plne. Conder the dynmc ngle-nput ngle-output (SISO) ytem n Fg... u G() y Fgure.. Dynmc ytem The trnfer functon defned the rto of the Lplce trnform of the output to the Lplce trnform of the nput n: 6 Y G yu (.) U where zero ntl condton re umed. A trnfer functon wrtten wth ubcrpt yu ndcte the nput u to the output y. Th notton helpful when there re multple loop nd multple dynmc ytem. The trnfer functon cn be epreed n pole-zero form or epnded to rto of polynoml: G yu K m z b b b b m m (.) n n n p

34 where m the number of zero z, n the number of pole p, K the trnfer functon gn, nd through n nd b through b m re polynoml coeffcent. The pole correpond to the locton on the -plne where the trnfer functon become nfnte whle the zero correpond to the locton on the -plne where the trnfer functon zero. Controller re degned to produce n nput to plnt (dynmc proce coupled wth n ctutor) tht cheve dered repone from the plnt. In the re of trcng control, th dered repone gven by reference gnl. In the followng dcuon, P repreent the plnt, C repreent the controller, r the reference gnl, u the control nput, d n unnown dturbnce, y the output of the plnt, nd e the error between the reference gnl nd the plnt output. Both open-loop (Fg..) nd cloed-loop (Fg..) control wll be emned ung clc control theory for SISO ytem. The followng crter wll be ued to e controller performnce: () Trcng: The error e between the reference gnl r nd meured repone y hould be mnmzed. The trnfer functon from the reference gnl to the plnt output G yr provde nght nto trcng. d r C() u + + P() y Controller Plnt r + Fgure.. Open-loop control d e u + y C() P() + Controller Plnt Fgure.. Cloed-loop control (b) Dturbnce Rejecton: The output of the plnt y hould not be gretly ffected by dturbnce n the ytem. The trnfer functon from the dturbnce to the plnt output G yd provde nght nto dturbnce rejecton. (c) Sentvty: Good trcng of the reference gnl hould be cheved even f the plnt model not ccurte or undergoe chnge. The entvty of the trnfer functon G yr to mll vrton n the plnt gven by: 7

35 where G yr Ngle, 995)... S G yr yr G G yr G P P P yr (.4) P the vrton n G yr cued by P, the vrton n Open-Loop Control P (Phllp nd Open-loop control (Fg..) modfe the reference gnl drectly to produce commnd to the plnt. Such controller cn be degned wth nowledge of the plnt dynmc, uch through n dentfed plnt model. The controller commnd doe not depend on the repone of the plnt, whch cn led to trcng problem. () Trcng: In open-loop control, the open-loop trnfer functon from the reference gnl to the plnt output gven by the followng: G yr Y C P (.5) R Perfect trcng would be ndcted by reference gnl over ll frequence, whch cn be cheved by choong G yr =, menng tht the output equl to the C P. However, plnt nveron not lwy trghtforwrd or poble. At the me tme, the modelng error cn led to n nvere tht wll not cncel out the true plnt dynmc. Thu, open-loop control provde the poblty for perfect trcng. (b) Dturbnce Rejecton: The trnfer functon from the dturbnce to the plnt output gven by the followng: G yd Y P (.6) D C doe not pper Open-loop control provde no men by whch to reject dturbnce, n qn. (.6). (c) Robutne: The entvty functon cn be reduced to unty n qn. (.7), ndctng tht the open-loop ytem provde no robutne... S Cloed-Loop Control G P yr G P yr C C P P Cloed-loop control ue the output of the plnt to djut the commnd gnl. In the cloed-loop control repreentton n Fg.., the control effort depend on the error between the plnt output nd the reference gnl. (.7) 8

36 () Trcng: In cloed-loop control, the trnfer functon from the reference gnl to the plnt output gven by the followng: G yr Y R C C P P G yr =, one cn chooe Snce perfect trcng would be ndcted by C = K where K very lrge contnt. Such controller would cheve good trcng cro ll frequence. Th controller not lwy prctcl nor the bet oluton, however, the poblty for good trcng et. (b) Dturbnce Rejecton: The trnfer functon from the dturbnce to the plnt output gven by the followng: G yd Y D P C In th ce, the trnfer functon G yd hould be mll poble, ndctng tht the dturbnce doe not ffect the output. If C = K where K very lrge contnt, then the trnfer functon become mll. Thu, cloed-loop control cn provde good dturbnce rejecton. (c) Robutne: The entvty functon cn be reduced to qn. (.). A wth trcng control nd dturbnce rejecton, f C = K where K very lrge contnt, mll entvty functon creted. Therefore, cloed-loop control cn provde good robutne... S PID Control G P yr G P yr C C P C C P P P P C P (.8) (.9) (.) Proportonl-Integrl-Dervtve (PID) control very common pproch to cloed-loop control (Fg..) nd generlly fvored when the dynmc of the plnt re unnown. The PID controller contn three gn tht cn be tuned to cheve the dered cloed-loop performnce: u t de K Pe t KI e dt KD (.) dt or, n the Lplce domn: C U K I K P K D (.) Note tht multplyng by equvlent to dfferentton n the tme domn whle dvdng by equvlent to ntegrton n the tme domn. 9

37 The proportonl gn, K P, dd control effort proportonl to the trcng error. Th gn generlly contrbute mot of the control effort. A hgh proportonl gn mprove the ytem repone tme, lthough f et too hgh the ytem my become untble. The ntegrl gn, K I, dd control effort proportonl to the ccumulted error. Integrl control mot ueful to elmnte tedy-tte error; however, t cn lo ntroduce overhoot nto the ytem. The dervtve gn, K D, dd control effort proportonl to the dervtve of the error. Dervtve control low the trnent repone of the ytem, reduce overhoot, nd mprove ytem tblty. However, dervtve control entve to noe nd cn led to ntblte n the preence of uch noe...4 Led nd Lg Compentor Mny lterntve compentor degn re vlble for cloed-loop control. Two mple yet effectve degn nclude led nd lg compentor, tng the form: C z K (.) p Thee compentor re typclly plced n the open-loop pth of the cloed-loop ytem n Fg... If z < p, then led compentor creted, ddng potve phe to the open-loop ytem. In the cloed loop ytem, led compentor ppromte the functon of proportonldervtve (PD) control, decreng re tme nd overhoot. If z > p, then lg compentor creted, ddng negtve phe to the open-loop ytem. In the cloed-loop ytem, lg compentor ppromte the functon of proportonl-ntegrl (PI) control, reducng tedytte error (Frnln et l., 6). In the ce tht the dered performnce cnnot be cheved wth ngle led or lg compentor, multple compentor cn be ccded. Alterntvely, f the led nd lg compentor re plced n the feedbc pth, the compentor hve the me effect on the cloed-loop ytem pole, however the trnent repone to reference nput wll chnge.. Modern Control Theory Where clcl control theory focue on trnfer functon pproche, modern control theory bed on ordnry dfferentl equton, cretng mthemtcl model of ytem dynmc n the tme domn. Ordnry dfferentl equton cn be wrtten n tte-pce form ytem of frt-order dfferentl equton. Stte-pce model provde convenent form to repreent mult-nput mult-output (MIMO) ytem, non-zero ntl condton, well nonlnerte. If the dynmc re lner nd tme-nvrnt, the tte-pce model cn be wrtten below for SISO ytem. A Bu (.4) y C Du (.5)

38 where the tte vrble vector wth ntl condton, t tme dervtve vector of the tte, u the ytem nput, y the meured ytem output nd A, B, C, nd D re the ytem, nput, tte output, nd feedthrough mtrce, repectvely. For the followng, t umed tht the feedthrough mtr D =, ndctng tht the nput doe not drectly enter the output... Stte Feedbc In tte-pce degn, the cloed-loop ytem wll typclly te the form of Fg..4 umng tht ll tte re vlble. Stte feedbc n th form wll brng the dervtve of the tte to zero, holdng the ytem output tedy gnt unnown dturbnce. Such controller clled regultor. u A Bu y C y Plnt Fgure.4. Stte feedbc By multplyng the tte by contnt gn K, the commnd to the plnt determned: u K (.6) Wth qn. (.6) n nput, the cloed-loop tte-pce model cn be wrtten : A BK (.7) y C (.8) The pole of the cloed loop ytem re the egenvlue of the mtr (A BK). If nd only f the cloed-loop ytem controllble, then the feedbc gn K cn be choen to cheve ny rbtrry pole n the cloed-loop ytem nd thu ny rbtrry cloed-loop repone. A dcuon on controllblty cn be found n Stengel (986). The cloed-loop pole cn be elected to meet degn objectve, uch re tme or trnent repone... Lner Qudrtc Regultor (LQR) K Controller An effectve nd wdely ued method for determnng the tte feedbc gn mtr K to mnmze n objectve cot functon. In the ce of lner ytem wth qudrtc cot functon,

39 LQR degn cn be ppled to crete n optml regultor degn. When degned for n nfnte tme horzon (tedy-tte control), the qudrtc functon cot gven by: J LQR T Q u R u u T dt (.9) J LQR the cot functon, where Q the weghtng mtr on the ytem output, nd R u the weghtng on the ytem nput. The lgebrc Rcct equton cn be olved to obtn the ymmetrc, potve defnte mtr P: A T P PA PB R u B T P Q (.) The optml feedbc gn mtr K LQR bed on the control weght elected gven by: K LQR T R B P (.) u.. Oberver Stte feedbc formulted umng tht ll of the tte re nown. In prctce, enor re requred to meure the tte of plnt. Senor cn be epenve nd ometme dffcult or mpoble to ntll. At the me tme, certn plnt tte mght not hve phycl repreentton nd re therefore unmeurble. In order to plce the cloed-loop pole ung tte feedbc, thee tte mut be recontructed from vlble dt. An oberver (lo clled n etmtor) cn combne the meurble quntte y, nown commnd u, well the modeled plnt dynmc to crete etmte of the tte. Frt, the oberver dynmc re creted to mmc the orgnl plnt, where ˆ re the etmted tte. If the ntl tte of the ytem re nown nd the plnt perfect model of the phycl ytem, then the tte cn be etmted ectly from the open-loop oberver: ˆ Aˆ Bu (.) However, ntl tte condton my not be nown nd the etmted tte my begn to dverge from the ctul tte due to noe or dturbnce n the ytem. Thu, correctve term dded to the oberver dynmc ung the vlble meurement y: ˆ Aˆ Bu L y Cˆ (.) where L the oberver gn. Th form of oberver clled Luenberger oberver. The cloedloop oberver nd plnt re hown together n Fg..5. The pole of the oberver re the egenvlue of the (A LC), whch cn be choen rbtrrly for n obervble ytem. A dcuon on obervblty cn be found n Stengel (986).

40 u A Bu y C Plnt y + ˆ Aˆ Bu L yˆ Cˆ Oberver y yˆ ˆ ŷ..4 Klmn Flter Fgure.5. Oberver The Klmn flter (Klmn, 96; Klmn nd Bucy, 96) n pproch to optml oberver degn. Ade from recontructng the tte of the ytem, Klmn flter remove noe from the meurement bed on the modeled plnt dynmc nd weghtng prmeter. Klmn flter do not dd lg to the ytem trdtonl noe flter do, mng them ttrctve lterntve towrd chevng clen meurement gnl n rel-tme pplcton. The ttepce model wth noe cn be epreed : A Bu w (.4) y v C v (.5) where w the proce noe (.e., dturbnce) umed to be zero-men Gun whte noe wth covrnce Q w wt wt nd v the meurement noe umed to be zeromen Gun whte noe wth covrnce R v v t v t, the epected vlue of the quntty n brcet, nd y the output meurement contmnted by noe. The noe v w nd v re condered ndependent uch tht v t wt. quton (.4) nd (.5) re repreented n Fg..6. u w A Bu w y C y + + y v Plnt v Fgure.6. Plnt wth proce nd meurement noe The reltve rto between the noe covrnce ffect the performnce of the Klmn flter. The error covrnce of the etmted tte defned by: P e lm t t ˆ t t ˆ t The ttonry error covrnce mtr cn be clculted from the lgebrc Rcct equton: T (.6)

41 AP e P e A T P C e T T R CP Q (.7) v e w The optml oberver gn L Kl tht mnmze the error covrnce bed on the elected noe covrnce cn be clculted by: T L Kl PeC Rv (.8) Note tht the Klmn flter degn ndependent of the nput commnd u...5 LQG Control Feedbc control, n the bence of complete tte nformton or n the preence of uncertnty, my requre combnton of controller nd oberver degn. In generl ce, the degn of the two component cnnot be eprted. However, for lner ytem wth qudrtc cot functon nd certn umpton on the proce nd meurement noe, the optml controller nd optml oberver cn be degned ndependently. The nfnte-horzon Lner-Qudrtc-Gun (LQG) control problem defned for qn. (.4) nd (.5) umng the qudrtc cot functon gven by: J LQR lm T T T T Q uruudt (.9) The optml controller cn be degned f there no proce or meurement noe, ung the control lw of qn. (.9), or LQR control, n the ce tht the noe Gun whte noe or Gun colored noe, well few other peclzed ce (Stengel, 986). Th property clled the certnty equvlence property, whereby the optml control lw cn be derved wthout conderng the uncertnty. Alo, the Klmn flter degn (optml oberver) of qn. (.8) doe not depend on the feedbc control effort. Thu, LQG nd Klmn flter degn cn be performed ndependently, llutrtng the eprton prncple. The combned ytem hown n Fg..7. The cloed-loop ytem cn be decrbed by the tte of the plnt nd oberver : A ˆ L Kl C BK A BK LQG LQG L Kl C ˆ (.) The egenvlue of mtr remn unchnged f mlrty trnform performed. A eg L KlC BK A BK LQG LQG L Kl I eg C I A I L KlC BK A BK LQG LQG L Kl A BK eg I C I LQG I BK A L LQG Kl C (.) 4

42 In the form of qn. (.) on the rght-hnd de, t pprent tht the egenvlue of the complete cloed loop ytem re the egenvlue of A BK LQG nd A LKlC, the me egenvlue obtned by ndependent degn regultor nd oberver degn. The eprton prncpl gurntee tht degn of the tte feedbc gn nd oberver gn cn be performed ndependently. v u w A Bu w y C y + + y v Plnt K LQR ˆ ˆ Aˆ Bu L y ˆ Kl y v Cˆ Oberver..6 Fgure.7. Combned controller nd oberver Trcng Control ung Stte-Spce Degn The controller obtned through combned tte feedbc degn nd oberver degn regultor, mntnng tedy-tte whle chevng good dturbnce rejecton. A complete trcng controller requre good trcng of reference nput well dturbnce rejecton. To formulte tte-pce trcng controller, reference nput mut be ntroduced. For mple emple, the reference gnl r, control effort u, nd meurement y re umed to be clr. Term proportonl to the reference gnl r wll be dded to the etmted tte nd control effort. A BK LCˆ Ly Mr ˆ (.) u Kˆ nr (.) where M vector, n clr, nd the proce nd meurement noe re not condered. Th formulton llutrted n Fg..8. 5

43 r n + u A Bu y C Plnt y K ˆ ˆ y out ˆ A LC ˆ Bu Ly Mr M Controller Oberver Fgure.8. Combned controller nd oberver wth reference nput Becue r n eternl gnl, the electon of M nd n do not nfluence the chrctertc equton of the combned controller nd oberver ytem n qn. (.). Ther electon only nfluence the trnent repone nd thu trcng performnce of the ytem. Three mple degn trtege re preented n Frnln et l. (6) follow: () Zero-gnment etmtor: M nd n cn be elected to plce the zero of the combned ytem t dered locton to cheve the dered trnent repone. The rto of M / n nfluence the locton of the zero. The followng two degn trtege (b) nd (c) re pecl ce of (). (b) Autonomou etmtor: M nd n cn be elected uch tht the error n the tte etmton ndependent of r. Th cheved by mng ure tht r doe not pper n ˆ, urng good etmtor performnce n the preence of reference gnl. The reult of uch degn tht M = Bn. (c) Trcng-error etmtor: M nd n cn be elected uch tht only the trcng error e = r y ued for control. Th pproch ueful f enor cn only meure error, n ome thermott nd ome rdr trcng ytem. The reult tht M = L nd n =. Mny other pproche to trcng control n tte-pce re vlble. In prtculr, n pproch ung regultor redegn preented n Chpter 5 prt of the propoed model-bed ctutor control cheme. By trnformng the trcng problem nto regultor problem, optml regultor degn cn be ppled.. Dcrete Tme Dcrete tme equvlent, epreed n z-plne, cn be epreed for ll of the prevouly dcued control theory. In uch ce, the trnfer functon wrtten : G yu z Y U z z K m z z b b z b z b m m (.4) n n z z n z z p z 6

44 where z comple number n the z-plne, not to be confued wth the z commonly ued to repreent zero. Or, n the tme domn, dcrete tte-pce repreentton cn be creted: A Bu (.5) y C Du (.6) where the dcrete tme tte-pce mtrce re dfferent from the contnuou tme tte-pce mtrce. Contnuou controller degn, ncludng ctutor controller, mut be epreed n dcrete tme for ue n dgtl gnl proceor (DSP) for RTHS. Dcrete controller degn cn be creted ether drectly or by convertng contnuou controller degn to dcrete tme. A few lterntve for cretng dcrete tme repreentton of contnuou ytem re preented heren. MATLAB contn bult-n lgorthm to trnlte between contnuou nd dcrete ytem ung mot of the method preented... Zero-Order Hold A zero-order hold (ZOH) ppromton crete dcrete model by mplng nd holdng ech nput for one mple perod. ZOH ppromton re ect when the nput to the ytem trce nd cn be ued for MIMO ytem. u t u for t t t (.7).. Frt-Order Hold A frt-order hold (FOH) ppromton crete dcrete model through mlr mple nd hold procedure the ZOH converon. In th ce, the hold lner nterpolton between mple. ther cul (qn..8) or cul (qn..9) nterpolton my be ued. u t u u u for t t t t t t t t t u t u u u for t t t (.8) (.9) FOH ppromton re ect when the nput to the ytem pecewe-lner nd cn be ued for MIMO ytem. The dcrete ppromton G z of contnuou ytem G repreented n Fg..9 for both ZOH nd FOH. 7

45 u u(t) y(t) y ZOH/FOH G() t Fgure.9. ZOH nd FOH.. Pole-Zero Mtchng t A pole or zero n the -plne t equvlent to pole or zero n the z-plne t followng reltonhp cn be etblhed between the -plne nd the z-plne: z e. The t e (.4) Pole-zero mtchng cheve good mtch n the frequency domn between contnuou nd dcrete ytem, however t only pplcble to SISO ytem...4 Numercl Integrton quvlence G(z) A fmly of dcrete tme equvlent cheved by equtng ntegrton n both the -plne nd the z-plne nd pplcble to MIMO ytem. In the -plne, ntegrton gven by /. In the z-plne, three dcrete tme ntegrton equvlent re preented n Fg.., ncludng the forwrd rectngulr rule, bcwrd rectngulr rule, nd trpezodl rule. Wth the forwrd rectngulr rule between conecutve mple, the followng reltonhp between contnuou nd dcrete tme cn be derved: z t (.4) z t (.4) Wth the bcwrd rectngulr rule between conecutve mple, the followng reltonhp between contnuou nd dcrete tme cn be derved: z t (.4) z zt (.44) Tutn method, lo nown the blner ppromton, cheved by ung the trpezodl rule between conecutve mple. Wth th method, the followng reltonhp cn be derved: 8

46 t / z (.45) t / z (.46) t z Tutn method cheve good mtch n the frequency domn between contnuou nd dcrete ytem, mppng the entre tble regon of the -plne to the tble regon of the z- plne, lthough ome frequency dtorton occur. Technque re vlble to compente for th frequency dtorton through prewrpng (Frnln et l., 6). Δt t Δt t Δt t Forwrd Rectngulr Rule Bcwrd Rectngulr Rule Trpezodl Rule.4 Servo-Hydrulc Sytem Modelng Fgure.. Dcrete tme ntegrton The ervo-hydrulc ytem n emblge of mechncl nd electrcl component ued to ecte pecmen, typclly to precrbed dplcement (ee Fg..). Indvdul component model cn be embled to crete dynmc model for the complete ervo-hydrulc ytem. Component wth nonlner behvor wll be repreented by lner model wth repect to n opertng pont uch tht the complete ytem model lo lner. The lner model wll fcltte the ue of frequency domn technque ncludng the Lplce trnform well frequency domn bed ytem dentfcton. The trnfer functon model cn lo be epreed n tte-pce form to pply modern control theory pproche. Servo-Hydrulc Sytem G u () + u e n Q L f Servo- Controller Servo- Vlve + Actutor Nturl Velocty Feedbc Specmen Fgure.. Component of the ervo-hydrulc ytem 9

47 .4. Vlve Flow The flow of ol through the ctutor chmber cn be ppromted by the followng lnerzton (Mertt, 967): Q L K K p (.47) ' q v ' c L ' where Q L the ol flow through the lod, K q the vlve flow gn, v the poton of the ' vlve pool, K c the vlve flow-preure gn, nd p L preure drop cro the lod. The ytem n qn. (.47) h been lnerzed bout the orgn where Q L =, v =, nd p L =..4. Actutor The behvor of the ctutor cn be decrbed by force equlbrum of the flow rte (Mertt, 967): Q L V t A C l p L p L (.48) 4 e where C l the totl lege coeffcent of the ctutor pton, V t the totl volume of flud under compreon n both ctutor chmber, e the effectve bul modulu of the ytem, nd A the re of the ctutor pton. quton (.48) cn be rewrtten n the Lplce domn : Q L p L A C l Vt 4 e (.49) The force generted by the ctutor f nd thu mprted on the pecmen gven by: f ApL (.5).4. Specmen The pecmen ected ctutor, movng due to the ppled force. The equton of moton of the pecmen (SDOF) gven by: m c F f (.5) where m, c, nd repreent the m, dmpng, nd tffne vlue of the pecmen nd ttchment (whch my nclude the pton rod, lod cell, clev, etc.), F S repreent the frcton n the pton rod, repreent the dplcement of the pecmen, nd dot ndcte dfferentton wth repect to tme. Modern ctutor often ue low-frcton el uch tht the frcton force cn be umed neglgble. The equton of moton cn be rewrtten wthout frcton the followng trnfer functon: 4

48 G f (.5) f m c An etenon to MDOF pecmen wll be eplored n Chpter Servo-Controller The ervo-controller ued to tblze the nherently untble hydrulc ctutor. Wth dplcement feedbc, the error gnl e c equl to the dfference between the commnd u nd meured dplcement. e c u (.5) Servo-controller often ue PID control to elmnte the error. For rel-tme pplcton, proportonl gn lone generlly dequte, vodng the lg ntroduced by ntegrl control nd entvty to noe of dervtve control. Wth proportonl controller, the ervo-controller dynmc cn be epreed : K e (.54) c where K P the proportonl feedbc gn of the ervo-controller nd c the commnd gnl to the ervo-vlve..4.5 Servo-Vlve The ervo-vlve provde n nterfce between the electrcl nd mechncl component of the ytem. The ervo-vlve receve n electrcl gnl from the ervo-controller whch move the poton of the vlve pool, controllng the flow of ol nto the ctutor. A contnt gn my be ued to ppromte the ervo-vlve dynmc over low-frequency rnge (Mertt, 967; Dye et l., 995, Crron 7). v P c (.55) where v the vlve gn. In the Lplce domn, qn. (.55) cn be wrtten : G v v c v v (.56) c If contnt gn ndequte over the frequency rnge of nteret, frt order model my be ued. Th model nclude tme lg, preented below: where v the ervo-vlve tme contnt. v G v (.57) v 4

49 4 Complete Model.4.6 The component of the ervo-hydrulc ytem cn be combned nto the bloc dgrm model of Fg... Fgure.. Bloc dgrm model of the ervo-hydrulc ytem Wth contnt gn repreentng the ervo-vlve dynmc, the ervo-hydrulc ytem model cn be repreented by the followng three-pole trnfer functon: c q P c e t c e t c e t c q P K A K K K A K V c c K V m m K V K A K K G c u (.58) where v ' q q K K the ervo-vlve gn nd l ' c c C K K the totl flow-preure coeffcent. Wth frt-order model for the ervo-vlve dynmc, the trnfer functon would contn four pole n: 4 4 c q P D D D D D K A K K G u (.59) where v c e t 4 4 m K V D (.6) v c e t v c e t 4 4 c K V m m K V D (.6) + + Servo-Hydrulc Sytem G u () Nturl Velocty Feedbc Servo- Controller Servo-Vlve Dynmc Actutor Specmen Servo-Vlve Flow P K G v L ' c v ' q L K K p Q e t l 4β V C c m A A u v Q L p L f c e c

50 V t A V t D m c v c v v (.6) 4 e K c K c 4 e K c V t A D c v (.6) 4 e K c K c K q A D K (.64) P K c.4.7 quvlent Smplfed Model For mplcty, the model of Fg.. equvlently rerrnged hown n Fg... Th mplfcton wll fcltte the preentton of MIMO ytem control n Chpter 5. In th fgure, G, G, nd G f, repreent the trnfer functon of the ervo-controller nd ervo-vlve, ctutor, nd pecmen, repectvely. Servo-Hydrulc Sytem G u () u + + f G G f G Servo-Controller nd Servo-Vlve Actutor A Specmen Nturl Velocty Feedbc Fgure.. Servo-hydrulc ytem wth CSI The ndvdul bloc model re preented : G (.65) p G f (.66) m c where 4 A e (.67) V t 4

51 44 c t e 4 K V p (.68) Furthermore, for contnt gn ervo-vlve model: G (.69) where q p K K (.7) And for frt-order ervo-vlve model: p G (.7) where v q p K K (.7) v p (.7) The reultng mplfed thrd-order model for the ervo-hydrulc ytem : p A c p c m p m G u (.74) And the mplfed fourth-order model for the ervo-hydrulc ytem : 4 4 D D D D D G u (.75) where 4 m D (.76) m p p c D (.77) A c p p m p p D (.78)

52 .5 Summry D p p c p p p A (.79) D p p (.8) Th chpter provded bcground on control theory tht eentl to the development of the propoed reerch. Both clc control theory nd modern control theory re eplored. In ddton, totl model of the ervo-hydrulc ytem derved from component model. Th model wll form the b of the propoed model-bed ctutor control. 45

53 Chpter 4 MR DAMPR MODLING AND CONTROL Sem-ctve devce uch MR dmper combne the derble properte of both pve nd ctve control ytem. They hve the blty to dpt to lodng demnd on the tructure, wth ctve control ytem; however, wth pve ytem, they cnnot nject energy nto the tructure, elmntng tblty concern. Alo, n the event of power lo or controller dmge, the devce functon pve energy dpter. Wth n MR dmper, chnge n the nput current cn be ued to cheve force predctbly n em-ctve control lgorthm (Spencer et l., 997). RTHS llow for the dynmc performnce evluton of MR dmper devce n coteffectve nd repetble frmewor. An olted lrge-cle MR dmper cn be condered the epermentl ubtructure whle the ret of the tructure multed numerclly, reducng demnd on lbortory pce nd equpment whle tll fully cpturng the true nonlner nd current-dependent dynmc. Th chpter nvetgte the modelng nd control of n MR dmper, the pecmen ued throughout th reerch for RTHS. Frt, the dynmc performnce of lrge-cle N MR dmper pecmen dentfed through ere of chrcterzton tet. A numercl model of the MR dmper then developed from the epermentl dt to d n offlne multon tude on em-ctve control nd to verfy RTHS reult. The oberved dynmc behvor of the MR dmper ued to develop dvnced em-ctve control trtege. Both tructurl control (e.g., em-ctve control lgorthm) nd the ccurcy of the RTHS frmewor (e.g., ctutor control trtege) cn be nvetgted ung th pecmen. The focu of th report plced on the RTHS frmewor wth the MR dmper een n emple pplcton whch necette reltme epermentl evluton. 4. MR Dmper Specmen The pecmen econd-generton, lrge-cle N MR dmper mnufctured by the Lord Corporton (ee Fg. 4.) on lon from Profeor Rchrd. Chrtenon. The dmper h troe of ±9 mm (± n) nd cn generte force lghtly hgher thn the nomnl N. The dmper h n ccumultor chrged to 5.7 MP (75 p) to compente for the therml epnon of the MR flud (Chrtenon et l., 8). The unque properte of MR dmper re derved from the nternl MR flud. In the preence of mgnetc feld, the flud chnge from lner vcou flud to em-old wth controllble yeld trength (Crlon nd Jolly, ). Th yeld trength dependent upon the trength of the mgnetc feld, whle the mmum yeld trength determned by the compoton of the MR flud. The ource of the mgnetc feld n electromgnet locted n the pton hed, ected by n eternl current whch cn vry requred by tructurl control lgorthm. The current to the MR dmper controlled ung pule-wdth modultor (PWM), whch cont of n Advnced Moton Control model PSW unregulted power upply provdng 8 VDC to n Advnced Moton Control model 8 nlog ervo-drve, hown n Fg

54 Fgure 4.. Cro-ecton of the N MR dmper Fgure 4.. PWM for MR dmper ectton current The nlog ervo-drve cn meure the current n the cloed-loop crcut for current feedbc control, whch utble for MR dmper pplcton. The beneft of ung PWM power effcency nd quc repone tme. An AC lne flter dded to prevent noe from the PWM from leng nto the AC upply nd contmntng nerby equpment. A ferrte uppreon core dded to ttenute noe from the wtchng of the PWM. 47

55 4. Chrcterzton Tet 4.. Sne Wve Tet A ere of ne wve tet re ued to chrcterze the frequency, mpltude, nd current dependency of the MR dmper dynmc. ch tet run for dplcement ne wve of fed frequency nd mpltude wth fed current to the MR dmper crcut. The reult re preented n Fg. 4. through Fg. 4., wth ech fgure preentng multple current level for the me dplcement ne wve. The MR dmper repond to ncree n current wth correpondng ncree n the retorng force durng dynmc event. The mgntude of the retorng force chnge drmtclly, yet predctbly wth the nput current. Th chrctertc me MR dmper del for em-ctve tructurl control. At the me tme, the rte-dependent behvor requre rel-tme epermentl evluton, mng MR dmper cnddte for RTHS. Force (N) Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.. MR dmper wth 5.4 mm,. Hz ne wve Force (N) 5 5 Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.4. MR dmper wth 5.4 mm,.5 Hz ne wve 48

56 Force (N) 5 5 Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.5. MR dmper wth 5.4 mm,. Hz ne wve Force (N) Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.6. MR dmper wth 5.4 mm,. Hz ne wve Force (N) 5 5 Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.7. MR dmper wth 5.4 mm,.5 Hz ne wve 49

57 Force (N) 5 5 Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.8. MR dmper wth.54 mm, 5. Hz ne wve Force (N) 5 5 Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.9. MR dmper wth.54 mm,. Hz ne wve Force (N) 5 5 Dplcement (mm) Velocty (mm/ec) A.5 A A.5 A A.5 A Fgure 4.. MR dmper wth.54 mm,.5 Hz ne wve 5

58 4.. Force Re Tme Tet The MR dmper doe not repond ntntneouly to n nput current. To nvetgte th dynmc current behvor, tep n nput current re commnded over contnt velocty. The epermentl reult durng the contnt velocty (5 mm/ec) tet for tep n current from. Amp to hgher current level re hown n Fg. 4.. Force (N) Current (A) A.5 A A 4 A 5 A 6 A 7 A 8 A Fgure 4.. Over-drven current durng contnt 5 mm/ec Reult how tht commndng hgher current to the MR dmper reult n fter force re tme. Th mproved re tme cn be ncluded n em-ctve controller degn (Yng et l., ). For emple, to qucly cheve force of N, reltvely hgh current (uch 8 Amp) could be ppled untl N cheved (.e., over-drvng the crcut), then dropped to lower current (uch.5 Amp) to mntn th force. Levng hgh current on for long perod of tme h the potentl of both overhootng the dered force nd overhetng the MR dmper col, o t mportnt to only ue hgh current level for overdrvng the crcut, not mntnng force level. Note tht there re two lg preent n the ytem. The frt lg the mount of tme t te to relze the dered current n the MR dmper crcut. The econd lg, whch much lrger, due to the mount of tme requred to relze the correpondng retorng force. Both lg cn be een n Fg Tme (ec) Force Decy Tme If hgh level of force et n the MR dmper reult of n nput current, the force cn be reduced by ettng the current to zero. Th pproch nlogou to drvng bot t hgh velocty nd toppng the engne to rech zero velocty. However, bot engne cn lo be et n 5

59 revere, nd dong o would brng the velocty to zero much more qucly. Lewe, the current n the MR dmper could be commnded n the oppote drecton rther thn et to zero (.e. bc-drvng the crcut), whch d n dptng ny redul mgnetc feld tht would cue low force decy tme. The concept of bc-drvng the current complement to over-drvng the current, whch cn lo be ncluded n em-ctve controller degn (Yng et l., ). Deleterouly, f the bc-drven current were left on for too long, the force would eventully trt to re gn mgnetc feld generted n the oppote drecton. Therefore, ome ntellgence mut be dded to control the durton of the bc-drven current. Fgure 4. how epermentl reult for pplyng bc-drven current durng contnt velocty (5 mm/ec) fter lrge force cheved (7 N) ung.5 Amp. A bc-drven current of -7.5 Amp ppled begnnng t. econd for vrou durton ( dentfed n the fgure legend), fter whch the current returned to. Amp. Reult how tht ung bc-drven current reduce the force decy tme conderbly. However, noted prevouly, levng the bc-drven current on for too long cue the force to re gn. Through trl nd error, n optml current commnd to brng the MR dmper force to zero qucly poble determned, preented n Fg. 4.. In th optml ce, the current bc-drven for. econd nd therefter the current et to decy eponentlly to zero. 5 Force (N) Current (A) Tme (ec) ec.96 ec. ec.5 ec.4 ec. ec Optml Fgure 4.. Bc-drven current durng contnt 5 mm/ec 4. Hgh-Fdelty MR Dmper Model To t n developng em-ctve control lgorthm, hgh-fdelty MR dmper model dentfed. Th model cn lo be ued to e the tblty nd feblty of RTHS offlne; however the reult of uch multon re retrcted by the ccurcy of the model. 5

60 The comprehenve chrcterzton of the MR dmper behvor ued to develop prmeter for the phenomenologcl model orgnlly propoed by Spencer et l. (997) whch bed on Bouc-Wen hyteretc model. Other MR dmper model hve been propoed bed on Dhl frcton model (Ihoune nd Dye, 7) nd hyperbolc tngent functon (Kwo et l., 6; B nd Chrtenon, 7; Jng nd Chrtenon, ). Thee model bot fewer prmeter wth comprble reult to the phenomenologcl model (Kwo et l., 6; Ihoune nd Dye, 7). A comprehenve evluton of MR dmper model cn be found n Jng nd Chrtenon (). Lttle effort w requred to ft the prmeter of the phenomenologcl model to the N MR dmper chrcterzton tet, therefore th welletblhed model w employed wthout dffculty. Fgure 4. llutrte the underlyng mechnc of the model. entlly the model output the retorng force F for gven nput dplcement nd velocty. qutng the force on ether de of the center rgd br n Fg. 4. led to the followng reltonhp: y c y c y z (4.) y BW c c F Fgure 4.. Phenomenologcl model of n MR dmper The force z determned by the evolutonry vrble z modeled by Bouc-Wen hyteretc element (Bber nd Wen, 98). z y z z n n y z A y (4.) The retorng force F cn be decrbed by equtng the force on ether de of the rght-hndde rgd br n Fg. 4.. y y F z c (4.) Becue the MR dmper pton rod double-ended, no force offet preent under zero dplcement; thu, the tffne term cn be et to zero. The other model prmeter re ft ung Smuln prmeter etmton tool wthn MATLAB. To model the current-dependent behvor of the MR dmper, qn. (4.4) through (4.8) re ncorported nto the model, where c 5

61 the nput current. Prmeter wth the ubcrpt were ft to. Amp dt whle prmeter wth ubcrpt b were ft to.5 Amp dt. An eponentl reltonhp between the etreme w found bet to mtch the behvor ntermedte level of current, wth the rte of chnge decrbed by the prmeter wth ubcrpt c. The optmzed prmeter re preented n Tble 4.. (4.4) b b ep cc c c c c c,b,, b ep, cc (4.5) c c c c c,b,, b ep, cc (4.6) (4.7) b b ep cc (4.8) b b ep cc Tble 4.. Phenomenologcl Model Prmeter for N MR Dmper Prmeter Vlue Prmeter Vlue Prmeter Vlue c,.8 N ec/mm c,. N ec/mm,.5 mm - c,b. N ec/mm c, b 5. N ec/mm, b b. mm - c,c.5 A - c, c. A -, c c 5. A -. N/mm. N/mm A. N/mm b.55 N/mm n.. mm c. A - In ddton to the current-dependent behvor of the MR dmper t ttc level of current, chnge n current ntroduce dynmc tht mut be modeled. Thee dynmc cn be decrbed tme lg contng of two component: () the lg between when current commnded to the PWM devce nd t relzed n the MR dmper crcut, nd (b) the lg between when the current relzed n the MR dmper crcut nd the correpondng retorng force cheved n the MR dmper. The ggregte effect of both lg re modeled by frt order trnfer functon (qn. 4.9) curve ft to mtch epermentl dt. The dered current d nput to the trnfer functon nd the effectve reultng current c then nput to the MR dmper model. Note tht econd-order low p flter wth cutoff frequency of 75 Hz dded n ere wth qn. (4.9) to vod numercl tblty ue ometme found for qucly chngng current n numercl multon. 9 c 9 d (4.9) 54

62 To verfy the propoed MR dmper model under em-ctve condton (vryng current), bnd-lmted whte noe (BLWN) wth to 5 Hz bndwdth nd.78 mm RMS w nput to the phycl MR dmper. At the me tme, current pule between. nd.5 Amp w nput t frequency of Hz (5% duty cycle). The reultng dplcement, velocty, nd current htore from the eperment were then nput nto the numercl model. A compron between the retorng force of the phycl MR dmper nd model MR dmper preented n Fg Force tme htore, well force-dplcement nd force-velocty hytere loop, re hown. The model een to wor well even under vryng pecmen condton, lthough ome nccurce re pprent, epeclly the current decree. Dfference between the model nd phycl pecmen hghlght the need for RTHS n tht the hghly nonlner behvor of the MR dmper cnnot be completely cptured by current modelng pproche. Force (N) Force (N) Model Phycl Current (A) 5 5 Dplcement (mm) Tme (ec) Fgure 4.4. Performnce of MR dmper model under em-ctve condton 4.4 Advnced Sem-Actve Control Algorthm Velocty (mm/ec) Sem-ctve control lgorthm for the MR dmper ue eternl enor to determne the optml current commnd to the MR dmper. One of the mot trghtforwrd pproche to em-ctve control to crete two-tge controller. The frt tge ued to determne the optml control force through feedbc control degn. If n LQG controller choen for the frt tge, then the optml control force depend upon weghtng of the tructurl repone wth the control effort. The econd tge ued to turn the optml control force nto the control effort (current commnd) of the em-ctve devce. 55

63 4.4. Clpped-Optml (CO) Control A commonly referenced econd-tge controller for MR dmper devce the clpped-optml controller (Dye et l., 996). Th em-ctve controller bed on clpped-optml (CO) control lgorthm,.e., d m d m m H f f f (4.) where d the dered current (ent to MR dmper), m the mmum current (.5 Amp n th ce), f d the dered force, f m the meured force, nd H the Hevde functon. In hort, when the dered force f d greter n mgntude thn the meured force f m nd of the me gn, the mmum current m ent to the dmper. Thu, the mgntude of the force f m wll ncree n n ttempt to rech f d. In ll other ce, the current et to. Amp. The dered force f d determned ung n LQG controller. The clpped-optml controller logc llutrted n Fg f d d = m d = d = d = d = f m d = m Fgure 4.5. Grphcl repreentton of clpped-optml control lgorthm 4.4. Over-Drven Bc-Drven Clpped-Optml (ODBDCO) Control In order to cheve qucer repone from the clpped-optml control lgorthm, over-drven nd bc-drven concept re ncorported. When the current wtched on by the clpped-optml control lgorthm, nted of jumpng to the mmum current (.5 Amp), PI feedbc loop ued. Through the feedbc loop, more current ppled when the force error greter (over rnge of to 7.5 Amp). To prevent the MR dmper col from overhetng, the mmum llowble current decreed (to.5 Amp) fter few econd. To cheve qucer force decy tme, when the current wtched off (from prevou on-tte), negtve current ppled. Three condton re et, nd f ny of them re met then the bc-drven current would be dengged. () When, fter engged for mnmum mount of tme to llow for the force to begn to decree n mgntude, the force begn to ncree n mgntude. Th condton ndcte tht mgnetc feld beng generted n the oppote drecton, n underble outcome. (b) When the precedng commnded current. Amp. 56

64 Becue bc-drvng the current cn only reduce MR dmper force cued by current oppoed to velocty, t mportnt to enure tht uch current-nduced force et. (c) When the meured current le thn 5 N n mgntude. Lttle beneft gned by bc-drvng the current t thee low level of force. Th condton would lo turn the bc-drven current off the meured force enter th threhold from hgher mgntude, complmentng condton () wthout the tme retrcton. A wth the CO controller, the dered force f d determned ung n LQG controller. 4.5 Force Trcng erce To evlute the blty of the econd-tge controller to trc dered force, n rbtrry dplcement nd force htory were generted numerclly. Then, the dplcement htory w mpoed on the phycl MR dmper pecmen. Aumng tht the force htory the dered force, econd-tge controller were ued to trc the force htory. Both the CO nd ODBDCO controller were evluted. A cn be een n Fg. 4.6, the ODBDCO controller offer ome lght mprovement n force trcng, epeclly on the force decy t 4. econd. Reult for pve-off nd pve-on re lo preented rough envelope of the rnge of poble MR dmper performnce. The velocty lo hown n ndcton of the drecton of the MR dmper moton. Only when the velocty nd dered force re n the me drecton cn the dered force ctully be cheved. For emple, from 4. to 4.5 econd, the dered force nd velocty re n oppote drecton nd thu no current ppled. Force (N) Velocty (mm/ec) Dered Pve Off Pve On CO ODBDCO Current (A) Tme (ec) Fgure 4.6. Force trcng eerce 57

65 4.6 MR Dmper Flud Settlng Over tme, the ron prtcle n the MR flud my ettle nd cue ncontent behvor. Wth n olted MR dmper n lbortory ettng, the MR flud cn be cycled repetedly before tetng. However, nde lterl lod retng frme, t my be dffcult to cycle the MR dmper nd mntn flud contency. The behvor of the MR dmper fter remnng dle of nteret for prctcl pplcton, where the MR dmper my t dle for yer before gnfcnt dynmc event. The cyclc behvor of the MR dmper fter hort dle tme nd under lrge dplcement hown n Fg The nput dplcement 5.4 mm, Hz ne wve wth cycle rmp tme under n MR dmper current of.5 Amp wtched on t zero econd. In the meured force, there mll rregulrty for the frt full cycle of the.5 wee dle tet; however the MR dmper behvor reltvely tble. Dp (mm) Cycled Dy Idle 5 Dy Idle.5 Wee Idle Force (N) Tme (ec) Fgure 4.7. MR dmper behvor fter hort dle tme Aeng the MR dmper behvor for longer dle perod dffcult n tht t te up epermentl reource. Over the coure of th reerch, one wndow of month dle tme w vlble, fter whch tet w conducted for 7.6 mm, Hz ne wve wth for.5 Amp current wtched on t zero econd. The lower dplcement w to prevent the frt cycle from mng the flud conderbly. After the precrbed fve cycle tet (ncludng the one cycle rmp), the orgnl retorng force w not reched. Therefore, the cyclc tet w repeted fve tme untl content behvor w oberved. Longer dle tme followed by mller ectton hve notceble effect on the performnce of the MR dmper. For emc pplcton, lrge mpule my m up the flud dequtely, however further tudy of th phenomenon requred. Smlrly, f lrger troe ne wve w ued, the mng mght hve occurred ooner, thu rechng tble performnce n 58

66 more reonble tme frme. The phenomenon lo dependent upon the MR flud, dfferent ddtve nfluence ettng tme. Dp (mm) Run Run Run Run 4 Run 5 Force (N) Tme (ec) 4.7 Summry Fgure 4.8. MR dmper behvor fter month dle tme Chrcterzton of the MR dmper behvor led to the development of numercl model to fcltte tude on em-ctve control. The numercl model lo erve to confrm the feblty of RTHS before phycl eperment re run well verfy the reult. However, the model cnnot perfectly cpture the true dynmc of the devce nd therefore RTHS requred to confrm ny controller degn or nght gned from numercl multon. The chrcterzton tet hve lo demontrted the beneft of over-drvng nd bcdrvng the MR dmper crcut to mprove repone tme. Sem-ctve controller hve been preented to ncorporte thee de. Future tude on em-ctve control utlzng the propoed RTHS frmewor re plnned. Alo, the oberved phenomenon of MR dmper flud ettlng requre further nvetgton. 59

67 MODL-BASD ACTUATOR CONTROL FOR RTHS Chpter 5 In th chpter, model-bed ctutor control trtegy for RTHS propoed. The equton of moton decrbng the tructurl ytem re prttoned for hybrd multon nd preented longde the dynmc of the ervo-hydrulc ytem. The gol of the propoed ctutor control trtegy to elmnte the dynmc of the ervo-hydrulc ytem uch tht comptblty cheved between numercl nd epermentl component. Model-bed control developed round lnerzed model of the ervo-hydrulc ytem ncludng feedforwrd nd feedbc ln. The formulton fleble to ccommodte mult-ctutor ytem conderng ctutor couplng well mult-metrc feedbc control. 5. Problem Formulton The equton of moton governng the dynmc repone of lner tructure ubjected to n nput ground moton cn be repreented follow: M C K M Γ g (5.) where M the m mtr, C the dmpng mtr, K tffne mtr, Γ the m nfluence mtr, g the ground ccelerton, the vector of dplcement reltve to the ground, nd the dot repreent dfferentton wth repect to tme. A lner ytem preented here for clrty of preentton, lthough the formulton cn be dpted to nclude nonlner ytem. In hybrd multon, the equton of moton cn be eprted nto numercl nd epermentl component ndcted by upercrpt N nd, repectvely: N N N N M M C C K K M M Γ g (5.) Trdtonlly, numercl ntegrton performed on ll DOF ung ngle tme ntegrton cheme (Shng, 8). The repone cn thu be prttoned nto DOF tht re purely numercl nd DOF tht re t the nterfce between numercl nd epermentl component, repreented by upercrpt N nd I, repectvely. Wth the totl dplcement N I vector rrnged T, the followng prtton of the m, dmpng, nd tffne mtrce re creted: N N N N N N N M M NN NI N C NN C NI N K NN K NI M N N C N N K (5.) N N M IN M II C IN C II K IN K II M C M K II C (5.4) II K II The retorng force of the epermentl component cn be lumped nto the vector contn contrbuton from ttc, dmpng, nd nertl force: R, whch 6

68 M N N,, M M Γ g N N C K R (5.5) The loop of cton nd recton between numercl nd epermentl component durng RTHS llutrted n Fg. 5.. From numercl ntegrton of qn. (5.5), the tructure ected nd dplcement re clculted. To cheve comptblty between numercl nd epermentl component, the ubet of correpondng to the nterfce DOF I re commnded to the epermentl component ung ervo-hydrulc ctutor. Inner-loop ctutor control provde nomnl trcng of the commnd vector u to the ervo-hydrulc ytem meured by, the vector of nterfce DOF phyclly relzed by the epermentl I component. Outer-loop ctutor control typclly dded to determne u uch tht trc very ccurtely nd n rel-tme. The equton of moton of the epermentl component cn be repreented below, repondng to n nput force f from the ervo-hydrulc ctutor. M II CII K II f (5.6) I I Further comptblty of nd dered, but typclly t umed tht I relzng the dplcement ccurtely n rel-tme wll enure comptblty of hgher-order dervtve. The retorng force of the pecmen, meured by the ctutor lod cell or eternl lod cell, re returned to the numercl ntegrton cheme R. Ltly, through the nturl velocty feedbc loop, the dynmc of the pecmen drectly nfluence the dynmc of the ervo-hydrulc ytem (Dye et l., 995). Dgtl Controller Servo-Hydrulc Sytem G u () g R Numercl Component Outer-Loop Feedbc Control I Retorng Force Outer-Loop Control u Inner-Loop Feedbc Control Nturl Velocty Feedbc Servo-Hyd. qupment f permentl Component Fgure 5.. Multple feedbc loop n rel-tme hybrd multon In model-bed control, the outer-loop controller creted to cncel out the dynmc of the ervo-hydrulc ytem, ncludng pecmen dependency through the nturl velocty feedbc loop (Crron nd Spencer, 7). Conder the nput-output trnfer functon model G u of the lnerzed ervo-hydrulc ytem, ncludng the ctutor, ervo-vlve, ervocontroller, nd pecmen (epermentl component), repreented n Fg. 5.. The dynmc of the ervo-controller nd ervo-vlve, ctutor, nd pecmen hve been condened nto trnfer functon G, G, nd G, repectvely. The prmeter A repreent the effectve f 6

69 cro-ectonl re of the ctutor pton. The nput-output trnfer functon cn be wrtten n the Lplce domn : G u G G G f G A G G X (5.7) U I Fgure 5. cn repreent both SISO nd MIMO ytem for ngle nd mult-ctutor ytem, repectvely. Servo-Hydrulc Sytem G u () f u + + f G G f G Servo-Controller Actutor Specmen nd Servo-Vlve A Nturl Velocty Feedbc 5. Regultor Redegn Fgure 5.. Servo-hydrulc ytem wth CSI The model-bed control pproch propoed heren bed on lnerzed model of the ervohydrulc ytem, n qn. (5.7), whch repreented n tte-pce form to fcltte modern control theory degn (Phllp nd Spencer, ): z Az Bu (5.8) Cz (5.9) where z the tte vector nd A, B, nd C re the ytem, nput, nd output mtrce, I repectvely. The trcng error between the dered nd meured dplcement (or nd, repectvely) gven by: e I (5.) The commnd u hould be choen uch tht the trcng error mnmzed. If perfect trcng cheved, n del tte z nd n del nput u ledng to n output mut et I uch tht. The del ytem decrbed : z Az Bu (5.) 6

70 I Cz (5.) Devton of the tte, control, nd output from th del ytem wth repect to the orgnl ytem re defned : ~ z z z (5.) u ~ u u (5.4) ~ (5.5) The dynmc of the devton ytem re then: ~ z Az ~ Bu~ (5.6) ~ Cz ~ e (5.7) The trcng problem h now been redefned regultor problem bout etpont (Lew nd Syrmo, 995). The control lw n qn. (5.4) cn be rewrtten n term of the orgnl ytem, whch cont of feedforwrd component u uff determned from the del ytem nd feedbc component u ~ u determned from the devton ytem,.e., FB u u u ~ u u (5.8) The model-bed controller ncorportng both feedforwrd nd feedbc ln repreented chemtclly n Fg. 5.. The ervo-hydrulc ytem of Fg. 5. h been condened to how the detl of the model-bed controller, whch ct n outer-loop controller round the ytem. FF FB G FF () u FF Feedforwrd Controller I + u FB e LQG + Feedbc Controller + u G u () Servo-Hydrulc Sytem Fgure 5.. Model-bed ctutor control wth feedforwrd nd feedbc ln 6

71 5. Model-Bed Controller The development of the feedforwrd nd feedbc ln for model-bed control wll be preented for the generl ce followed by emple for ngle nd mult-ctutor ytem. 5.. Feedforwrd Controller The feedforwrd controller degned to cncel the modeled dynmc of the ervo-hydrulc ytem. Plced n ere wth the ervo-hydrulc ytem, the nvere of the ervo-hydrulc ytem model wll erve the feedforwrd controller. U G G AG FF G FF G u I G I f (5.9) X To llutrte mplementton ue octed wth model nveron, SISO ytem wll be emned. A hown n Chpter, the ervo-hydrulc ytem cn be repreented by the followng trnfer functon model: G u b b b m m (5.) n n For n ccurte model of ervo-hydrulc ytem, the number of pole generlly lrger thn the number of zero, w the ce for the model n Chpter. For the model n qn. (5.), the feedforwrd controller cn be epreed the nvere, or: 5.. Proper veru Improper Invere G n n (5.) FF m b b b m If qn. (5.) both proper nd tble, menng m n nd ll pole re tble, then the feedforwrd controller cn be mplemented wthout modfcton. For ue wth dgtl controller, dcrete tme ppromton, uch pole-zero mtchng or Tutn method my be ued. If m < n, the feedforwrd controller mproper nd requre modfcton. A low-p flter could be dded to qn. (5.) to reduce the degree to whch the nvere mproper. Wth enough pole, the low-p flter could even crete proper ytem (Crron nd Spencer, 7): G FF b b b n m n m c c c nm nm (5.) where c through cn m re the coeffcent of the low-p flter. However, low-p flter typclly ntroduce unwnted dynmc nto the feedforwrd controller. The pproch propoed heren for ccommodtng the mproper trnfer functon to me ue of hgher-order 64

72 65 dervtve whch re vlble from numercl ntegrton durng RTHS. The mproper feedforwrd model of qn. (5.) cn be eprted nto proper nd mproper term: m n m m m n m m m m n m m m m b b b b b b b b b G FF (5.) quton (5.) cn be epreed n the tme domn : m n m m m n m m m m n m m m m t r b b b t r b b b t r b b b t u FF (5.4) For emple, f m = nd n =, the feedforwrd controller could be wrtten : t r b t r b t r b t r b t u FF (5.5) Or f m = nd n = 5, t r b b b t r b b b t r b b b t r b b b t u 5 4 FF (5.6) For mplementton wth dgtl controller, the proper component cn be dcretzed before nd the hgher-order dervtve cn be clculted t ech tme tep v numercl ntegrton. Alo, n ome other pplcton, the dered trjectory nown pror (e.g., erthque moton reproducton on hng tble); for uch ce, mooth dervtve cn be creted offlne. Potve Zero 5.. If the ervo-hydrulc ytem contn zero wth potve rel component, the reultng nvere (.e., feedfowrd controller) would be untble due to potve pole. The mot trghtforwrd oluton to crete the bet poble model wthout the ue of potve zero, vodng tblty concern n the nvere. In the ce tht potve model zero cnnot be voded, zero phe error trcng controller (ZPTC) cn be ppled to the feedfowrd controller (Tomzu, 987). Frt, the ytem model decrbed by numertor nd denomntor polynoml: d n G u (5.7) wth nvere (feedforwrd controller) gven by: n d G FF (5.8)

73 The feedforwrd controller pole hould be eprted nto cceptble (negtve) nd uncceptble (potve) pole, ndcted by ubcrpt nd u, repectvely. 66 d n GFF (5.9) n The uncceptble pole re then removed nd the DC gn djuted for ther bence: u d n GFF (5.) n To mntn the me phe the orgnl untble controller, the followng djutment mde: u * nu n d GFF (5.) n where * ndcte the comple conjugte. From qn. (5.), t cn be een tht n uncceptble nvere pole wll led to n ddtonl zero n the feedforwrd controller. The ZPTC pproch mtche the phe of the untble nvere, but dtort mgntude t hgher frequence. The mgntude dtorton my negte the beneft of ncreed model ccurcy through ncluon of potve zero Feedbc Controller The feedbc controller dded to complement the feedforwrd controller, provdng robutne n the preence of chngng pecmen condton, modelng error, nd dturbnce. For the propoed model-bed feedbc controller, LQG control ppled to brng the devton tte to zero nd thu reduce the trcng error. The devton ytem of qn. (5.6) nd (5.7) rewrtten : FB u ~ z Az ~ Bu w (5.) ~ Cz ~ v f f (5.) where w f vector of dturbnce to the ytem, mtr tht decrbe how the dturbnce enter the ytem, nd v f the vector of meurement noe. It umed tht B, uch tht the dturbnce enter the ervo-hydrulc ytem n the me wy the I commnd. Only the output of the devton ytem (.e., ~ ) meurble. Thu, n oberver needed to etmte the unnown tte of the devton ytem. vong the eprton prncpl, n LQG controller cn be degned from ndependent LQR (optml tte feedbc control) nd Klmn flter (optml oberver) degn (Stengel, 986). To mprove the LQG controller performnce nd robutne n the frequency rnge of nteret, the dturbnce vector w f umed to be vector of ndependent Gun whtenoe w, ech ped through econd-order hpng flter,.e.,

74 67 w z A z f f f f (5.4) f f f z C w (5.5) where n n f f f f f f f A (5.6) nn f (5.7) n n f f f f f f f f f C (5.8) nd f z the tte vector the hpng flter, f z t tme dervtve, nd the prmeter f, f, nd f control the pe, bndwdth, nd roll-off of the dturbnce, repectvely. Snce t umed tht B, n equl to the number of control nput (.e., one dturbnce per nput to the devton ytem). The devton ytem cn be rewrtten n ugmented ytem tht nclude the dynmc of the hpng flter. Th ugmented ytem, denoted by the ubcrpt, gven by: z z z ~ f (5.9) w u B z A z FB (5.4) f ~ v z C (5.4) where A C A A f f (5.4)

75 B B (5.4) C f C (5.44) (5.45) nd the meurement noe vector v f umed to be compred of ndependent Gun whte noe. The control u FB cn be obtned ung LQR degn umng full tte feedbc nd output weghtng follow: J LQR T T Q ~ LQR u FBR LQRu FB ~ dt (5.46) u K z (5.47) FB where K LQR the optml tte feedbc gn mtr, J LQR the cot functon mnmzed by LQR degn, Q LQR the weghtng mtr on the ytem output, nd R LQR the weghtng mtr on the ytem nput. Wth the certnty equvlence property, LQR degn cn be performed wthout regrd to the proce nd meurement noe. The ugmented ytem tte z cn be etmted ung Klmn flter: LQR ~ z ˆ A zˆ ˆ B u FB L Kl C z (5.48) Where ẑ repreent the etmted tte nd L Kl the optml oberver gn mtr. The control lw n qn. (5.47) then wrtten n term of the etmted tte nd ncluded n the etmtor: FB LQR u K ẑ (5.49) A L C B K zˆ L ~ zˆ (5.5) Kl The control ytem toolbo n MATLAB ued for both LQR nd Klmn flter degn. 5.4 SISO mple The propoed model-bed ctutor control trtegy wll be emned for ngle-ctutor ytem. A prmeterzed ervo-hydrulc ytem model preented n Chpter wll be ued n emple to develop both feedforwrd nd feedbc controller. The model contn three pole nd no zero: LQR Kl 68

76 G u X U m p m c p c A p (5.5) 5.4. Feedforwrd Controller The feedforwrd controller ten the nvere of ervo-hydrulc ytem: p A m c U FF G FF (5.5) I X The feedforwrd controller cn be rewrtten : G FF (5.5) where the coeffcent through cn be determned by epndng qn. (5.5). The feedforwrd controller mproper by three degree. In the tme domn, qn. (5.5) become: u FF I I I I t t t t t (5.54) where dot denote dfferentton wth repect to tme nd, before, I refer to the nterfce DOF. In generl, the equton of moton re olved t tme tep for the dplcement t tme tep (.e., tme-teppng numercl ntegrton) nd the dplcement re mpoed on the phycl pecmen. In dcrete tme, quton (5.54) cn be wrtten : u FF, (5.55) I I I I Thu, the feedforwrd controller for the emple ctutor ytem requre the clculton of dplcement, velocty, ccelerton, nd jer (dervtve of the ccelerton) t tme tep ; however, mot numercl ntegrton cheme re only eplct n dplcement. Two method for clcultng the necery hgher-order dervtve re propoed, ncludng the CDM wth lner ccelerton etrpolton nd the bcwrd dfference method (BDM). Note tht thee method re propoed mply to etmte the hgher-order dervtve t the requred tme tep nd cn be elected ndependently from the numercl ntegrton cheme. In ddton dcrete model fttng pproch propoed to vod the need for etmtng hgher-order dervtve. Centrl Dfference Method wth Lner Accelerton trpolton Wth mot eplct numercl ntegrton cheme, only the dered dplcement I nown. The dered ccelerton cn be lnerly etrpolted over one tme tep: (5.56) I I I Note tht the ccelerton (nd ll other gnl) mut be n reltve coordnte uch tht they decrbe the dered trjectory of the phycl pecmen. The dered velocty cn be computed ung qn. (5.57), whch cn be derved from qn. (.) nd (.4). 69

77 7 I I I I t (5.57) Fnlly, the dered jer cn be clculted drectly from the ccelerton. Snce lner etrpolton of the ccelerton choen, the jer cn be clculted the lope of the etrpolton: I I I t (5.58) The propoed feedfowrd controller coupled wth the CDM for numercl ntegrton llutrted n Fg. 5.4 t would be mplemented by dgtl controller for RTHS. Fgure 5.4. Implementton of propoed feedfowrd controller n dcrete tme When the CDM ued for numercl ntegrton, both velocty nd ccelerton cn be epreed n term of dplcement. Thu, the feedforwrd controller ung the CDM nd lner ccelerton etrpolton wth the CDM for numercl ntegrton cn be epreed eplctly : I I I I FF, t t t t t t t t t t t t u (5.59) Or, dcrete tme trnfer functon: FF z t t t z t t t z t t t t t t z G t Clculte (CDM):,, Predct:,, Clculte: u, FF Meure: R Commnd:, FF u t Clculte (CDM):,, Predct:,, Clculte:, FF u Meure: R Commnd: u, FF t Meure: R Commnd:, FF u Smple: Computton: t

78 7 (5.6) Bcwrd Dfference Method The BDM provde n lterntve to dcretze n mproper contnuou tme ytem. Dervtve up to the thrd order clculted ung the BDM re gven by: I I I I 4 t (5.6) I I I I I 4 5 t (5.6) I 4 I I I I I t (5.6) where the dervtve re econd order ccurte. Snce the dervtve re clculted from vlble dplcement, the feedforwrd controller n qn. (5.55) cn be epreed : I 4 I I I I FF, t t t t t t t t t t t t u (5.64) Or, dcrete tme trnfer functon: 4 FF z t z t t z t t t z t t t t t t z G (5.65) The CDM wth lner ccelerton etrpolton degned to clculte up to the thrd order dervtve. On the other hnd, the BDM cn be ppled redly to computer hgher order dervtve, mng t more fleble for wder rnge of model. The CDM wth lner ccelerton etrpolton nd BDM method to cretng dcrete tme trnfer functon re compred to the contnuou tme trnfer functon n Fg. 5.5 for multple mplng rte. The prmeter for the emple feedforwrd controller re ten =., = , =.497-5, nd = For both method, the dcrete tme ppromton pproche the contnuou tme model the mplng rte ncree. The BDM more ccurte over the frequency rnge of nteret, however requre one more dt pont n the clculton.

79 Dcrete Model Fttng Fgure 5.5. Dcrete tme ppromton of feedforwrd controller mnng qn. (5.59) nd (5.64), the dcrete tme mproper feedforwrd controller cn be een model-bed etrpolton. Tht, ere of prevou dplcement commnd re ued to etrpolte future dplcement wth coeffcent determned by the ervo-hydrulc ytem model. Therefore, rther thn dcretzng contnuou tme model, the trnfer functon model could be drectly ft n dcrete tme by djutng the prmeter through n n: G z n FF z z n z (5.66) More generlly, the trnfer functon could be drectly ft dcrete tme ytem wth both pole nd zero n the ce tht the ervo-hydrulc ytem model poee zero: 5.4. Phe ( ) Mgntude CDM Hz CDM Hz CDM 55Hz Frequency (Hz) BDM Hz BDM Hz 5 BDM 5Hz Frequency (Hz) Frequency (Hz) G Feedbc Controller z Tme Lg (mec) z n n z (5.67) FF m b b z b z b m z A tte-pce model of the ervo-hydrulc ytem n qn. (5.5) ued to develop the modelbed feedbc controller. A prmetrc tte-pce model for the ngle-ctutor ytem cn be creted by emnng the dynmc of the force ppled by the ctutor n Fg..: f u A f p (5.68) z Contnuou The tte-pce repreentton of the ytem gven by: 7

80 7 u f p A m m c m f (5.69) Wth phycl ervo-hydrulc ytem, t my be dffcult to ft prmeterzed model. Therefore, nonprmetrc tte-pce model (ft ung frequency domn ytem dentfcton) cn lo be ued for feedbc degn; n uch ce, qn. (5.69) provde nght nto the menng of the nonprmetrc relzton. 5.5 MIMO Sytem wth Actutor Couplng When multple ctutor re connected to the me pecmen, the dynmc of the ctutor become coupled through the pecmen (.e., when n ctutor pple force to the tructure, the other ctutor wll lo eperence th force). Actutor couplng wll be demontrted ung the DOF lner buldng tructure hown n Fg Fgure 5.6. mple DOF lner tructure Th pecmen employ three ervo-hydrulc ytem, ech compred of ervo-vlve, ervo-controller, nd n ctutor whch re commnded ndependently nd cn be repreented n Fg. 5. by the followng dgonl mtrce: G (5.7) Actutor Actutor Actutor

81 74 p p p G (5.7) A A A A (5.7) where the prmeter ubcrpt dentfy the DOF to whch the ctutor ttched for the generl ce where the ervo-hydrulc hrdwre not dentcl. Lewe, the commnded dplcement, meured force, nd meured dplcement cn be wrtten T u u u u, T f f f f, nd T, repectvely. The ervocontroller nd ervo-vlve dynmc (qn. 5.7) re choen contnt gn, whle the ctutor dynmc (qn. 5.7) re choen frt-order model. For generlty, the m, dmpng, nd tffne mtrce of the tructure re umed fully coupled; n uch ce, qn. (5.6) cn be wrtten : f f f c c c c c c c c c m m m m m m m m m (5.7) where m, c, nd repreent entre n the m, dmpng, nd tffne mtrce, repectvely, wth ther poton ndcted by the ubcrpt. Tng the Lplce trnform of qn. (5.7) yeld the trnfer functon reltng the nput force from the ctutor to the output dplcement: c m c m c m c m c m c m c m c m c m f F X G (5.74) The off-dgonl term n qn. (5.74) re the ource of the ntercton between the three ervohydrulc ytem. Subttutng qn. (5.7) through (5.7) nd qn. (5.74) nto qn. (5.7), the MIMO ervo-hydrulc ytem trnfer functon model obtned:

82 X z, z, z, z, z, z, z, z, z, G u (5.75) 9 U p where z nd p repreent the model zero nd pole, repectvely. Note tht the model trnfer functon, wth ech nput-output pr poeng zero nd nne pole. The ctul pole nd zero cn be obtned n cloed-form, lthough they re too complcted for conce preentton. In qn. (5.75), the off-dgonl term decrbe the ntercton between the three ervo-hydrulc ytem Feedforwrd Controller The feedforwrd controller for the mult-ctutor ytem conderng ctutor couplng cn be creted from qn. (5.9). Subttutng qn. (5.7) through (5.7) nd qn. (5.74) nto qn. (5.9) yeld: G FF p A p p m c m c m c p p A p m c m c m c p p p A m c m c m c (5.76) ven wth the complety of the ervo-hydrulc ytem trnfer functon model of qn. (5.75), qn. (5.76) reltvely mple (three zero for ech nput-output pr). For ech nput-output pr of qn. (5.76), there re two zero tht pper reult of the econd-order pecmen dynmc. If the m, dmpng, or tffne mtrce re not fully populted, n lumped m ytem or her buldng, then qn. (5.76) could be further mplfed. Thu, n undertndng of the behvor of the phycl pecmen cn d n determnng the number of zero (nd pole) to ue n the feedforwrd controller. The thrd zero n ech nput-output pr re from the frt-order ctutor model. Note tht ech column h the me ctutor prmeter ( een by the ubcrpt), nce ech column octed wth the nput to one ctutor. I U G X cn be rewrtten : The feedforwrd controller FF FF 75

83 U U U FF, FF, FF, b b b c c c d d d b b b c c c d d d b b b c c c d d d X X X I I I (5.77) where though d re coeffcent wth ther poton ndcted by the ubcrpt nd the feedforwrd controller een to be mproper. The propoed pproch for ccommodtng the mproper trnfer functon to me ue of hgher-order dervtve whch re vlble from numercl ntegrton durng RTHS. In uch ce, the feedforwrd controller cn be rewrtten n the tme domn : u u u FF, FF, FF, b b b c c c d d d b b b c c c d d d b b b c c c d d d I I I I I I I I I I I I (5.78) Thu, wth the nowledge of the dered dplcement, velocty, ccelerton, nd jer t the nterfce DOF, the feedforwrd control reduced to mtr multplcton. Method for ccurtely etmtng the hgher-order dervtve durng RTHS re dcued prevouly for the ngle-ctutor ytem Feedbc Controller Model-bed feedbc control cn be derved from tte-pce repreentton of the trnfer functon gven n qn. (5.75). A tte-pce repreentton cn lo be creted by emnng the dynmc of the force n ech of the ctutor. From Fg. 5., qn. (5.7) through (5.7), nd qn. (5.74), the equton governng the ctutor repone re: f (5.79) u A f p f (5.8) u A f p 76

84 77 p f A u f (5.8) The tte-pce repreentton of the ytem thu: I u u u f f f p p p A A A M C M K M f f f (5.8) A epected, the tte-pce model contn nne pole. In prctcl tuton where the pecmen dynmc mut be determned from ytem dentfcton, dentfyng the nvere model frt (qn. 5.76) nd then clcultng the ervo-hydrulc ytem model (qn. 5.75) from the nvere my be eer. Such n pproch dcued nd ppled n Chpter 7. A wth the ngle-ctutor ytem, t my be eer to dentfy nonprmetrc model for control degn. The precedng model-bed mult-ctutor control cheme w preented for threectutor ytem. The me pproch cn be ppled to n rbtrry number of ctutor. Lewe, the pproch cn be ely dpted to hgher-order ervo-hydrulc ytem model. 5.6 Mult-Metrc Feedbc Control RTHS ued to tet the rte-dependent behvor of tructurl component. Actutor control cheme to dte focu on ccurte dplcement trcng wthout concern for the hgher-order dervtve. The propoed model-bed trtegy h the fleblty to nclude feedbc from ddtonl meurement devce to get better etmte of the tte of the ytem through the Klmn flter. At the me tme, feedbc controller weght cn be plced on the ddtonl meurement through LQR control. By ncorportng hgher-order dervtve n the modelbed controller, more ccurte trcng of hgher-order dervtve cn be cheved towrd better repreentton of rte-dependent pecmen behvor.

85 For emple, ccelerometer cn be dded to the ctutor n lne wth ech dplcement trnducer. In th ce, the ervo-hydrulc ytem model wll hve twce mny output nput. G yu X X U Y U (5.8) The tte-pce relzton would contn th ddtonl output. z Az Bu (5.84) y Cz (5.85) where y T I I I y T. Wth dered dplcement nd ccelerton gnl gven by, the trcng error between the dered nd meured gnl : e I y y (5.86) Through regultor redegn, the devton ytem output re: y ~ I I (5.87) where the ddtonl output equl to the dfference between the meured nd dered ccelerton. The dynmc of the ugmented devton ytem ncludng the proce noe hpng flter nd meurement noe re gven by: z A z B u w (5.88) FB ~ y C v z f f (5.89) where the meurement noe vector nclude both dplcement nd ccelerton noe. The LQR controller cn be degned bed on output weghtng ncludng both the dplcement nd ccelerton output: J LQR T T Q ~ LQRy u FBR LQRu FB ~ y dt (5.9) Accelerton meurement ncree n mgntude wth the qure of the frequency reltve to dplcement meurement. Thu, the hpng flter contned wthn the ugmented ytem epeclly mportnt to ttenute the repone of the feedbc controller t hgh 78

86 frequence. The ugmented ytem tte z cn be etmted ung Klmn flter degned for n umed proce noe nd dplcement nd ccelerton meurement noe: ~ z ˆ Azˆ ˆ BuFB LKl y Cz (5.9) The totl combned feedbc controller would hve the dynmc: A L C B K zˆ L ~ y z ˆ (5.9) Kl A chemtc of the propoed mult-metrc feedbc controller preented n Fg LQR Kl G FF () u FF Feedforwrd Controller I + e e LQG Feedbc Controller u FB + + u G yu () Servo-Hydrulc Sytem I + Fgure 5.7. Mult-metrc feedbc control Note tht the feedforwrd controller ued to cheve the del ytem n the regultor redegn h not been chnged. 5.7 Summry Th chpter preented frmewor for model-bed ctutor control ncludng both feedforwrd nd feedbc ln. mple degn re preented for both ngle nd mult-ctutor ytem. In the ngle-ctutor ytem emple, focu plced on the mplementton of mproper feedforwrd controller, whch re typcl of ervo-hydrulc ytem. In the mult-ctutor ytem emple, focu plced on llutrtng the phenomenon of ctutor couplng. A frmewor for ncorportng mult-metrc feedbc lo preented towrd better trcng of hgher-order dervtve. 79

87 Chpter 6 SINGL ACTUATOR CONTROL Model-bed ctutor control frt ppled to lrge-cle, ngle-ctutor ytem. An epermentl frmewor combnng dvnced computtonl hrdwre nd oftwre wth hghperformnce ervo-hydrulc ytem h been developed to evlute the performnce of rtedependent tructurl component n RTHS. The phycl pecmen choen lrge-cle MR dmper, whch ehbt hghly nonlner, uer controllble behvor. Through repetble chnge n the pecmen behvor, the robutne of the propoed ctutor control trtege cn be nvetgted. Control performnce evluted n the tme domn nd frequency domn for predefned commnd well for both SDOF nd MDOF tructure n RTHS. 6. permentl Setup The RTHS tetng frmewor t the Unverty of Illno locted n the Newmr Structurl ngneerng Lbortory (NSL, nd prt of the Smrt Structure Technology Lbortory (SSTL, The ervo-hydrulc ytem hrdwre hown n Fg. 6., ccelerometer plcement n Fg. 6., nd the computtonl hrdwre nd ervo-controller n Fg. 6.. The component depcted re decrbed ubequently. Fgure 6.. Servo-hydrulc hrdwre for RTHS 8

88 Fgure 6.. Accelerometer plcement on ctutor hed Fgure 6.. Computtonl hrdwre for RTHS 6.. Tet Frme The ctutor nd pecmen re both mounted on 7.6 cm ( n) thc teel plte ung recton ngle. Steel bloc nd wedge re ued to prevent dfferentl movement of the ctutor nd pecmen. The teel plte ecured to the NSL trong floor ung threded rod pced 45.7 cm (.5 ft) on center to prevent fleng of the plte nd her ey re ued to prevent longtudnl trnlton of the plte. The frme degned to mnmze bclh nd eltc deformton under the hgh force produced durng tetng. Th etup (ee Fg. 6.4) h proven 8

89 ucceful for the dynmc tetng of lrge-cle MR dmper (Yng et l., ; Phllp et l., ; Phllp nd Spencer, ). Te Down Recton Angle Accelerometer 445 N Lod Cell 556 N Actutor ±5 mm Stroe Recton Angle Bloc nd Wedge Sher Key Bloc nd Wedge Te Down Internl AC LVDT Sher Key 6.. Servo-Hydrulc Sytem Fgure 6.4. Tet frme nd fturng (not to cle) The ctutor, mnufctured by the Shore Wetern Corporton, rted t 556 N (5 p) wth troe of ±5.4 mm (±6 n), h n effectve pton re of 7 cm (4 n ), nd double ended to provde equl performnce both etendng nd retrctng. A Schenc-Pegu model 8 three-tge ervo-vlve rted t lpm (8 gpm) employed wth model B rted t.6 lpm (.86 gpm) the plot ervo-vlve, hown n Fg Three-tge ervo-vlve re typclly ued n dynmc pplcton to cheve hgh flow rte requred for the fter repone of lrge ctutor. Both flow rtng ume 6.89 MP ( p) preure drop. Fgure 6.5. Schenc-Pegu model 8 three-tge ervo-vlve wth plot vlve The ytem connected to the mn hydrulc power upply of NSL, provdng.7 MP ( p) t 4 lpm (9 gpm). Hydrulc ol routed through Schenc-Pegu model 784S hydrulc ervce mnfold (HSM), whch rted t lpm (8 gpm). The HSM h ccumultor for the plot preure, mn preure, nd return preure of. MP (5 p), 5.7 MP (75 p), nd.45 MP (5 p) repectvely, to provde ddtonl flow for hort 8

90 durton. A Shore Wetern model 4 dgtl ervo-controller ued to control the ctutor n dplcement feedbc mode. Th ervo-controller contn n nlog proportonl feedbc loop ued for nner-loop control. Shore Wetern SC6 oftwre ued to nterfce wth the ervo-controller. The ervo-controller confgured to ccept eternl commnd from the DSP bord controllng the RTHS. 6.. Senor The dplcement of the ctutor meured ung n nternl AC LVDT wth entvty of 46. mv/mm. A 445 N ( p) Key Trnducer, Inc. model 4-4- lod cell wth entvty of.4 mv/n mounted n lne wth the ctutor, meurng the retorng force of the ttched pecmen. In ddton, the temperture montored contnuouly durng tetng ung three Omeg ngneerng model SAXL-J thermocouple nd model SMCJ-J nlog converter wth entvty of mv/ F. Accelerton re meured ung model 7GFAG cpctve ccelerometer mnufctured by PCB Pezotronc. The ccelerometer hve meurement rnge of ± g, frequency rnge of - Hz, nd entvty of mv/g. Two ccelerometer re plced on the ctutor pton rod for compron; however the ccelerometer cloet to the ctutor houng n Fg. 6. ued for ll reported ccelerton meurement. The current n the MR dmper crcut meured ung Tetron current probe wth entvty of mv/a Dgtl Sgnl Proceor The RTHS controlled by dspac model DSP bord wth PPC 75GX proceor. An I/O bord CLP ued to nterfce wth the ervo-controller. The DSP bord h A/D chnnel nd 8 D/A chnnel, ech wth reoluton of 6-bt. The DSP bord mounted n n eternl ch nd connected to hot computer v fber optc cble. Th bord ued to perform numercl ntegrton of the equton of moton for the numercl ubtructure, pply the outer-loop ctutor control cheme, nd control the MR dmper current bed on emctve control lgorthm. Thee three numercl component re progrmmed on the hot computer ung Smuln, bloc dgrm progrmmng tool wthn MATLAB. The Smuln model converted to C lnguge ung MATLAB Rel-Tme Worhop nd trnferred to the DSP bord. Rel-tme eecuton of the code controlled nd montored from the hot computer ung dspac ControlDe oftwre. An emple ControlDe nterfce pnel preented n Fg. 6.6, llowng the uer to trt, pue, nd top the code eecuton, elect the nput ground moton, elect the tructurl control trtegy, elect the ctutor control trtegy, nd montor the enor redng n rel-tme. The hot computer lo ct the DAQ, loggng dt from the DSP bord. The flow of nformton from the hot computer to the epermentl equpment hown n Fg Sold rrow ndcte communcton n rel-tme (e.g., durng RTHS). 8

91 Fgure 6.6. mple ControlDe oftwre nterfce pnel Mtlb Hot Computer Smuln Rel-Tme Worhop Control De DSP Bord DSP I/O Pnel permentl qupment Fgure 6.7. Communcton between oftwre nd hrdwre 84

92 6. Chrcterzton of the Servo-Hydrulc Sytem The ervo-hydrulc ytem h dynmc performnce lmtton whch cn be more retrctve thn the lod rtng of the ctutor. An undertndng of thee lmtton wll help to develop the dynmc opertng rnge of the ytem. To eplore the couplng between force nd velocty, the dynmc of the ervo-vlve wll be nvetgted. The output flow of ervo-vlve (qn. 6.) depend on the commnded vlve current well the preure drop cro the vlve (Mertt, 967). Q L Q R c R P S P P L (6.) where Q L the output flow, Q R the rted flow, c the nput current, R the mmum nput current, P S the upply preure, P L the preure drop cro the lod, nd P the rted vlve preure drop. For the ervo-hydrulc ytem n th tudy, the mmum nput current R 5 ma nd the upply preure P S p. The rted flow Q R for th prtculr ervo-vlve 8 gpm for rted vlve preure drop P of p. Servo-vlve re rted t th vlve preure drop becue t correpond to the lrget output power (force tme velocty) for p upply preure ytem. The output flow plotted gnt the rto of preure drop cro the lod to upply preure for vrety of nput current rto n Fg. 6.8 bed on qn. (6.). When the lod to upply preure rto equl to /, the rted flow of 8 gpm cheved t the mmum nput current vlue. Output flow greter thn the rted flow cn be cheved, lthough the output power wll not be t mmum. Output Flow, Q L (gpm) c / r =. c / r =.4 c / r =.6 c / r =.8 c / r = Lod to Supply Preure Rto, P L /P S Fgure 6.8. Flow-preure reltonhp of ervo-vlve 85

93 The force on the pton rod equl to the preure drop cro the lod multpled by the pton cro-ectonl re n: f P A (6.) where f the pton force nd A the pton cro-ectonl re. The pton force compred of the force mprted on the pecmen, the nertl force of the pton rod, well the frcton force. The nertl force typclly neglgble. The frcton force depend on the frcton between the pton rod nd the ctutor houng. Actutor ue low-frcton el to mnmze th force, enurng tht mot of the totl force cn be ued to ecte the pecmen. The velocty of the pton rod v equl to: L QL v (6.) A By combnng qn. (6.) through (6.) for the mmum current, the followng reltonhp between force nd velocty for the ervo-vlve nd ctutor pr cn be derved: f v A P PS A (6.4) Q R At the me tme, there flow lmtton mpoed by the upply ol preure. The hydrulc pump re lmted to 9 gpm. Further downtrem, the ervo-hydrulc mnfold rted t 8 gpm. Wth the 8 gpm lmt, econd velocty lmt cn be derved bed on the ol upply Q flow nd the equton below. S QS v (6.5) A The opertng rnge of the ervo-hydrulc ytem preented n Fg. 6.9 wth lmt bed on the ervo-vlve nd ctutor force-velocty reltonhp, ol upply lmt, nd pecmen rtng. The upply lmt trghtforwrd; bed on the rted flow rte of the ervo-hydrulc mnfold, no more thn 86 mm/ec cn be cheved n the pton rod. Th lmt conervtve, becue the ccumultor n the ervo-hydrulc mnfold wll llow for hort burt of hgher velocte. The force lmt of the ervo-vlve nd ctutor follow prbolc reltonhp wth the pton velocty (qn. 6.4). For low pton force, the flow rte cn eceed the rted flow; however the upply lmt cnnot be eceeded. The opertng rnge of the ervo-hydrulc ytem h been dentfed nd eperment wll be degned uch tht thee lmt, nmely the mmum velocty, re not eceeded. At the me tme, the MR dmper rted t nomnl N, o force much hgher thn N re not epected. 86

94 Pton Force (N) Servo Vlve Lmt Supply Lmt MR Dmper Rtng Opertng Rnge Specmen Rnge Pton Velocty (mm/) Sytem Identfcton Fgure 6.9. Hydrulc power curve The trnfer functon from the nput commnded dplcement to the output meured dplcement (nd ccelerton for mult-metrc feedbc) ued to chrcterze the dynmc of the ervo-hydrulc ytem. Th trnfer functon nclude the dynmc of the ctutor, ervovlve, ervo-controller, pecmen, nd enor. Note tht ome tme dely (e.g. dt communcton, A/D nd D/A converon) wll nturlly be ncluded n the chrcterzton of the ervo-hydrulc ytem dynmc. Unle otherwe mentoned, the nput elected BLWN from to 5 Hz wth dplcement RMS of.54 mm, provdng nght nto the ervohydrulc dynmc over th rnge of frequence. The dspac ytem ued to generte the commnded gnl nd meure the repone t 48 Hz. Dt down-mpled to 8 Hz nd the trnfer functon clculted ung 48 FFT pont, Hnnng wndow wth 5% overlp, nd verge. The tme lg clculted by dvdng the phe by the frequency, whch notcebly entve to noe t the lower frequence. 6.. Actutor Tunng The uer h control over the nner-loop PID gn of the ervo-controller. For RTHS pplcton, ntegrl gn typclly not ued becue t dd dely to the repone of the ervohydrulc ytem nd h lttle mpct on the dynmc performnce of the ytem. Alo, dervtve gn not ued becue t cue the ervo-hydrulc ytem to be more entve to noe. Therefore, focu plced on tunng the proportonl gn. Fgure 6. how the ervohydrulc ytem trnfer functon wth the MR dmper pecmen ttched (et t. Amp) for vrou proportonl gn vlue. A proportonl gn of 6 elected for t uperor performnce before the onet of tblty concern een by further ncreng the gn. Note tht when pecmen wth hgher retorng force ttched, uch the MR dmper t.5 Amp, 87

95 the ervo-hydrulc ytem performnce wll degrde due to lrger retorng force retng the moton..5 Mgntude.5 Phe ( ) 5 K P = K P = 4 K P = 5 K P = Frequency (Hz) Frequency (Hz) Tme Lg (mec) 4 5 Frequency (Hz) Fgure 6.. Tunng of the ervo-hydrulc ytem t. Amp 6.. Servo-Hydrulc Sytem Lnerzton The epermentl trnfer functon lner repreentton of the nput-output dynmc of the ervo-hydrulc ytem. The lnerzton occur bout the opertng pont of the ytem; therefore dfferent trnfer functon could be dentfed for dfferent nput mpltude, frequence, or pecmen condton. To qulttvely nvetgte the entvty of the dentfed model to nput condton, the ervo-hydrulc ytem trnfer functon nvetgted t three dfferent mpltude rnge. To fely ccommodte hgher mpltude, the frequency rnge of the nput BLWN re reduced. Sytem dentfcton performed wth RMS vlue of.54 mm,.4 mm, nd.6 mm wth BLWN frequency rnge of to 5 Hz, to 5 Hz, nd to 5 Hz, repectvely. Smple tme htory gnl re hown n Fg. 6.. The correpondng trnfer functon re hown n Fg. 6., where both. Amp nd.5 Amp condton re nvetgted. The chnge mde to the nput do not gnfcntly ffect trnfer functon of the ytem, howng tht lnerzed model cceptble for fed pecmen condton. On the other hnd, chnge to the pecmen clerly led to chnge n the ytem dynmc, phenomenon tht wll be ddreed through the propoed controller

96 Dp (mm) 5 Hz,.54 mm 5 Hz,.4 mm 5 Hz,.6 mm Vel (mm/ec) Tme (ec) Fgure 6.. Tme htory of BLWN nput gnl.5 Mgntude.5 Phe ( ) Hz,.54 mm,. A Hz, 45.4 mm, 5. A Frequency (Hz) 5 Hz,.6 mm,. A 5 Hz,.54 mm,.5 A 5 Hz,.4 mm,.5 A 5 Hz,.6 mm,.5 A Frequency (Hz) Fgure 6.. Sytem repone t multple mpltude nd frequency rnge Model Development Tme Lg (mec) Wth the nner-loop PID gn et nd confdence n the lner behvor of the ervo-hydrulc ytem for fed pecmen condton, epermentlly derved trnfer functon wll be ued to Frequency (Hz)

97 develop trnfer functon model. A nonprmetrc ytem dentfcton technque, MFDID (Km et l., 995), ued to ft the epermentl trnfer functon dt to SISO or ngle-nput mult-output (SIMO) model of pole nd zero. Becue the current to the MR dmper cn chnge durng the RTHS, the ervo-hydrulc dynmc mut be nvetgted t multple current level. The meured dplcement trnfer functon mgntude, phe, nd tme lg re preented n Fg. 6. for two condton:. nd.5 Amp. The reult re lo verged to crete thrd trnfer functon pproprte for when the pecmen condton re unnown or chngng..5 Mgntude.5. A.5 A Averge Frequency (Hz) Phe ( ) Frequency (Hz) Tme Lg (mec) Frequency (Hz) Fgure 6.. Meured dplcement trnfer functon t elect current level Identfed trnfer functon model re overln on Fg. 6. n dhed blc lne. Three pole model re found uffcent to ccurtely repreent the dynmc over the frequency rnge of nteret (up to 4 Hz). Model of the ervo-hydrulc dynmc t. nd.5 Amp, well the verge of the two pecmen condton, re gven by: 7 X.7 G u,.a (6.6) U,.5A G u (6.7),vgA G u (6.8)

98 Fgure 6. how tht the behvor of the ervo-hydrulc ytem frequency dependent, where the mgntude nd phe (or equvlently, the tme lg) vre wth frequency. Trdtonl dely compenton pproche bed on ngle contnt tme dely would be ndequte for ytem tht repond t multple frequence, uch MDOF tructure. Lewe, trdtonl pproche do not ddre the decy n mgntude oberved. Typcl tme dely/lg reported n the lterture rnge from 8 to mec (Horuch et l., 999; Nhm nd Mo, 999; Drby et l., ; Crron nd Spencer, 7; Wllce et l., 7; Chen nd Rcle, ). The tme lg n th epermentl etup w found to vry between 8 nd mec dependng on the frequency of ectton nd the pecmen condton, whch reltvely mll for uch lrge ctutor. Subequent tet comprng the lg between nput ne wve nd meured repone confrmed thee reult. In ddton to dplcement bed feedbc, mult-metrc feedbc pproche wll be condered. To mplement mult-metrc feedbc control, the output ccelerton re lo meured, cretng SIMO ytem. The trnfer functon from nput commnd to meured ccelerton dentfed, hown n Fg Ftted trnfer functon model re overln on Fg. 6.4 n dhed blc lne. The combned SIMO ytem model (nput commnd to output dplcement nd ccelerton) re gven by: X.7 G yu,. A 4 U (6.9) A G yu (6.),.5 A,vgA G yu (6.) When the retorng force low n the MR dmper (. Amp), the meurement n the LVDT nd ccelerometer correlte well. A een n qn. (6.9), the ccelerton trnfer functon cn be ccurtely repreented by the econd dervtve of the dplcement trnfer functon. However, when the retorng force n the MR dmper hgh (.5 Amp), the eltc deformton of the tetng frme wll be lrger. Snce the ccelerometer mounted on the epoed ctutor pton hed nd the LVDT mounted nternlly n the rer of the ctutor houng, the eltc deformton wll led to dcrepnce n meurement. At low dplcement, ome of the meured dplcement wll go nto the eltc deformton of the frme whle the ccelerometer re meurng bolute ccelerton. Th decree n ccelerton meurement reltve to the dplcement meurement cn be een by the gn djutment n qn. (6.) nd (6.). 9

99 Future wor wll eplore lterntve enor plcement for better meurement correlton n the preence of eltc deformton Mgntude Phe ( ) 8. A.5 A Averge 4 5 Frequency (Hz) Frequency (Hz) Fgure 6.4. Meured ccelerton trnfer functon t elect current level 6. Controller Degn Actutor controller re creted bed on () the propoed model-bed trtegy, (b) prevou model-bed trtegy (Crron nd Spencer, 7), (c) the polynoml etrpolton method (Horuch et l., 996), nd (d) the led compentor method (Zho et l., ; Jung et l., 7). Model-bed controller re degned bed on the dentfed ervo-hydrulc model whle the polynoml etrpolton nd led compentor controller were degned to compente for the DC (.e., zero frequency) tme lg. The ddtonl controller wll erve compron for the propoed model-bed controller mong other wdely-ppled pproche to ctutor control for RTHS. 6.. Propoed Model-Bed Controller Bed on the method propoed n Chpter 5, three model-bed feedforwrd controller re creted ung the trnfer functon model n qn. (6.6), (6.7), nd (6.8) nd dentfed G FF,.A, G FF,.5A, nd G FF, vga, repectvely. The frt two controller re ued when the pecmen condton re nown nd unchngng, whle the thrd controller ued when the pecmen condton my be chngng. Wth the propoed feedforwrd controller, hgher-order dervtve re requred. For predefned dplcement, the hgher-order dervtve re clculted offlne. In RTHS, hgher-order dervtve re clculted n rel-tme ung the CDM wth lner ccelerton etrpolton. To mprove performnce nd compente for ytem modelng error nd chnge n pecmen condton, n LQG feedbc controller creted ung tte-pce repreentton of the model n qn. (6.8) nd (6.) for dplcement-bed nd mult-metrc feedbc controller, repectvely. The complete controller wth feedbc control re dentfed 9

100 G FF, vga + LQG nd G FF, vga + LQG for dplcement nd mult-metrc feedbc, repectvely. 6.. Prevou Model-Bed Controller The prevou model-bed pproch bed on pole-only model of the ervo-hydrulc ytem gven by: G u n p K (6.) The feedforwrd controller ten the nvere n combnton wth low-p flter to crete proper ytem: G FF n n p n (6.) p where the prmeter control the locton of the pole of the feedforwrd controller. Wth, the feedforwrd control effort equl to unty (.e., no compenton) whle pproche nfnty, the feedforwrd controller pproche n mproper nvere. Crron nd Spencer (7) recommend ung uch tht the pole of the feedforwrd controller do not gnfcntly nterfere wth the nvere dynmc whle the pole re mll enough to be mplemented wth reonble mplng rte for RTHS. Two feedforwrd controller re creted bed on the trnfer functon model n qn. (6.6) nd (6.7), repreentng the etreme of the pecmen condton. The feedforwrd controller wth low-p flter ( ) re dentfed G FF,.A + LP nd G FF,.5A + LP. For ce when the pecmen condton my be chngng, bumple trnfer creted between the two feedforwrd controller bed on the nput current. d.5 Amp. The bumple trnfer llutrted n Fg The trnfer functon G t provde mooth trnton between controller bed on the nput current to the MR dmper. By emnng the repone tme of the MR dmper, the followng lg trnfer functon w elected:.5 G t (6.4).5 9

101 G FF,.A () Feedforwrd Controller u FF,.A + + u FF I G FF,.5A () u FF,.5A + Feedforwrd Controller Product d G t () Dely 6.. Polynoml trpolton Fgure 6.5. Bumple trnfer controller The polynoml etrpolton technque ft the current dered dplcement wth prevou dplcement to polynoml nd etrpolte the dplcement commnd fter fed tme tep. The commnd to the ervo-hydrulc ytem cn be clculted by: n I u FF, j j (6.5) j I where n the order of the polynoml, j the dplcement T d j unt of tme go, T d the etmted dely, nd j re contnt of etrpolton, dependng on the order n. For thrdorder etrpolton, u FF, (6.6) I I I I 4 6 T T T d 4 d d To ccommodte dfferent pecmen condton, three thrd-order polynoml etrpolton compentor re creted, bed on 8 mec dely for. Amp, mec dely for.5 Amp, nd 9 mec dely for chngng pecmen condton Led Compentor The led compentor pole-zero pr whch tuned to elmnte the low-frequency tme lg: z GFF K (6.7) p 94

102 The DC tme lg compenton provded cn be clculted by qn. (6.8) to d n determnng p nd z whle K choen uch tht the DC gn of the controller unty. The phe ngle cn be clculted ung qn. (6.9). tmelg(ec) lm p z (6.8) Im G FF tn Re G (6.9) FF Three led compentor degn re creted, bed on 8 mec dely for. Amp, mec dely for.5 Amp, nd 9 mec dely for chngng pecmen condton. Tble 6. ummrze the controller eplored, dentfed by the controller type nd pecmen condton. Tble 6.. Rel-Tme Actutor Controller Method Specmen Condton Short Nme Propoed Model-Bed Trcng Control Model-Bed Control wth Low-P Flter (Crron nd Spencer, 7) Thrd-Order Polynoml trpolton (Horuch et l., 996) Led Compentor (Zho et l., Jung et l., 7). Amp G FF,.A.5 Amp G FF,.5A Averge / Generl Averge / Generl G FF, vga + LQG G FF, vga. Amp G FF,.A.5 Amp G FF,.5A Averge / Generl + LQG + LP + LP Bumple + LP. Amp rd Poly 8m.5 Amp rd Poly m Averge / Generl rd Poly 9m. Amp Led Comp 8m.5 Amp Led Comp m Averge / Generl Led Comp 9m 6.4 Trcng Performnce n the Frequency Domn To evlute performnce n the frequency domn, the ctutor controller were mplemented n dspac ung mplng rte of 48 Hz. Then, BLWN from to 5 Hz wth dplcement RMS of.54 mm w commnded to epermentlly determne the ervo-hydrulc ytem trnfer functon wth outer-loop control. 95

103 6.4. Contnt Specmen Condton Controller were degned to mtch the pecmen condton, wth reult for the. Amp condton n Fg. 6. nd the.5 Amp condton n Fg Perfect controller performnce would be ndcted by unt mgntude, zero phe, nd zero tme lg. The polynoml etrpolton technque provde good compenton t low-frequence. However, mgntude underhoot found from 5 to 5 Hz, where bove 5 Hz the mgntude begn to ncree drmtclly. Becue of th mplfcton, the ytem w not ected bove Hz for fety. At the me tme, the polynoml etrpolton technque overcompente for the tme lg fter Hz. Th overcompenton cn dd potve dmpng to the RTHS loop, ddng tblty whle compromng ccurcy. After bout 5 Hz, the polynoml etrpolton technque begn to undercompente. The led compentor lo provde good compenton t low-frequence. However, t bout Hz, the mgntude begn to ncree nd the tme lg become undercompented. A ngle pole nd zero pr re not enough to provde dequte compenton over brod frequency rnge, whch cn be problemtc f hgh-frequency repone epected. Mgntude 6 rd Poly 8m Led Comp 8m G FF,.A + LP G FF,.A Frequency (Hz) Phe ( ) Frequency (Hz) Tme Lg (mec) Frequency (Hz) Fgure 6.6. Trnfer functon for vrou control technque wth. Amp n dmper Thee reult demontrte the model-bed pproche to hve gnfcntly better performnce n term of both mgntude nd phe (or tme lg). cellent reult cn be een n mgntude performnce for model-bed pproche up to 5 Hz. In term of phe, the modelbed pproch ung low-p flter h lghtly poorer tme lg compenton, whch due to 96

104 the dynmc of the low-p flter dverely ddng phe lg to the model-bed nvere. The propoed model-bed pproch reduce th lg. Mgntude rd Poly m Led Comp m G FF,.5A + LP G FF,.5A Frequency (Hz) Phe ( ) Frequency (Hz) Tme Lg (mec) Frequency (Hz) 6.4. Fgure 6.7. Trnfer functon for vrou control technque wth.5 Amp n dmper Tme Vryng Specmen Condton Durng RTHS wth em-ctve control, the current to the MR dmper wll be vryng. Therefore, repreenttve em-ctve commnd rngng from. to.5 Amp creted, wth oneecond wndow hown n Fg The meured current n the MR dmper crcut lo preented, llutrtng the lg between commnd nd meured current. Three ctutor control cheme re nvetgted for the em-ctve MR dmper ce, wth the frequency domn reult hown n Fg The feedforwrd controller lone bed on verge pecmen condton provde good control. Addng model-bed feedbc gnfcntly mprove the mgntude repone. Model-bed mult-metrc feedbc, ncludng ccelerton feedbc meurement, further mprove the rnge of ecellent ctutor control n both mgntude nd phe. 97

105 .5 Current (A) Commnd Meured Tme (ec) Fgure 6.8. mple em-ctve current n MR dmper.5 Mgntude Phe ( ).5 G FF,vgA G FF,vgA + LQG G FF,vgA + LQG Frequency (Hz) Frequency (Hz) Tme Lg (mec) Fgure 6.9. Trnfer functon for vrou control technque wth em-ctve condton 6.5 Trcng Performnce n the Tme Domn Frequency (Hz) The controller re lo evluted n the tme domn ung predefned dplcement nd current commnd htory. Two dplcement htore were eplored () BLWN wth bndwdth of to 5 Hz nd n RMS of.78 mm nd (b) BLWN wth bndwdth of to 5 Hz nd n RMS of.595 mm. Durng th dplcement, the current commnd to the MR dmper w ether 98

106 mntned t. Amp (pve-off),.5 Amp (pve-on), or pule between. Amp nd.5 Amp t.5 Hz (5% duty cycle, mmcng em-ctve control condton). Good trcng ndcted by low RMS error (norm) between the dered nd meured gnl clculted by: RMS error (norm) N r y N r % (6.) where r the dered gnl nd y the meured gnl t tme tep. quton (6.) lo ued to clculte velocty nd ccelerton trcng error Dplcement Trcng Reult of the tme domn dplcement trcng tet re preented n Tble 6.. Reult hghlght tht the propoed model-bed control technque provde conderble mprovement n ytem performnce through reducton of the dplcement RMS error for ll pecmen condton. Model-bed feedforwrd controller degned to mtch the pecmen condton performed well whle the model-bed feedforwrd-feedbc controller performed well under ll pecmen condton. Addng mult-metrc feedbc lghtly mprove the trcng performnce of the propoed model-bed controller. Fgure 6. how the tme htory reult for the dplcement trcng tet correpondng to the.5 Amp pule. Both to 5 Hz BLWN nd to 5 Hz BLWN reult re preented for hort wndow wth dentcl clng n both dplcement nd tme. At econd, the current wtched from. Amp to.5 Amp, thu the reult how trnton perod n pecmen condton. Wthout compenton, the effect of the ervo-hydrulc dynmc on mgntude nd phe re pprent. The tme htory reult reflect the obervton mde n the frequency domn tudy. The polynoml etrpolton technque how lght underhoot t thee frequence. At the me tme, the tme lg overcompented, epeclly n the to 5 Hz BLWN ce. The led compentor ehbt conderble overhoot, epeclly n the to 5 Hz BLWN ce. The tme lg lghtly overcompented n the to 5 BLWN Hz ce before econd becue the led compentor degned for verge condton nd the pecmen t. Amp. In the to 5 Hz BLWN ce, the tme lg undercompented becue the effectvene of the led compentor dmnhe t hgh-frequence. Wth the bumple trnfer pproch, the tme lg well compented under chngng pecmen condton however there lght overhoot n mgntude. Wth the propoed model-bed feedforwrd-feedbc controller, ccurte trcng of both mgntude nd phe cheved. Both dplcement nd mult-metrc feedbc controller ehbt mlr performnce. 99

107 Tble 6.. Trcng Performnce for Predefned Dplcement Htore Specmen Condton. Amp.5 Amp.5 Amp Pule Controller RMS rror (%) RMS rror (%) to 5 Hz BLWN to 5 Hz BLWN None rd Poly 8m..8 Led Comp 8m.95. G FF,.A + LP. 4.7 G FF,.A G FF,vgA + LQG.6.89 G FF,vgA + LQG None. 5.7 rd Poly m Led Comp m.4 5. G FF,.5A + LP G FF,.5A G FF,vgA + LQG G FF,vgA + LQG. 4.5 None rd Poly 9m.8 8. Led Comp 9m Bumple + LP G FF,vgA G FF,vgA + LQG G FF,vgA + LQG.87 4.

108 6.5 Dered No Comp Hz BLWN rd Poly 9m Led Comp 9m Bumple + LP G FF,vgA + LQG 5 Hz BLWN. G FF,vgA + LQG Dp (mm) Dp (mm) Tme (ec) Tme (ec) 6.5. Fgure 6.. Dplcement trcng durng pule n current Velocty nd Accelerton Trcng The velocty nd ccelerton trcng performnce of the propoed model-bed controller nvetgted for both dplcement feedbc nd mult-metrc feedbc pproche. Rtedependent devce re entve to hgher-order dervtve, o ccurte trcng of velocte nd ccelerton cn led to more ccurte RTHS reult. Tble 6. how the RMS error between dered nd meured dplcement, velocte, nd ccelerton for to 5 Hz BLWN predefned dplcement. Tble 6.4 how the me quntte for to 5 Hz BLWN predefned dplcement. Dered velocte nd ccelerton re clculted by dfferenttng the dered dplcement. Velocty meurement re clculted by dfferenttng the dplcement meurement whle ccelerton meurement re ten from the ttched ccelerometer. Snce the ccelerton redng enter the DSP unfltered to vod ntroducng tme lg nto the feedbc loop, the ccelerton meurement hve been fltered n pot-proceng ung low-p flter wth cutoff frequency of 5 Hz. The mprovement n dplcement trcng cheved by the dplcement feedbc controller lo dd hgher frequency dynmc whch mnfet degrded velocty nd ccelerton trcng. Through mult-metrc feedbc control, mproved trcng een for dplcement, velocty, nd ccelerton. In both ce, the LQG feedbc controller weghtng were tuned to get good performnce; however dfferent controller weghtng cn led to lghtly better or wore performnce. Fgure 6. preent the tme htory reult for the.5 Amp pule ce, wth the current wtchng from Amp to.5 Amp t econd. The ccelerton pe re hghet wth dplcement feedbc control nd reduced ung mult-metrc feedbc control.

109 Moreover, the noe n the ccelerton redng demontrte the mportnce of ncludng Klmn flter n feedbc control degn. Tble 6.. Trcng Performnce for Hgher-Order Dervtve, to 5 Hz BLWN Specmen Condton. Amp.5 Amp.5 Amp Pule Controller RMS rror (%) to 5 Hz BLWN Dplcement Velocty Accelerton G FF,vgA + LQG G FF,vgA + LQG G FF,vgA + LQG G FF,vgA + LQG G FF,vgA G FF,vgA + LQG G FF,vgA + LQG Tble 6.4. Trcng Performnce for Hgher-Order Dervtve, to 5 Hz BLWN Specmen Condton. Amp.5 Amp.5 Amp Pule Controller RMS rror (%) to 5 Hz BLWN Dplcement Velocty Accelerton G FF,vgA + LQG G FF,vgA + LQG G FF,vgA + LQG G FF,vgA + LQG G FF,vgA G FF,vgA + LQG G FF,vgA + LQG

110 Accelerton (mm/ec ) 5 4 Accelerton (mm/ec ) Hz BLWN Tme (ec) Hz BLWN Tme (ec) G FF,vgA G FF,vgA + LQG G FF,vgA + LQG Dered Fgure 6.. Accelerton trcng durng pule n current 6.6 Prelmnry Rel-Tme Hybrd Smulton Study To llutrte the ctutor controller performnce n cloed-loop RTHS, mple SDOF tructure elected. M, dmpng, nd tffne re multed numerclly whle n MR dmper t. Amp ued the phycl ubtructure. At th level of current, the MR dmper cn obtn ppromtely N retorng force, whch would provde n pproprte level of control (ppromtely % of the m) for, g tructure. Wth the m held contnt, the tffne vred to cheve et of tructure wth nturl frequence rngng from.5 Hz to Hz. Although t not lely tht cvl engneerng tructure wll hve ngle mode t uch hgh frequence, MDOF tructure my poe mode n th rnge or beyond. For ech tructure, the dmpng coeffcent choen to cheve % modl dmpng. ch tructure ected wth BLWN ground ccelerton from to 5 Hz. The RMS vlue of the ground ccelerton were choen 5 mm/ for the.5,, 5, nd Hz tructure nd 5 mm/ for the nd Hz tructure. Thee RMS vlue re choen to provde fe level of ectton whle chevng repone gnfcntly bove the noe floor of the meurement devce. ch tructure teted ung no compenton, the polynoml etrpolton technque, the led compentor, the model-bed feedforwrd controller wth low-p flter, the propoed model-bed feedforwrd controller, the propoed model-bed controller wth dplcement feedbc, nd the propoed model-bed controller wth multmetrc feedbc. Snce the pecmen condton re unchngng, ll controller re degned for. Amp n the MR dmper. Numercl ntegrton performed ung the CDM t Hz.

111 Reult re preented n Fg. 6. wth ech eperment ummrzed by the RMS error between the dered nd meured dplcement. 4 5 RMS rror Dplcement (%) RMS rror Dplcement (%) 5 5 No Comp rd Order Poly 8m Led Comp 8m G FF,.A + LP G FF,.A G FF,.A + LQG G FF,.A + LQG Nturl Frequency of Structure (Hz) Nturl Frequency of Structure (Hz) Fgure 6.. RMS error n dplcement for RTHS of SDOF tructure All rel-tme ctutor control cheme provde mproved trcng when compred to the uncompented ce, ecept for the polynoml etrpolton for the Hz tructure. In th ce, the repone becme mplfed o gretly tht the eperment w unfe to contnue. The polynoml etrpolton nd led compentor re not ccurte n mgntude or phe t hgher frequence, ledng to poor performnce n RTHS. The model-bed feedforwrd controller wth low-p flter wor well, however the dded flter dynmc detrct from controller performnce t hgh frequence. The propoed model-bed feedfowrd controller ehbt the bet reult over wde rnge of frequence. Thu, f tructure ehbt hgher frequency repone, the propoed method would be ble to provde the bet trcng nd vod ntblty. Addng model-bed dplcement or mult-metrc feedbc control further mprove dplcement trcng performnce t lower frequence ( w degned ung the LQG hpng flter). However, nce the pecmen condton re unchngng, the propoed modelbed feedforwrd controller lone perform very well. Loong t the velocty nted (ee Fg. 6.), model-bed pproche provde the bet velocty trcng performnce. Model-bed dplcement feedbc control lghtly detrct from velocty trcng compred to the feedforwrd controller lone, whle mult-metrc feedbc control mprove velocty trcng. A before, velocte re clculted by dfferenttng the dplcement. 4

112 RMS rror Velocty (%) RMS rror Velocty (%) No Comp rd Order Poly 8m Led Comp 8m G FF,.A + LP G FF,.A G FF,.A + LQG G FF,.A + LQG Nturl Frequency of Structure (Hz) Nturl Frequency of Structure (Hz) Fgure 6.. RMS error n velocty for RTHS of SDOF tructure Loong t the ccelerton trcng n Fg. 6.4, the model-bed mult-metrc feedbc controller een to mprove the ccelerton trcng over the entre frequency rnge beyond the feedforwrd controller lone. On the other hnd, dplcement feedbc control degrde ccelerton trcng. Wth mult-metrc feedbc, the blnce between good dplcement nd ccelerton trcng cn be djuted through the LQG controller gn to ut the control objectve. The model-bed feedforwrd controller wth low-p flter perform the bet, however h wore dplcement nd velocty trcng thn the propoed model-bed controller. A before, the ccelerton meurement hve been pot-proceed ung low-p flter wth 5 Hz cutoff frequency. 6 RMS rror Accelerton (%) 5 4 RMS rror Accelerton (%) No Comp rd Order Poly 8m Led Comp 8m G FF,.A + LP G FF,.A G FF,.A + LQG G FF,.A + LQG Nturl Frequency of Structure (Hz) Nturl Frequency of Structure (Hz) Fgure 6.4. RMS error n ccelerton for RTHS of SDOF tructure 5

113 6.7 Rel-Tme Hybrd Smulton of Sem-Actvely Controlled Structure To verfy the model-bed ctutor control trtegy for lrge-cle RTHS, well-reerched nne-tory teel frme benchmr her buldng choen (Ohtor et l., 994). Th tructure w degned to meet emc code nd repreent typcl medum-re buldng n Lo Angele, Clforn. Th tructure h fve by n both the NS nd W drecton. The NS lterl lod ytem cont of two dentcl moment retng frme hown n Fg For th tudy, lner model of one of thee NS moment retng frme ued wth hlf of the totl emc m of the tructure nd ected n the NS drecton. The nturl frequence of the tructure correpondng to the frt fve mode re.44,.8,.5,.9, nd 4.7 Hz, repectvely, wth mmum nturl frequency of 6.6 Hz for the 9 th mode. All mode re umed to hve % dmpng. Fgure 6.5. levton vew of nne-tory tructure (Ohtor et l., 994) Structurl control provded by MR dmper (dded to the tructure for th tudy) umed to eep repone of the tructure n the lner rnge for the erthque nvetgted. In th RTHS, the MR dmper repreented by phycl pecmen, whle the ret of the tructure multed numerclly. The emc m tht ech NS moment frme mut ret g whch equvlent to 44, N. A reonble level of control cn be cheved wth bout % of th force, or 44 N. Becue N MR dmper vlble the phycl pecmen, 8 of thee devce re umed to be ued n conjuncton wth the moment frme to ret lterl lod. MR dmper wth hgher cpcte hve been developed, o t poble to 6

114 reduce the number of dmper n phycl mplementton of th tudy. All 8 devce wll be plced between the ground nd the frt tory. By dong o, the need to tet multple devce elmnted the force from one MR dmper cn be ued to ppromte ll 8. The tructure umed to be equpped wth enor meurng the bolute tory ccelerton n the frt, thrd, ffth, eventh, nd nnth floor, the MR dmper dplcement, nd the MR dmper force. Thee meurement re vlble to the em-ctve controller for ue n determnng the nput current to the MR dmper. Two pve controller re condered n ddton to one em-ctve controller. In the pve controller, the nput current mntned t. or.5 Amp for pve-off nd pve-on, repectvely. The em-ctve control bed on the clpped-optml control lgorthm (Dye et l., 996) wth equl ccelerton weghtng on ll tore pred wth very low weghtng of the MR dmper force. Thee weghtng cheve good em-ctve control reult n multon over wde rnge of erthque record. Reference erthque ground moton from th benchmr tudy re ued throughout th report. Thee nclude: () the NS component of the Imperl Vlley Irrgton Dtrct ubtton n l Centro, Clforn durng the l Centro erthque of My 8 th, 94, (b) the NS component of the Hchnohe Cty record durng the Toch-O erthque of My 6 th, 968, (c) the NS component of the Sylmr County Hoptl prng lot n Sylmr, Clforn durng the Northrdge erthque of Jnury 7 th, 994, nd (d) the NS component of the Jpnee Meteorologcl Agency tton durng the Kobe erthque of Jnury 7 th, 995. The frt econd of ech record re hown n Fg RTHS ued to evlute the repone of the nne-tory tructure ubjected to the NS component of the 94 l Centro erthque wth cle fctor of.5 (PGA.74 g). The numercl model, tructurl control lgorthm, nd rel-tme ctutor control technque re mplemented n Smuln. A mplng rte of Hz found dequte t chevng both numercl ntegrton ccurcy (ung the CDM) nd ccurcy of the ppled velocty to the MR dmper. Reult from the RTHS re preented for the phycl pecmen n pve-off, pve-on nd em-ctve control mode n Fg. 6.7 through Fg Thee fgure how the tme htore of the dplcement nd force of the MR dmper, the nnth-tory ccelerton, well the force-dplcement hytere nd the force-velocty hytere of the MR dmper. Numercl multon reult re lo preented ung the propoed phenomenologcl model of Chpter 4 to repreent the phycl MR dmper. The propoed model-bed ctutor control trtegy for th pplcton (three-pole trnfer functon model wth the CDM nd lner ccelerton etrpolton) requre n etrpolton of the ccelerton followed by predcton of velocty. The RMS error between the etrpolted ccelerton nd the ctul ccelerton one tme tep lter re.%,.%, nd.8% for the pve-off, pve-on, nd em-ctve control ce. The RMS error between the predcted velocty nd ctul velocty one tme tep lter re.9%,.9%, nd.6% for the pve-off, pve-on, nd em-ctve control ce. The low RMS error ndcte tht the etrpolted nd predcted vlue provde ccurte etmte towrd mplementng n mproper nvere. In ll ce, the me model-bed controller ued (.e., feedforwrd controller bed on verge pecmen condton wth feedbc controller). 7

115 Accel (g) Accel (g) Accel (g) Accel (g).4 l Centro Hchnohe Northrdge Kobe Tme (ec) Fgure 6.6. Htorc erthque ground moton The reult for pve-off control re preented n Fg Whle the RMS error.5% wthout compenton nd.8% wth model-bed feedforwrd-feedbc control, the two reult from the RTHS re qute mlr. Th cloe greement due to the fct tht n pve-off control, the retorng force returned to the numercl ubtructure reltvely mll. Thu, even f the retorng force h ome tme lg, t h lttle nfluence on the overll tructurl repone. Alo, the MR dmper nturlly dd ome dmpng to the ytem whch cn counterct the negtve dmpng ncluded by the tme lg. Smulton mtch the RTHS well, ndctng tht the MR dmper model dong good job cpturng the MR dmper nonlnerte nd provdng confdence n the reult. 8

116 Me Dp (mm) Top Story Accel (g) Force (N) Force (N) 4 Sm No Comp G FF,vgA + LQG Tme (ec) 4 4 Dplcement (mm) Velocty (mm/ec) Fgure 6.7. MR Dmper repone ung pve-off control The reult for pve-on control re preented n Fg Unle pve-off control, the RTHS could not be completed n the bence of compenton due to lrge, unfe ocllton n the ervo-hydrulc ctutor. In leu of uncompented reult, reult ung polynoml etrpolton bed on mec dely re preented. The force tme htory how tht for the polynoml etrpolton, ome hgh-frequency ocllton re ntroduced becue of the poor compenton provded t the hgher frequence. Thee ocllton re lo preent n the dplcement tme htory, but much le pprent. Model-bed feedforwrd-feedbc control ehbt ecellent performnce nd doe not ntroduce hgh-frequency ocllton. The RMS error re.% nd.57% for polynoml etrpolton nd model-bed ce, repectvely. The multon mtche the RTHS well, howng tht the MR dmper model lo replcte the phycl MR dmper behvor for pve-on condton. 9

117 Me Dp (mm) Top Story Accel (g) Sm rd Poly m G FF,vgA + LQG Force (N) Force (N) Tme (ec) Dplcement (mm) Velocty (mm/ec) Fgure 6.8. MR Dmper repone ung pve-on control Accurte rel-tme ctutor control crtcl for pve-on control, whch counterntutve, pve-on control ntroduce more dmpng to the ytem thn pve-off control. However, wth the ncree n dmpng lo come n ncree n tffne. At very mll dplcement (e.g. from to 4 econd n Fg. 6.8) the MR dmper behve more le prng, becue the MR flud not yeldng nd the frme undergong eltc deformton. Hgher tffne led to more negtve dmpng n the preence of tme lg (Horuch et l., 996). When the MR dmper trt to move more gnfcntly under the erthque lod, the ddtonl dmpng provded by the MR dmper help to tblze the ocllton. For the me reon, the ocllton do not grow wthout bound. The more the MR dmper ocllte, the more potve dmpng dded to the ytem, tblzng t. However, thee ocllton cn be dmgng to the ervo-hydrulc equpment. Alo f the ocllton occur t lghtly dmped mode or mode gnfcnt to the tructurl repone, the RTHS ccurcy would be reduced. In the fnl tructurl controller eplored, the MR dmper current w llowed to vry ung the em-ctve clpped-optml control cheme, wth reult preented n Fg A wth the pve-on ce, the RTHS qucly becme untble n the bence of compenton. Sem-ctve control wtche the pecmen condton between the etreme very qucly, ddng hgh-frequency dynmc to the tructure. The polynoml etrpolton technque hndle thee

118 ddtonl dynmc poorly, ledng towrd hgh mpltude ocllton n the force, mot pprent n the hytere. On the other hnd, reult re mlr for both the model-bed bumple trnfer controller (Crron nd Spencer, 7) nd propoed model-bed feedforwrd-feedbc controller. Smll ocllton n the force re pprent wth the bumple trnfer controller, whch re lely due to the low-p flter ddng phe lg to the controller t thee frequence. The RMS error re.%,.% nd.79% for polynoml etrpolton, bumple trnfer, nd feedforwrd-feedbc controller, repectvely. Me Dp (mm) Top Story Accel (g) Sm rd Poly 9m Bumple + LP G FF,vg A + LQG Current (A) Force (N) Force (N) Tme (ec) Dplcement (mm) Velocty (mm/ec) Fgure 6.9. MR Dmper repone ung clpped-optml control A wth the other tructurl control ce (pve-off nd pve-on), the numercl multon mtche the RTHS well. The dfference cn be ttrbuted to the dffculty n modelng the behvor of the MR dmper under chngng current, well the em-ctve

119 control ffectng future control effort. Thee chllenge de, the model provde good compron even for the em-ctve ce nd more mportntly, ueful tool for em-ctve controller degn. In regrd to the performnce of the MR dmper em-ctve devce, reducton n top tory ccelerton een when compred to the pve-on ce. The mmum ccelerton drop from.5 g to. g whle the RMS ccelerton drop from.5 g to.45 g. At the me tme, the mmum control force decree from 6 N to 8 N. Sem-ctve control een to be n effectve men to blnce good dplcement nd ccelerton performnce (of the tructure) under wde rnge of nput lod. To further nvetgte the propoed model-bed controller, the em-ctve ce repeted for feedforwrd control lone, feedforwrd wth dplcement feedbc control, nd feedforwrd wth mult-metrc feedbc control. The reult re hown n Fg. 6.. Me Dp (mm) Top Story Accel (g) Force (N) Force (N) G FF,vg A G FF,vg A + LQG G FF,vg A + LQG Current (A) Dplcement (mm) Tme (ec) Velocty (mm/ec) Fgure 6.. Compron of feedbc controller durng RTHS

120 The RMS error n dplcement re.54%,.44%, nd.4% for ech controller, repectvely. Feedbc control lghtly mprove the trcng performnce; however, nce the feedforwrd controller lone provde ecellent control for th tructure, the overll reult re very mlr. The RTHS conducted w n epeclly chllengng ce for ctutor control. Th dffculty re from the fct tht the buldng lghtly dmped t hgh frequence nd the CDM dd no numercl dmpng. Lght dmpng brng the tructure cloer to ntblty when coupled ndequtely compented tme dely nd tme lg. At the me tme, ngle phycl MR dmper ued to repreent 8 devce. Any meurement noe n the dmper mplfed nd completely correlted. Alo, the hrmful effect of tme dely nd tme lg, uch negtve dmpng, re concentrted n one locton nd mplfed. In pte of thee chllenge, modelbed ctutor control provded ecellent reult n RTHS. Alo, note tht the repone of the overll tructure do not chnge much wth the compenton method eplored. The mot gnfcnt effect re locl to the MR dmper, nmely tblty of the phycl eperment nd undered ocllton t floor connected to the MR dmper. However, thee hgher frequency ocllton re not gnfcnt to the overll repone of the tructure (n th ce) nd do not trvel fr from the ource. It worth mentonng tht f the MR dmper plcement were dfferent, the lod cell meurement noe nd ny detblzng negtve dmpng would enter dfferent tore of the tructure nd thu ffect dfference mode. 6.8 Summry A frmewor for RTHS h been developed t the Unverty of Illno, ncludng tte-of-thert oftwre nd hrdwre. The dynmc chrcterzton how tht the ytem cpble of ft lodng rte requred for RTHS. The ccurcy of ctutor control, crtcl to RTHS, mproved wth the propoed model-bed controller. Wth predefned dplcement, reult howed ner perfect trcng of the dered dplcement gnl. Mult-metrc feedbc control w demontrted men to blnce good dplcement, velocty, nd ccelerton trcng. In RTHS, the propoed model-bed controller w proven ucceful for tetng SDOF tructure n prmetrc tudy nd lghtly dmped MDOF tructure, both ung N MR dmper the phycl ubtructure. In the SDOF tet, the propoed model-bed controller provded the bet trcng mong the method condered, epeclly when the nturl frequency of the tructure eceeded 5 Hz. In the MDOF tet, the current n the MR dmper w llowed to vry under em-ctve control. ven under thee chngng pecmen condton, the propoed modelbed controller howed ecellent performnce. Numercl multon reult compre well to RTHS, provng confdence n RTHS reult.

121 MULTI-ACTUATOR CONTROL 4 Chpter 7 The propoed model-bed ctutor control trtegy fleble to ccommodte mult-ctutor ytem. However, few epermentl fclte re cpble of mult-ctutor RTHS. For th reon, focu frt plced on cretng multed RTHS bed on well-reerched three-tory tructure. The multed RTHS h ll of the component hown n Fg. 5., ncludng the dynmc of the ervo-hydrulc ytem. The mult-ctutor control trtegy ubequently verfed for lrge-cle three-tory teel frme pecmen, whch prt of lrger project on performnce bed degn ung em-ctve control devce. For the tudy on mult-ctutor control, feedbc pproche re retrcted to dplcement-bed feedbc controller for mplcty. 7. Mult-Actutor Nonlner Numercl Study To demontrte the performnce of the propoed model-bed mult-ctutor control trtegy, three-tory em-ctvely controlled buldng condered. For mplcty, ll DOF wll be elected nterfce DOF (hvng both numercl nd epermentl component). The epermentl component elected the mll-cle three-tory buldng model from multple tude on ctve nd em-ctve control (Dye et l., 995; Dye et l., 996). The mplfed model prmeter, reported from ytem dentfcton, re gven by: M 98. N mm (7.) C 5 5 N mm (7.) K N mm (7.) The correpondng nturl frequence re 5.46, 5.8, nd.6 Hz, wth dmpng rto of.,.6, nd.6%. A numercl component dded wth m mtr equl to 9 tme the m mtr of qn. (7.), brngng the nturl frequence of the totl tructure (combnng numercl nd epermentl component) to.7, 5., nd 7.48 Hz. Rylegh dmpng dded to the totl tructure to crete dmpng rto of.,., nd.57%. The ddtonl dmpng

122 requred to cheve thee dmpng rto dded numerclly. Fnlly, mll-cle MR dmper dded between the ground nd frt tory of the tructure. Th MR dmper condered prt of the epermentl component nd modeled ung the phenomenologcl model nd prmeter propoed by Spencer et l. (997). The MR dmper h mmum force of ppromtely.5 N, whch bout 5% of the emc m of the totl tructure. The numercl nd epermentl component re llutrted n Fg. 7.. Actutor I Actutor I Actutor I MR Dmper g permentl Component Numercl Component Fgure 7.. Three-tory nonlner tructure Servo-hydrulc ctutor re connected to ech of the three floor of the epermentl tructure to enforce comptblty wth the numercl component nd provde retorng force feedbc from the lod cell. The ervo-hydrulc ytem prmeter for ll three ctutor re bed on the mll-cle ctutor model of Dye et l. (995). Thee prmeter re p 66.7 rd ec, 5. A, nd 8./ A. From the orgnl prmeter, h been multpled by nd dvded by to cle the ctutor model pproprtely for the confgurton of Fg. 7.. The epermentl component umed to be equpped wth enor meurng the ctutor dplcement, the ctutor retorng force, the bolute tory ccelerton, the MR dmper dplcement, nd the MR dmper retorng force. Meurement noe multed wth to Hz BLWN wth RMS vlue of 8 mm/ for ccelerton,.54 mm for dplcement, nd.5 N for force. Thee vlue re choen by emnng the noe floor for pproprte enor found n the Smrt Structure Technology Lbortory t the Unverty of Illno. The bolute tory ccelerton, the MR dmper dplcement, nd the MR dmper force re vlble to em-ctve controller for ue n determnng the nput voltge to the MR dmper. A em-ctve controller creted bed on clpped-optml control lgorthm nd controller weghtng from Dye et l. (996). The component of the numerclly multed RTHS re preented n the Smuln bloc dgrm of Fg

123 rthque Ground Accel ' = A+Bu y = C+Du Numercl Component,d,dd u Model -Bed Actutor Control u f,d,dd Actutor Dynmc ' = A+Bu y = C+Du permentl Subtructure (Lner Porton ) ddg,d,dd V f Sem -Actve Controller,d,dd f V MR Dmper 7.. Fgure 7.. Smuln dgrm of multed RTHS MIMO Sytem Identfcton nd Controller Degn In the lely ce tht the prmeter of the pecmen nd ervo-hydrulc ytem re unnown, nonprmetrc ytem dentfcton cn be ued to obtn the ervo-hydrulc ytem trnfer functon model (Km et l., 5). A ndcted prevouly, the ervo-hydrulc ytem trnfer functon model of the MIMO ytem h mny pole nd zero to ft, where the nvere h reltvely few pole nd zero to ft. The mplcty of the nvere the b for the propoed ytem dentfcton method for model-bed mult-ctutor control. Step : Determne the epermentl MIMO trnfer functon. The frt tep to conduct ytem dentfcton on coupled ctutor ytem ttched to pecmen. One ctutor hould ecte the pecmen wth BLWN (over the frequency rnge of nteret) nd the repone be meured t ll ctutor. The proce hould be repeted for ech ctutor; the MIMO trnfer functon wll thu be bult one nput t tme. Durng ech tet, the unected ctutor hould ether be held t zero dplcement or gven very low-mpltude BLWN to overcome ttc frcton force whch cn dd dmpng to the ytem (Chng, ). In the ce when uercontrollble devce ttched to the pecmen, uch n MR dmper, the devce hould be ctng t would durng RTHS to crete the mot ccurte lnerzed model for RTHS. Step : MIMO trnfer functon nveron. At th tep, the epermentl MIMO trnfer functon hould be nverted. The operton wll be mtr nveron t ech frequency. Step : Fttng the nvere. Net, ech nput-output pr of the nvere MIMO trnfer functon hould be ft wth SISO trnfer functon model. The SISO trnfer functon model cn then be combned to crete n nvere MIMO trnfer functon model, whch cn be ued the feedforwrd controller. Inght from qn. (5.76) cn d n the model fttng. Step 4: Cretng the ervo-hydrulc ytem trnfer functon model. The nvere of the nvere MIMO trnfer functon model wll be equl to the ervo-hydrulc ytem trnfer functon model. Th model, n tte-pce form, cn be ued for feedbc control degn. Note tht when MIMO trnfer functon model converted nto tte-pce model, t wll not necerly be mnml relzton. A mnml tte-pce relzton contn the mnml number of tte necery to repreent the ytem dynmc. Such relzton lo necerly both controllble nd obervble. ffort hould be mde to crete mnml relzton; method for cretng mnml relzton re dcued n Chng (). quton (5.8) demontrte tht mnml relzton poble, whereby there re no duplcte or unnecery tte nd ll of the tte re controllble through the ctutor well obervble ung lod cell nd dplcement trnducer. 6

124 The four tep bove re llutrted n Fg. 7. nd Fg. 7.4 for the epermentl component of Fg. 7. ncludng the modeled ctutor dynmc. ch ctutor ected one t tme ung to 5 Hz BLWN for totl of three dt et. Durng th ectton, the other ctutor re held t zero dplcement (nce the phenomenon of ttc frcton not ncluded n the numercl ctutor model). Alo, the mll-cle MR dmper model rndomly wtched from. to. Amp (. V to.5 V) to multe em-ctve condton durng RTHS. The ftted feedforwrd model contn three zero n ech of the dgonl, one zero n ech of the mmedte off-dgonl, nd no dynmc for the etreme off-dgonl. The reultng ervohydrulc ytem model contn zero nd nne pole n ech of the dgonl, four zero nd nne pole n ech of the mmedte off-dgonl, nd two zero nd nne pole n the etreme off-dgonl. Fgure 7. nd Fg. 7.4 llutrte the ccurcy of the model compred to the numerclly multed dt. In the fgure, column one through three correpond to nput to ctutor one through three whle row one through three correpond to output from ctutor one through three. Model-bed control developed ung the nvere model nd ytem model for the feedforwrd nd feedbc controller, repectvely : TF Dt : Inv TF Dt : Inv Model 4: Model.. Mgntude Frequency (Hz) Fgure 7.. MIMO trnfer functon mgntude of the DOF epermentl ubtructure 7

125 : TF Dt : Inv TF Dt : Inv Model 4: Model Phe ( ) Frequency (Hz) Fgure 7.4. MIMO trnfer functon phe of the DOF epermentl ubtructure RTHS of MDOF Structure RTHS ued to evlute the repone of the three-tory nonlner tructure employng emctve control ubjected to.5 the NS component of the 94 l Centro erthque. The multon run t Hz ung the fourth-order Runge-Kutt cheme for numercl ntegrton. Both the numercl nd epermentl component re multed numerclly ung MATLAB Smuln envronment wth the effect of ctutor dynmc ncluded ( n Fg. 5. nd Fg. 7.). Smulted meurement noe ncluded n ll feedbc loop (e.g., retorng force of epermentl component, meured dplcement for model-bed feedbc control, nd nput for the em-ctve controller) wth vlue prevouly mentoned. Th noe not ncluded n the mpled meurement ued for pot-proceng, equvlent to perfect flterng of the noe. S ce re condered to evlute the tructurl repone: () delzed multon (.e., no ctutor dynmc, ubtructurng, or meurement noe), (b) RTHS wth ctutor dynmc nd no compenton, (c) RTHS wth ctutor dynmc nd model-bed feedforwrd control neglectng ctutor couplng, (d) RTHS wth ctutor dynmc nd model-bed feedforwrd control conderng ctutor couplng, (e) RTHS wth ctutor dynmc nd model-bed feedforwrd-feedbc control neglectng ctutor couplng, nd (f) RTHS wth ctutor dynmc nd model-bed feedforwrd-feedbc control conderng ctutor couplng. The multon ce () condered the correct reult from whch compron of RTHS ce (b) through (f) wll be mde. For ce (b), the RTHS mmedtely went untble, llutrtng the need for ctutor control n the preence of ctutor dynmc. A repreenttve 8

126 ce, (f) preented longde ce () n Fg. 7.5 for dplcement nd bolute ccelerton of the frt tory, well MR dmper hytere loop. cellent correlton between the two ce oberved for ll quntte. Dp (mm) Ab Accel (g) Current (A) Force (N) () Smulton (f) FF + FB w/ Couplng Tme (ec) Dplcement (mm) Fgure 7.5. Frt tory tme htore nd MR dmper hytere Grphclly dtnguhng ce (c) through (f) dffcult. Therefore, RMS error wll be ued quntttve meure of ctutor controller performnce: Velocty (mm/ec) RMS error N N r y y % (7.4) where the tme tep of numercl ntegrton performed over N tep. Compron re mde for ce (c) through (f) n Tble 7. for both trcng error nd repone error. To clculte I trcng error from qn. (7.4), r nd y (from the me ce t the me tory). Trcng error llutrte how well the ctutor controller perform phyclly trcng the dered dplcement. To clculte repone error from qn. (7.4), r the repone quntty from ce () nd y the repone quntty from the other ce (t the me tory). Repone quntty error llutrte how much the RTHS oluton dvergng from the del multon 9

127 oluton. Wth em-ctve control, where future control effort depend on pt repone, oluton cn dverge qucly due to mll dfference. Tble 7.. RMS rror of Trcng nd Repone for Actutor Control Strtege Actutor Control Strtegy Trcng rror (%) Repone rror (%) e e e I I I I I (c) FF w/o Couplng (d) FF w/ Couplng (e) FF + FB w/o Couplng (f) FF + FB w/ Couplng I In th tudy, the effect of ctutor couplng nvetgted long wth the beneft of feedbc control. In ce when ctutor couplng neglected (.e., gnorng off-dgonl term of qn. (5.76) nd (5.75) for feedforwrd nd feedbc controller degn, repectvely), pprecble trcng error found, ledng to lrge repone error. On the other hnd, conderng ctutor couplng when degnng mult-ctutor control mprove the ccurcy of the RTHS meured by both trcng error nd repone error. A the mount of ctutor couplng ncree, for emple due to tffer pecmen reltve to the ctutor cpcty, the beneft of conderng the couplng for control degn wll lo ncree. In ll ce, feedbc control mprove the ccurcy of the RTHS compred to feedfowrd control lone. Becue the feedforwrd controller bed on lner model of the ervo-hydrulc ytem, the feedbc controller wll dd robutne to chngng pecmen condton, modelng error, nd nonlnerte (ll of whch re preent n th numercl tudy). 7. Lrge-Scle Mult-Actutor permentl Frmewor An ongong tudy on performnce bed degn ung em-ctve control wll be leverged to evlute the propoed model-bed ctutor control trtegy for RTHS on phycl pecmen. Advnced energy dpton devce uch MR dmper hve gret potentl towrd mtgtng dmge prt of emc retnce ytem. However, lc of procedure pproprte for ncorportng MR dmper n degn lmt ther cceptnce nd ue n cvl nfrtructure. At the me tme, lrge-cle epermentl verfcton requred to confrm the performnce tructure degned wth MR dmper. Tetng of lterl lod retng ytem wth MR dmper requre rel-tme epermentl evluton, nturlly lendng telf to RTHS. A three-tory prototype buldng h been degned ung performnce bed degn ncorportng MR dmper n the lterl lod retng ytem (Dong, ; ee Fg. 7.6). To evlute the degn nd em-ctve control lgorthm, moment retng frme (MRF) nd dmped brced frme (DBF) wll be phyclly contructed, repreentng the lterl ytem for qurter of the totl trbutry emc re n one drecton. The remnng component wthn the trbutry emc re, nmely the emc m, re multed numerclly len-on column.

128 Fgure 7.6. Prototype tructure for RTHS 7.. qupment An epermentl frmewor for lrge-cle RTHS h been developed t the Rel-Tme Mult- Drectonl (RTMD) tetng fclty t Lehgh Unverty. ch floor of frme ected by ervo-hydrulc ctutor mnufctured by Servotet Sytem Ltd.; the frt tory ue model --7 wth N (5 p) cpcty nd ±5 mm (±9.7 n) troe whle the econd nd thrd tory ue model --5 wth 7 N (8 p) cpcty nd ±5 mm (±9.7 n) troe. The ctutor contn hydrottc berng to reduce frcton nd re confgurble to upport one to three ervo-vlve. ch ctutor powered by two three-tge model SV ervo-vlve mnufctured by Servotet Sytem Ltd. The ervo-vlve hve mmum ndvdul flow rte of 8 lpm (55 gpm), model G77-4 Moog plot vlue, nd ther own model B55-4 hydrulc ervce mnfold mnufctured by Servotet Sytem Ltd. The hydrulc ol upply cont of fve 45 lpm (9 gpm) pump nd 6 ccumultor wth 9 lter (5. gllon) cpcty connected to 9 Ntrogen g bottle of 5 lter (85 gllon) cpcty mnufctured by Prer Hnnfn Corporton. The ctutor re controlled n dplcement feedbc mode by model DCS dgtl ervo-controller mnufctured by Servotet Sytem Ltd. The controller run wth cloc peed of 4 Hz nd h 6-bt reoluton on the A/D nd D/A crd. The ervo-controller cont of DSP rel-tme control crd (Module ) connected to computer dentfed RTMDctrl. The numercl component of the RTHS, outer-loop ctutor control, nd em-ctve control lgorthm re progrmed n MATLAB Smuln progrmmng lnguge on computer dentfed RTMDm. The Smuln fle compled nd downloded to n PC computer tht run Mthwor rel-tme Trget PC oftwre (dentfed RTMDPC). The RTHS controlled by the uer on the RTMDm computer through n RTMDPC module. RTMDPC communcte wth RTMDctrl n rel-tme (t 4 Hz) over SCRAMNet whch propretry hred memory bu tht erve the underlyng communcton mechnm between RTMD module. Dt collected ung DAS 6 DAQ ytem mnufctured by Pcfc Intrument Inc., opertng RTMDdq.

129 7.. Specmen For mult-ctutor control proof-of-concept tudy, mplfed lner DOF model creted to cpture the dynmc of the MRF, DBF, nd len-on column. The nturl frequence of th mplfed model re.7, 4.4, nd 8.8 Hz wth umed modl dmpng of %, 6%, nd 6%, repectvely. The correpondng m, dmpng, nd tffne mtrce re:. M. N m (7.5) C N m (7.6) K N m (7.7) The DBF h been contructed frt nd wll be ten the epermentl ubtructure whle the remnng component (moment retng frme nd len-on column) wll be multed numerclly. A chemtc of the DBF wth member ze hown n Fg The DBF cpble of houng one MR dmper t ech tory; however for th tudy only one MR dmper ntlled t the brcng of the frt tory. The MR dmper pecmen n dentcl model to the lrge-cle N MR dmper dentfed n Chpter 4 nd ued n the ngle-ctutor tudy of Chpter 6. The DBF contructed wthn n outer upport frme degned to prevent out of plne deformton (ee Fg. 7.8). Hydrulc ctutor re connected to ech of the tore ung lodng bem wth multple connecton to dtrbute the ppled force cro the entre floor. The MR dmper cn be een ntlled n the frt tory brcng. The m, dmpng, nd tffne mtrce of the DBF wll be etmted nd ubtrcted from the totl ytem to determne the remnng component to be multed numerclly n RTHS. The m of the DBF, ncludng lodng bem nd other fturng, clculted nd lumped t ech of the tore..47 M.47 N m (7.8).47

130 Fgure 7.7. Three-tory DBF wth MR dmper

131 The ttc tffne mtr determned epermentlly ung the ttched hydrulc ctutor nd lod cell K N m (7.9) Fnlly, dmpng mtr elected to mtch the trnent reult of prelmnry dynmc tetng C N m (7.) Fgure 7.8. Three-tory DBF wthn tet frme 4

132 7.. Sytem Identfcton nd Model-Bed Control Sytem dentfcton performed on the mult-ctutor ytem ung to 5 Hz BLWN. ch ctutor ected one t tme, cretng three SIMO ytem tht re embled nto MIMO trnfer functon mtr. The ctutor re ected to mmum fe rnge, whch determned to be.8 mm,.6 mm, nd.7 mm RMS n the frt, econd, nd thrd ctutor, repectvely. Durng ytem dentfcton, the current to the MR dmper wtched from. to.5 Amp, cretng lnerzed model for em-ctve condton. The MIMO trnfer functon nd t nvere re preented for mgntude n Fg. 7.9 nd for phe n Fg. 7.. Sytem dentfcton performed ung the me pproch the MIMO numercl emple. The nvere model contn three zero n ech of the dgonl nd one zero n ech of the off-dgonl. The feedforwrd controller ten the nvere model. The ytem model contn nne pole n ech entry, zero n the dgonl, nd four zero n the off-dgonl. The feedbc controller degned bed on the ytem model. Model-bed controller re creted tht both conder ctutor couplng (.e., ncludng the off-dgonl term) nd neglect ctutor couplng (.e., gnorng the off-dgonl term) TF Dt Inv TF Dt Inv Model Model Mgntude Frequency (Hz).. Fgure 7.9. MIMO trnfer functon mgntude of the DBF 5

133 TF Dt Inv TF Dt Inv Model Model Phe ( ) Frequency (Hz) 7..4 Fgure 7.. MIMO trnfer functon phe of the DBF Trcng Performnce The trcng performnce of the propoed model-bed mult-ctutor controller evluted by multneouly ectng ech ctutor wth to 5 Hz BLWN wth n RMS of mm. The low RMS vlue choen to vod dmge to the frme n the preence of ynchronou ctutor moton. The trcng performnce wthout compenton well for the propoed modelbed feedforwrd-feedbc pproch wth ctutor couplng hown n Fg. 7.. The frt, econd, nd thrd tory ctutor re condered ctutor one, two, nd three, repectvely. In ll trcng eerce, the current commnd predefned, vryng t would durng em-ctve control. The propoed controller perform very well, mtchng lmot ectly wth the dered dplcement gnl n ech ctutor. The trcng eerce repeted for to 5 Hz BLWN n ech ctutor wth n RMS of.5 mm. Reult re preented wthout compenton well for the propoed model-bed feedforwrd-feedbc pproch wth ctutor couplng n Fg. 7.. The controller h more dffculty trcng the hgher frequency gnl, but tll perform well n both mgntude nd phe. The trcng eerce re repeted for multple controller degn, wth ummry of the RMS error n Tble 7.. From Tble 7., the model-bed feedforwrd-feedbc control conderng ctutor couplng cheve the bet trcng performnce; however the beneft re not notceble n the numercl multon tudy. In numercl multon, even for low level of ctutor couplng, mprovement cn clerly be een when conderng ctutor couplng n controller degn. However, t low level of ctutor couplng n the preence of epermentl error, the beneft re reduced. 6

134 Dp (mm) dered No Comp FF + FB w/ Couplng Dp (mm) Dp (mm) Current (A) Tme (ec) Fgure 7.. Dplcement trcng of to 5 Hz BLWN Tble 7.. Dplcement Trcng Performnce for Predefned Dplcement Actutor Control Strtegy RMS Trcng rror (%) to 5 Hz BLWN to 5 Hz BLWN Dp Dp Dp Dp Dp Dp No Compenton FF w/o Couplng FF w/ Couplng FF + FB w/o Couplng FF + FB w/ Couplng

135 Dp (mm) dered No Comp FF + FB w/ Couplng Dp (mm) Dp (mm) Current (A) Tme (ec) Fgure 7.. Dplcement trcng of to 5 Hz BLWN The trcng performnce of the ctutor controller re further nvetgted for ctutor moton more repreenttve of RTHS. Wth the propoed lrge-cle phenomenologcl model of Chpter 4 repreentng the MR dmper, the repone of the totl tructure multed n RTHS offlne. For th multed RTHS, the tructure ected ung the NS component of the Hchnohe Cty record of the 968 Toch-O erthque (ee Fg. 6.6) wth cle fctor of.5 (PGA.57 g). The dplcement determned from numercl multon re mpoed on DBF predefned nput. For MR dmper control, em-ctve control lgorthm degned bed on the clpped-optml control lgorthm (Dye et l., 996) ued wth ccelerton weghtng on the top tory nd low weghtng on the MR dmper force. The MR dmper current commnd from multon ent to the phycl MR dmper durng the trcng eerce. Trcng of the predefned dplcement re hown n Fg. 7.. Trcng reult for multple controller re preented n Tble 7.. In the prevou trcng eerce, the ctutor moton re ynchronou. In th ce, the ctutor move together, motly n the frt mode of the tructure. Thu, the ctutor re not fghtng ech other much nd the beneft of conderng couplng re further reduced. However, the trcng performnce overll ecellent nd contently mproved by ddng model-bed feedbc control. 8

136 7..5 Dp (mm) Dp (mm) Dp (mm) Current (A) Fgure 7.. Dplcement trcng of predefned RTHS reult Tble 7.. Dplcement Trcng Performnce for Predefned RTHS Actutor Control Strtegy RMS Trcng rror (%) Dp Dp Dp No Compenton FF w/o Couplng FF w/ Couplng FF + FB w/o Couplng FF + FB w/ Couplng Rel-Tme Hybrd Smulton RTHS choen to evlute the dynmc performnce of the DBF under emc lodng. For proof-of-concept tudy on ctutor control, the DBF lone ten the epermentl ubtructure whle the ret of the tructure multed numerclly. Numercl ntegrton performed ung the CDM t 4 Hz. The em-ctve control cheme decrbed for the predefned RTHS trcng tudy gn ued for RTHS. For compron, numercl multon 9 dered No Comp FF + FB w/ Couplng Tme (ec)

137 of the RTHS performed ung the totl tructure long wth the phenomenologcl model of the MR dmper. The tructure ected ung the NS component of the 94 l Centro erthque wth cle fctor of. (PGA.7 g). The ectton choen to vod yeldng the DBF uch tht multple tet could be fely conducted. Although the DBF remn nomnlly lner, nonlnerty ntroduced to the tructure through the MR dmper. Reult re preented for the ctutor dplcement, MR dmper current commnd, MR dmper force-dplcement hytere nd MR dmper force-velocty hytere n Fg. 7.4 ung the model-bed feedforwrd-feedbc controller wth ctutor couplng. The RTHS reult compre very well wth multon lthough further mprovement epected wth more rgorou numercl model of the DBF ncludng modelng of the brcng to whch the MR dmper ttched. Dp (mm) Dp (mm) Dp (mm) Force (N) 5 Sm FF + FB w/ Couplng Tme (ec) Current (A) Dplcement (mm) Velocty (mm/) Fgure 7.4. RTHS of prototype tructure for l Centro

138 The trcng performnce for multple controller n RTHS re preented n Tble 7.4. Overll the controller perform very well, chevng comprble reult wth the numercl model. Model-bed feedbc control een to mprove the trcng performnce beyond feedforwrd control lone, whle conderng ctutor couplng h lmted beneft n th ce. Note tht unle predefned dplcement, RTHS not performed n the bence of outer-loop ctutor control to vod ntblte. Tble 7.4. Dplcement Trcng Performnce durng RTHS for l Centro Actutor Control Strtegy RMS Trcng rror (%) Dp Dp Dp FF w/o Couplng FF + FB w/o Couplng FF w/ Couplng.54.. FF + FB w/ Couplng The tructure lo evluted for the NS component of the 994 Northrdge erthque (ee Fg. 6.6) wth cle fctor of. (PGA. g). Reult ung the model-bed feedforwrd-feedbc controller wth ctutor couplng re preented n Fg Agn, the reult compre very well to numercl multon. The trcng performnce of multple controller re preented n Tble 7.5. A wth the prevou erthque record, lttle beneft een conderng ctutor couplng whle the feedbc controller doe mprove trcng control n mot ce. Mot mportntly ecellent trcng cheved wth the propoed model-bed controller, ledng to ccurte nd tble reult. Tble 7.5. Dplcement Trcng Performnce durng RTHS for Northrdge Actutor Control Strtegy RMS Trcng rror (%) Dp Dp Dp FF w/o Couplng FF + FB w/o Couplng FF w/ Couplng FF + FB w/ Couplng.4..7

139 Dp (mm) Dp (mm) Dp (mm) Force (N) Current (A) 5 5 Sm FF + FB w/ Couplng Tme (ec) Dplcement (mm) Velocty (mm/) 7. Summry Fgure 7.5. RTHS of prototype tructure for Northrdge A frmewor for model-bed mult-ctutor control ncludng both model-bed feedforwrd nd feedbc ln h been developed to drectly ddre ctutor dynmc ncludng ctutor couplng. A mple pproch to dentfyng the ervo-hydrulc trnfer functon model nd t nvere for degnng model-bed multple-ctutor controller w outlned. The controller performed very well durng the multed RTHS of three-tory nonlner tructure. Through th emple, the beneft of conderng ctutor couplng were demontrted. Feedbc control w hown to further mprove the performnce of the feedforwrd controller n the preence of the nonlner MR dmper devce. The propoed model-bed mult-ctutor controller w then ppled to three-tory teel frme the epermentl ubtructure. cellent control w demontrted, lthough the low level of ctutor couplng long wth epermentl error led to

140 lmted beneft of ncludng the couplng n controller degn. More mportntly, the RTHS reult compred very well to numercl multon, demontrtng n ccurte nd tble frmewor for mult-ctutor RTHS. Numercl multon reult could further be mproved by modelng the brcng to whch the MR dmper ttched, nce there my be conderble dfference between the frt tory dplcement nd MR dmper dplcement for hgher level of MR dmper retorng force (due to deformton n the brcng).

141 ACTUATOR CONTROL FOR SHAK TABLS Chpter 8 She tble provde drect men by whch to evlute tructurl performnce under erthque ectton. entlly, be plte ected by n ctutor to replcte htorc or nlytclly generted ground ccelerton. Becue the entre tructure mounted on the be plte nd ubjected to the ground moton n rel-tme, dynmc effect nd rte-dependent behvor cn be repreented. The pylod (ncludng tble m) typclly lrge reltve to the cpcty of the ctutor, ledng to pronounced control-tructure ntercton. Through th ntercton, the dynmc of the pecmen nfluence the dynmc of the he tble, whch cn be problemtc when pecmen chnge behvor due to dmge or other nonlnerte. Moreover, he tble re nherently nonlner, mng t dffcult to ccurtely recrete dered ccelerton record ccurtely over brod frequency rnge. The propoed model-bed mult-metrc feedbc control trtegy wll be dpted to mprove trcng of the dered ccelerton, remnng robut to nonlnerte ncludng chnge n pecmen condton. The propoed trtegy verfed for the he tble tetng of both lner nd nonlner pecmen. She tble control not trghtforwrd the dered gnl n ccelerton record. Snce ccelerton meurement (.e. from ccelerometer) cnnot cpture contnt velocte or contnt dplcement, ccelerton feedbc lone cnnot provde tble control of he tble. For tblty, even n he tble pplcton where the dered record to be reproduced n ccelerton, ctutor operte n dplcement feedbc through n nner-loop PID controller. To enure tblty of the he tble when pplyng model-bed control to he tble tetng, the nner-loop dplcement feedbc control wll not be modfed. Rther, n outer-loop controller wth model-bed feedforwrd nd feedbc ln propoed to mprove ccelerton trcng on the tble nner-loop ytem. 8. Model-Bed Control for She Tble Tetng Model-bed control provde promng lterntve for he tble tetng; however, t requre modfcton from RTHS pplcton. Mot notbly, the gnl tht the controller hould trc n ccelerton gnl, nontrvl t for dplcement feedbc ytem. To ure ccurte ccelerton trcng, n ccelerometer ttched to the tble for both ytem dentfcton nd ctutor control. In th ecton, frt feedforwrd controller wll be developed for ccelerton trcng followed by pproche for ccelerton, dplcement, nd mult-metrc feedbc control. 8.. Feedforwrd Control To develop model of the he tble for feedforwrd control, the reltonhp from the nput commnd voltge u to the meured output ccelerton m emned, repreented by the trnfer functon model: 4

142 A G u (8.) U The feedforwrd controller, degned to cncel the dynmc of the he tble, elected the nvere of the he tble model: G u The feedforwrd controller provde the del control effort bout whch regultor redegn performed, decrbed ubequently for dfferent vlble feedbc meurement. An ccurte model of the he tble n qn. (8.), whch te dplcement bed commnd to n ccelerton meurement, wll cont of two zero t the orgn. Thu, pure nvere n qn. (8.) wll hve two pole t the orgn, whch cn led to low-frequency drft n the feedforwrd commnd. To vod uch drft, the reference ccelerton record hould be ped through hgh-p flter to unobtruvely remove very low-frequency behvor from the reference record. The fltered ccelerton gnl hould be compred wth the reference ccelerton pror to tetng to enure tht they mtch well. Moreover, the feedforwrd control effort cn be clculted completely offlne, llowng for lot of fleblty ncludng zero-phe dgtl flterng of the reference ccelerton nd the mplementton of mproper model nvere. 8.. Accelerton Feedbc Control Accelerton feedbc bed on the he tble model of qn. (8.). A tte-pce repreentton of qn. (8.) gven by: U A (8.) z Az Bu (8.) Cz (8.4) m A wth ctutor control for RTHS, regultor redegn cn be ued to crete model-bed feedforwrd-feedbc controller to mnmze the ccelerton trcng error gven by: e d m (8.5) where the dered ccelerton gven by d. For regultor redegn, the devton ytem output re: ~ (8.6) m The dynmc of the ugmented devton ytem ncludng the proce noe (wth hpng flter) nd ccelerton meurement noe re then: d z A z B u w (8.7) FB f 5

143 ~ C z v (8.8) The LQR control degn bed on ccelerton output weghtng wth the followng cot functon (ung the certnty equvlence property): Q LQR RLQRu FB f J ~ dt (8.9) LQR The Klmn flter cn be degned fter electng proce nd meurement noe covrnce. The totl combned feedbc controller wll hve the dynmc: A L C B K zˆ L ~ z ˆ (8.) Kl Accelerton feedbc control lone untble due to unobervble nd thu uncontrollble pole t the orgn. However, the nner-loop dplcement bed ervo-controller provde tblty to the he tble. A wth RTHS pplcton, the LQG controller proce noe hped by econd-order flter to ttenute the control effort t frequence beyond the regon of dered trcng performnce. The combned feedforwrd controller wth ccelerton feedbc preented n Fg. 8.. LQR Kl Offlne Onlne d G u u FF Feedforwrd Controller + e LQG Feedbc Controller u FB + + u G u She Tble Dynmc m 8.. Fgure 8.. Model-bed ccelerton feedbc control Dplcement Feedbc Control Alterntvely, the feedbc controller could be degned bed on dplcement meurement. A dplcement bed feedbc controller would requre model tht decrbe the reltonhp between nput commnd voltge u nd output meured dplcement m : 6

144 A tte-pce repreentton of qn. (8.) gven by: X G u (8.) U z Az Bu (8.) Cz (8.) m Regultor redegn cn be ued to crete model-bed feedforwrd-feedbc controller to mnmze the trcng error gven by: e d m (8.4) where the dered dplcement gven by d. Although regultor redegn performed ung the dplcement trcng error decrbed n qn. (8.4), the feedforwrd controller ued to cheve the del ytem wll tll be bed on ccelerton n qn. (8.) towrd the overll gol of ccelerton trcng. For regultor redegn, the devton ytem output re: ~ (8.5) m d The dynmc of the ugmented devton ytem ncludng the proce noe hpng flter nd meurement noe re then: z A z B u w (8.6) FB f f ~ C z v (8.7) where the meurement noe n the dplcement meurement. The LQR controller cn be bed on dplcement output weghtng ung the cot functon: Q LQR RLQRu FB J ~ dt (8.8) LQR After degnng Klmn flter bed on covrnce for proce nd meurement noe, the totl combned feedbc controller wll hve the followng dynmc: A L C B K zˆ L ~ zˆ (8.9) Kl To mplement dplcement feedbc control, the dered dplcement requred. Th dplcement cn be clculted from the double ntegrton of the dered ccelerton gnl. Alterntvely, the dered dplcement cn be clculted ung the feedforwrd controller (ccelerton to commnd) nd the he tble model (commnd to dplcement) n qn. LQR Kl 7

145 (8.), provdng better predcton of comptble dered dplcement (Nt, ). Snce the ccelerton gnl h been ped through hgh-p flter, drft n the dered dplcement wll be lmted. G u G u X U U A X A The combned feedforwrd controller wth dplcement feedbc hown n Fg. 8.. (8.) Offlne Onlne d G u u FF Feedforwrd Controller G u G u Dplcement Converon d + e LQG Feedbc Controller u FB + + u G yu She Tble Dynmc m m 8..4 Fgure 8.. Model-bed dplcement feedbc control Mult-Metrc Feedbc Control By combnng dplcement nd ccelerton meurement, mult-metrc feedbc pproch to he tble control cn be relzed. A greter number of meurement cn be ued for better etmte of the tte of the he tble ytem model through the Klmn flter. More mportntly, dplcement meurement re more entve n the lower frequency rnge whle ccelerton meurement re more entve n the hgher frequency rnge; thu, by combnng the two meurement, ccurte feedbc control cn be cheved over brod frequency rnge. The he tble ytem wll now be modeled SIMO ytem from nput commnd voltge to both output meured dplcement nd output meured ccelerton. U G yu A tte-pce repreentton of qn. (8.) gven by: X A (8.) z Az Bu (8.) 8

146 m y m Cz m (8.) Regultor redegn cn be ued to crete model-bed feedforwrd-feedbc to mnmze the trcng error gven by: e e e From regultor redegn, the devton ytem output re: d m y d y (8.4) m d m m d ~ y y y (8.5) The dynmc of the ugmented devton ytem ncludng the proce noe hpng flter nd meurement noe re then: z A z B u w (8.6) FB f f ~ y C z v (8.7) The meurement noe nclude both noe n the dplcement nd ccelerton meurement. The LQR controller cn be bed on output weghtng ncludng both the dplcement nd ccelerton output: J LQR T Q ~ LQRy RLQRu FB ~ y dt (8.8) The Klmn flter degn bed on umed proce nd meurement noe covrnce. The totl combned feedbc controller gven by: A L C B K zˆ L y z ˆ ~ (8.9) Kl The combned feedforwrd controller wth mult-metrc feedbc preented n Fg. 8.. For he tble control tude, four model-bed controller re condered: () feedfowrd controller (.e., qn. 8.), (b) feedforwrd controller wth dplcement feedbc (.e., Fg. 8.), (c) feedforwrd controller wth ccelerton feedbc (.e., Fg. 8.), nd (d) feedforwrd controller wth mult-metrc feedbc (.e., Fg. 8.). Note tht throughout th chpter, once controller degned to pecfc model of the he tble, no further modfcton performed (.e., controller re degned ndependently of the ground moton, requrng no terton). Reference erthque ground moton re elected from benchmr tudy on tructurl control (Ohtor et l., 994; ee Fg. 6.6). Both reference nd hgh-p fltered ground moton re hown n Fg. 8.4 for the frt econd of ech record. 9 LQR Kl

147 Offlne Onlne d G u Feedforwrd Controller u FF G u G u Dplcement Converon d e + e LQG Feedbc Controller u FB + + u G yu She Tble Dynmc m m + Fgure 8.. Model-bed mult-metrc feedbc control Accel (m/ ) Accel (m/ ) Accel (m/ ) Accel (m/ ) 4 l Centro Hchnohe Northrdge Kobe 5 5 Reference Fltered Tme (ec) Fgure 8.4. Fltered htorc ground moton 4

148 8. permentl Setup The model-bed control pproch for he tble tetng verfed ung mll-cle ngle he tble hown n Fg The he tble ue cutom bult ervo-motor mnufctured by SMI Technology to move 46 cm 46 cm top plte wth troe of ±5 cm. A Quner Conultng MultQ- Bord nd hot PC re ued to control the he tble n dplcement control wth PD controller. The A/D nd D/A of the bord re both -bt. Dplcement feedbc provded by dgtl encoder. Accelerton re meured ung model 7GFAG cpctve ccelerometer mnufctured by PCB Pezotronc. The ccelerometer hve meurement rnge of ± g, frequency rnge of - Hz, nd entvty of mv/g. For ytem dentfcton, nput gnl re generted ung Spectrl Dynmc Sglb pectrum nlyzer nd repone meured ung n m+p nterntonl VbPlot pectrum nlyzer. Model-bed outer-loop controller re mplemented ung dspac model DSP bord, the detl of whch re provded n Chpter 6. Fgure 8.5. Bre he tble 8. Bre She Tble Model-bed control frt eplored for the bre he tble. The he tble pltform dd conderble m, whch nfluence the dynmc of the he tble. However, wthout n ttched tructure, the phenomenon of CSI wll be mnmzed, ledng to mpler control problem. 8.. Sytem Identfcton The nput-output reltonhp of the he tble determned epermentlly ung to Hz BLWN commnd to the he tble. Meurement of the be plte re mde n both dplcement nd ccelerton. Four level of ectton re condered,.,.,.4, nd.6 V RMS, to nvetgte the nfluence of ectton mpltude on the he tble dynmc. Trnfer functon clculted ung 48 FFT pont, Hnnng wndow wth 5% overlp, nd verge. Trnfer functon re hown n Fg. 8.6 nd Fg. 8.7, whch dply the nput commnd to dplcement nd ccelerton trnfer functon, repectvely. The unt for 4

149 commnd, meured dplcement, nd meured ccelerton n the trnfer functon re Volt, cm, nd m/. It cler tht the he tble ehbt hghly nonlner behvor due to the mpltude dependency of the trnfer functon. At low mpltude, there gnfcnt frcton lmtng the ccurte trcng of the commnd gnl. The trnfer functon t.4 V RMS ectton repreent mpltude mlr to tht of the reference ccelerton ground moton. Therefore, the model-bed controller bed on model of the trnfer functon t th level of ectton. Identfed SISO model re preented n Fg. 8.6 nd Fg By degn, the feedbc controller wll me the ytem robut to nonlnerte, modelng nccurce, nd chnge n the ytem. Mgntude Frequency (Hz) Phe ( ) Frequency (Hz) Fgure 8.6. Bre he tble dplcement trnfer functon. V RMS. V RMS.4 V RMS.6 V RMS Model Mgntude 5 5 Frequency (Hz) Phe ( ) Frequency (Hz) Fgure 8.7. Bre he tble ccelerton trnfer functon V RMS. V RMS.4 V RMS.6 V RMS Model 4

150 The dentfed model from commnd to dplcement gven : G u (8.) The dentfed model from commnd to ccelerton gven : G u (8.) For the bre he tble, the gol to verfy the feblty of ccelerton feedbc control. Therefore, SIMO ytem not dentfed nd mult-metrc control not eplored (though t wll be when the tructure ttched). 8.. Trcng Performnce For th prelmnry tudy, the l Centro erthque record elected the reference ccelerton. In order to nvetgte nonlnerte octed wth the mpltude of the nput moton, both. nd.4 of the record re nvetgted. Controller nclude feedforwrd control (FF), feedforwrd control wth dplcement feedbc (FF + FB), nd feedforwrd control wth ccelerton feedbc (FF + FB). Reult re hown n Fg. 8.8 nd Fg. 8.9 for. l Centro nd.4 l Centro, repectvely. rror re reported the RMS dfference between the meured nd dered ccelerton (or meured nd dered dplcement) for the frt 5 econd of repone. Note tht the ccelerton reult hve been fltered by low-p flter wth cutoff frequency of 5 Hz, whch well bove the mmum nturl frequency of the pecmen tht to be tuded. Flterng necery n pot-proceng becue the ccelerton meurement enter the DSP unfltered to vod ntroducng lg nto the feedbc loop. The tme rnge for error clculton nd flterng content throughout th chpter. Accelerton feedbc control provde fr uperor ccelerton trcng for both erthque level nvetgted. Mot mportntly, the pe n ccelerton whch cn cue the lrget dmge to pecmen re very ccurtely trced. At hgher level of ground moton, the frcton tht plgue the low mpltude behvor of the he tble reduced. Therefore, mproved control een n ll pproche for the lrger erthque. Improvement cn be een vully or by normlzng the RMS error by the mmum mpltude of ccelerton n Tble 8.. The purpoe of controllng the bre he tble proof-of-concept. Therefore, only two mpltude of one erthque record re nvetgted nd mult-metrc control not condered. A more etenve controller evluton wth multple erthque nd mult-metrc control performed for the he tble wth pylod. 4

151 Accel (m/ ) Accel (m/ ) Accel (m/ ) FF Me De.79 m/ RMS rror FF + FB.5 m/ RMS rror FF + FB.45 m/ RMS rror Tme (ec) Fgure 8.8. Accelerton trcng of. l Centro wth bre he tble Accel (m/ ) Accel (m/ ) Accel (m/ ) FF Me De.8 m/ RMS rror FF + FB.4 m/ RMS rror FF + FB.57 m/ RMS rror Tme (ec) Fgure 8.9. Accelerton trcng of.4 l Centro wth bre he tble 44

152 Tble 8.. Normlzed Accelerton Trcng Performnce rthque Record RMS rror (normlzed by mmum ccelerton) FF FF + FB FF + FB. l Centro l Centro The dplcement trcng performnce reult re hown n Fg. 8. nd Fg. 8. for. l Centro nd.4 l Centro, repectvely. Dplcement feedbc control provde the bet dplcement trcng n ll ce, however lo hown to provde the wort ccelerton trcng. Dplcement feedbc control lghtly degrde ccelerton trcng performnce by ddng hgh-frequency content to the ccelerton meurement. Wth he tble control, the dered trjectory n ccelerton record, thu ccurte ccelerton trcng more derble objectve. Normlzed dplcement trcng error re ummrzed n Tble 8.. A wth ccelerton trcng, when the ground moton lrger nd frcton doe not nfluence the he tble behvor much, dplcement trcng more ccurte. Dp (cm) FF Me De.5 cm RMS rror FF + FB Dp (cm) Dp (cm).6 cm RMS rror FF + FB.69 cm RMS rror Tme (ec) Fgure 8.. Dplcement trcng of. l Centro wth bre he tble 45

153 Dp (cm) Dp (cm) Dp (cm) 4.65 cm RMS rror FF + FB 4 Fgure 8.. Dplcement trcng of.4 l Centro wth bre he tble Tble 8.. Normlzed Dplcement Trcng Performnce rthque Record RMS rror (normlzed by mmum dplcement) FF FF + FB FF + FB. l Centro l Centro FF Me.5 cm RMS rror FF + FB 4.85 cm RMS rror Tme (ec) De 8.4 Two-Story Lner Buldng A two tory teel frme tructure dded to the he tble to tudy the performnce of modelbed control n the preence of trong CSI. The buldng degned ung.7 cm (½ nch) teel plte connected by prng-teel column tht nomnlly contrn the moton to ngle, mnmzng toron. The prng-teel enure tht the buldng cn undergo lrge deformton wthout yeldng. The buldng hown mounted to the he tble n Fg. 8.. The m nd tffne mtrce re by degn: 4. M g (8.) K N / m (8.) 46

154 Fgure 8.. She tble wth lner tructure The m nd tffne mtrce reult n epermentlly verfed nturl frequence of.67 Hz nd 4.6 Hz wth correpondng epermentlly determned dmpng rto of.5% nd.%. The nturl frequence re degned to be mlr to thoe of typcl mdre teel tructure (ASC, ). In ddton, the tructure h vbro-mpct nonlner energy n ttched to the top tory, whch remnnt from eprte lne of reerch. In t unloced confgurton, th devce cont of m tht move on round rl ytem wth n mpct topper. In t current confgurton the m loced nto plce; therefore, the only effect on the ytem n ncree n m, whch ncluded n the m mtr Sytem Identfcton Sytem dentfcton performed on the he tble wth the me tetng protocol the bre he tble. Fgure 8. how the commnd to dplcement trnfer functon whle Fg. 8.4 how the commnd to ccelerton trnfer functon. Thee trnfer functon re very dfferent from the bre he tble ce, howng how nfluentl the pylod m nd dynmc re for th epermentl etup. In fct, the two nturl frequence of the tructure re pprent n the he tble trnfer functon. Due to the pronounced CSI, two modelng pproche re condered. The frt modelng pproch low-order model, where the pronounced pe nd vlley due to CSI re gnored. The econd modelng pproch hgh-order model, where greter number of pole nd zero re dded to model CSI ccurtely. Both model ft re llutrted n Fg. 8. nd Fg The low-order nd hgh-order model re dentfed SIMO ytem n qn. (8.4) nd (8.5), repectvely. 47

155 G yu G yu X A U (8.4) (8.5) In controller degn when only SISO ytem requred (uch ccelerton feedbc nd dplcement feedbc), the SISO ytem etrcted from the SIMO ytem. Mgntude Frequency (Hz) Phe ( ) Frequency (Hz) Fgure 8.. She tble wth lner buldng dplcement trnfer functon V RMS. V RMS.4 V RMS.6 V RMS Hgh Order Low Order Mgntude 5 5 Frequency (Hz) Phe ( ) Fgure 8.4. She tble wth lner buldng ccelerton trnfer functon V RMS. V RMS.4 V RMS.6 V RMS Hgh Order Low Order 5 5 Frequency (Hz)

156 8.4. Trcng Performnce The performnce of the he tble wth the buldng ttched nvetgted for model-bed controller bed on both low nd hgh-order model. The l Centro, Kobe, nd Northrdge erthque record re elected the reference ccelerton. Controller nclude feedforwrd control (FF), feedforwrd control wth dplcement feedbc (FF + FB), feedforwrd control wth ccelerton feedbc (FF + FB), nd feedforwrd control wth mult-metrc feedbc (FF + FB). The reult for Kobe erthque record ung the low-order controller degn re hown n Fg. 8.5 whle the reult ung the hgh-order controller degn re hown n Fg Accelerton feedbc mprove the performnce of ccelerton trcng, epeclly n reducng hgher frequency ocllton nd mtchng the pe ccelerton. The ddton of mult-metrc feedbc control lghtly mprove trcng performnce. The bet mult-metrc feedbc controller degn re cheved by plcng more mportnce on the ccelerton meurement reltve to the dplcement meurement (through LQG degn), llutrtng the vlue of ccelerton feedbc. Furthermore, the controller developed ung the hgh-order model perform better thn the lower-order model n mot ce. If the frequency content of the nput ground moton overlp wth the pronounced CSI effect oberved n the trnfer functon, the hgher-order model wll provde better control over th regon. Accel (m/ ) Accel (m/ ) Accel (m/ ) Accel (m/ ) Me FF De.5 m/ RMS rror FF + FB.6 m/ RMS rror FF + FB.76 m/ RMS rror 4 6 FF + FB 8.6 m/ RMS rror Tme (ec) Fgure 8.5. Accelerton trcng of Kobe wth lner tructure nd low-order controller 49

157 Accel (m/ ) Accel (m/ ) Accel (m/ ) Accel (m/ ). m/ RMS rror FF + FB Fgure 8.6. Accelerton trcng of Kobe wth lner tructure nd hgh-order controller The ccelerton trcng reult for ll erthque record, ummrzed by the RMS error, re preented for low-order controller n Tble 8. nd hgh-order controller n Tble 8.4. Reult from the other erthque record confrm tht the model-bed ccelerton feedbc controller perform very well nd, n mot ce, mproved lghtly by mult-metrc feedbc control. Agn, the controller bed on hgher-order model provde better control n mot ce. Tble 8.. Accelerton Trcng Performnce for Low-Order Controller rthque Record RMS rror (m/ ) FF FF + FB FF + FB FF + FB. l Centro l Centro Kobe Northrdge FF Me De.55 m/ RMS rror FF + FB.59 m/ RMS rror FF + FB.54 m/ RMS rror Tme (ec) 5

158 Tble 8.4. Accelerton Trcng Performnce for Hgh-Order Controller rthque Record RMS rror (m/ ) FF FF + FB FF + FB FF + FB. l Centro l Centro Kobe Northrdge Dplcement trcng reult re preented for Kobe erthque record ung the loworder controller degn n Fg. 8.7 nd the hgh-order controller n Fg Dplcement feedbc control gnfcntly mprove the trcng of the dered dplcement beyond other control cheme. Wth mult-metrc feedbc control, mot control weghtng plced on ccelerton; therefore the mult-metrc feedbc control reult cloely mtch the ccelerton feedbc control reult. A wth ccelerton trcng, the hgh-order controller reduce the dplcement trcng error beyond the low-order controller. Dp (cm) Dp (cm) Dp (cm) Dp (cm) Me FF De.6 cm RMS rror FF + FB.4 cm RMS rror FF + FB.65 cm RMS rror 4 6 FF + FB 8.6 cm RMS rror Tme (ec) Fgure 8.7. Dplcement trcng of Kobe wth lner tructure nd low-order controller 5

159 Dp (cm) Dp (cm) Dp (cm) Dp (cm) Me FF De.48 cm RMS rror FF + FB.9 cm RMS rror FF + FB.54 cm RMS rror FF + FB.5 cm RMS rror Tme (ec) Fgure 8.8. Dplcement trcng of Kobe wth lner tructure nd hgh-order controller The dplcement trcng reult for ll erthque record nvetgted, ummrzed by the RMS error, re preented for low-order controller n Tble 8.5 nd hgh-order controller n Tble 8.6. Overll, dplcement feedbc control provde the bet dplcement trcng. However, the control objectve ccelerton trcng, where dplcement feedbc control provde the wort performnce. Thu, dplcement feedbc lone my be ndequte towrd chevng ccurte ground moton replcton. Mult-metrc control llow for blnce between dplcement nd ccelerton trcng; however focu plced on the ccelerton trcng. 5

160 Tble 8.5. Dplcement Trcng Performnce for Low-Order Controller rthque Record RMS rror (cm) FF FF + FB FF + FB FF + FB. l Centro l Centro Kobe Northrdge Tble 8.6. Dplcement Trcng Performnce for Hgh-Order Controller rthque Record RMS rror (cm) FF FF + FB FF + FB FF + FB. l Centro l Centro Kobe Northrdge Nonlner Structure To verfy the robutne of the model-bed controller n the preence of nonlnerte, whch cn be cued by tructurl dmge durng epermentton, nonlner pecmen wll be nvetgted. Nonlner tructure provde prtculr control chllenge n the preence of trong CSI. For emple, gnfcntly pronounced tructure dynmc through CSI re preent n Fg. 8. nd Fg If the tructure w to become dmged nd the nturl frequence hft, then the model-bed controller would no longer be tuned to the tructure. Robut controller re needed to ccommodte th chnge n he tble behvor nd enure ccurte ccelerton trcng even fter dmge. A hft n nturl frequence my ffect the hgh-order model thn the low-order model nce the low-order model overhdow the pe nd vlley due to CSI; therefore both modelng pproche wll be eplored for the nonlner pecmen. To conder nonlner behvor, modfcton mde to the etng two tory frme tructure. Two wooden column contructed from bwood re dded to ech tory, ncreng the tffne of the tructure, hown n Fg ch wooden column 4.76 mm (/6 nch) thc over the entre length,.7 mm (/ nch) wde over 77.8 mm (7 nch) length, nd 5.8 mm ( nch) wde t the connecton. Sytem modelng nd controller degn wll be bed on the modfed tructure wth wooden column. Under etreme lodng, the column re degned to fl, reducng the nturl frequence to ppromtely tht of the lner teel-only tructure. The robutne of the controller wll be evluted n the preence of th hft n tructurl dynmc. 5

161 8.5. Sytem Identfcton Fgure 8.9. She tble wth nonlner tructure Sytem dentfcton performed on the he tble wth the me tetng protocol ued n prevou ce for.4 V RMS ectton. Fgure 8. how the commnd to dplcement trnfer functon whle Fg. 8. how the commnd to ccelerton trnfer functon. The orgnl epermentl trnfer functon wthout wooden column re hown to llutrte the chnge tht the wooden column brng to the dynmc of the he tble. Both low-order nd hgh-order model ft re hown. The low-order nd hgh-order SIMO trnfer functon model re dentfed qn. (8.6) nd (8.7) repectvely. G yu G yu.457 X A U (8.6) (8.7) 54

162 Mgntude Frequency (Hz) Frequency (Hz) Fgure 8.. She tble wth nonlner buldng dplcement trnfer functon Phe ( ) Orgnl Nonlner Hgh Order Low Order 8.5. Mgntude 5 5 Frequency (Hz) Fgure 8.. She tble wth nonlner buldng ccelerton trnfer functon Accelerton Trcng Performnce Phe ( ) The l Centro erthque record elected the reference ccelerton for trcng control wth mmum chevble mpltude of.4. A the pecmen wll undergo dmge, eperment re not ely repeted nd drectly compred; therefore, only the model-bed mult-metrc feedbc controller wll be eplored for both low-order nd hgh-order controller degn. To llutrte controller performnce durng pecmen chnge, the me erthque record run multple tme the wooden column receve dmge nd re eventully removed. Durng thee tet, the model-bed controller, whch bed on the tructure wth ntct wooden column, not djuted Orgnl Nonlner Hgh Order Low Order 5 5 Frequency (Hz)

163 The performnce of the model-bed mult-metrc feedbc controller bed on the hghorder model hown n Fg. 8.. The frt row of the fgure llutrte the performnce of the controller wth the column completely ntct throughout the ground moton. At mmum mpltude, the he tble unble to notcebly dmge the column. Therefore, pror to the net tet, the column re lghtly notched. The notche re ntroduced t the locton where the wdth of the column chnge nd the hghet bendng tree re epected. The performnce of the controller when the column go from notched to dmged tte hown n the net row. Net, the dmged column re gn ubjected to the me erthque nd dmged further, wth reult hown n the net row. Fnlly, performnce of the controller wth column removed hown n the lt row. A the condton of the pecmen chnge, the hgh-order controller no longer tuned, nd performnce degrde lghtly. The nturl frequence of the tructure re evluted before nd fter ech tet n Fg. 8. from the free repone to n mpule lod of low enough mpltude to prevent dmge to the column. The nturl frequence re reported n Tble 8.7, provdng quntttve vlue to chrcterze the chnge n dynmc. Accel (m/ ) Accel (m/ ) Accel (m/ ) Accel (m/ ) Intct Column Me De.78 m/ RMS rror Notched Column => Dmged Column. m/ RMS rror Dmged Column => Further Dmged Column. m/ RMS rror Column Removed.7 m/ RMS rror Tme (ec) Fgure 8.. Accelerton trcng wth nonlner tructure nd hgh-order controller 56

164 Tble 8.7. Nturl Frequence Before nd After Tetng Ung Hgh-Order Controller Nturl Frequency (Hz) Intct Column Notched Column Dmged Column Further Dmged Column Column Removed Frt Mode Second Mode The performnce of the model-bed ccelerton feedbc controller bed on the loworder model controller llutrted n Fg. 8.. For th controller, eperment re run ung notched column uch tht dmge ntroduced under ccelerton chevble by the he tble. The frt row how the performnce of the controller the notched column become dmged. In the econd row, the dmged column re gn ubjected to the me erthque lod nd become further dmged. In the thrd row, the column re removed. The low-order model controller le entve to chnge n the nturl frequency, thu the condton of the pecmen doe not ffect the controller performnce gnfcntly. The bet performnce n term of RMS error ctully een n the ce wth the column removed, perhp due to the removl of the nonlner behvor ntroduced by the wooden column. Accel (m/ ) Accel (m/ ) Accel (m/ ) Notched Column => Dmged Column.87 m/ RMS rror Dmged Column => Further Dmged Column Fgure 8.. Accelerton trcng wth nonlner tructure nd low-order controller The nturl frequence of the tructure re hown n Tble 8.8 evluted before nd fter ech tet n Fg. 8.. A typcl dmge ce for the wooden column hown n Fg Dmge occurred t two of the notch pont, epected. 57 Me De.87 m/ RMS rror Column Removed.8 m/ RMS rror Tme (ec)

165 Tble 8.8. Nturl Frequence Before nd After Tetng ung Low-Order Controller. Nturl Frequency (Hz) Notched Column Dmged Column Further Dmged Column Column Removed Frt Mode Second Mode Fgure 8.4. Typcl dmge to wooden column (be connecton on rght-hnd de) 8.6 Summry In th chpter, the propoed model-bed controller w dpted to he tble tetng. Hghfdelty trcng of the dered ccelerton w cheved through ccelerton nd mult-metrc feedbc pproche. Succe w cheved by enurng tblty through nner-loop dplcement feedbc control whle degnng the model-bed controller n outer-loop controller. Alo, the fleblty of LQG control for model-bed feedbc llow for hpng of the proce nd meurement noe. Through hpng flter, the feedbc controller cn be degned le entve to hgher frequence whch my led to hgh frequency ocllton nd ntblte. The model-bed controller w demontrted to be robut to chnge n pecmen condton due to dmge. In ce when dmge epected, the low-order controller le precely tuned to the pe nd vlley cued by CSI w hown to provde better control over ll pecmen condton. For lner pecmen, the hgh-order controller ectly tuned to the effect of CSI w hown to provde better control. In ether ce, model-bed control provde n ecellent lterntve to etng control technque ued for he tble tetng. Further mprovement epected when worng wth hgher-qulty hydrulc he tble where the behvor wll be le mpltude dependent. 58