Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique

Transcription

1 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, Degn of PID Controller for Hgher Order Contnuou Sytem ung MPSO bed Model Formulton Technque S. N. Deep, G. Sugumrn Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/9 Abtrct Th pper propoe new lgebrc cheme to degn PID controller for hgher order lner tme nvrnt contnuou ytem. Modfed PSO (MPSO) bed model order formulton technque hve ppled to obtn the effectve formulted econd order ytem. A controller tuned to meet the dered performnce pecfcton by ung pole-zero cncellton method. Propoed PID controller ttched wth both hgher order ytem nd formulted econd order ytem. The cloed loop repone oberved for tblzton proce nd compred wth generl PSO bed formulted econd order ytem. The propoed method llutrted through numercl exmple from lterture. Keyword Hgher Order Sytem, Model Order Formulton, Modfed Prtcle Swrm Optmzton, PID controller, Pole-Zero Cncellton. P I.INTRODUCTION ID controller hve been wdely ued n ndutre for vrou pplcton nd t ply vtl role n utomton. It h been crucl problem to tune properly the gn of the PID controller becue mny ndutrl plnt re often burdened wth the chrctertc uch hgher order, tme dely nd nonlnerte []. Whle modelng the complex ytem lke rcrft mechnm, Atomc plnt proce montorng, fuel njector nd prk tmng of uto moble t cn be noted tht the ytem order ncreed. The nly nd ynthe of hgher order ytem re dffcult nd generlly not derble on economc nd computtonl conderton. Thu, t necery to obtn lower order ytem o tht the obtned lower order mntn the chrctertc of the orgnl ytem. Th help n mnmzng the vrton durng degn nd relzton of utble control ytem component to be ttched to the orgnl ytem. Model order formulton the proce of dervng the lower order model from the hgher order model. Model order formulton pproxmte the complex ytem by mple one. The mn m of the formulton to fnd the bet poble pproxmton of the output of the orgnl ytem. Durng the pt four decde, numerou mpreve vrete of new technque [] - [6] hve been developed for obtnng lower Dr. S. N. Deep workng n Aocte Profeor n the Deprtment of Electrcl nd Electronc Engneerng, Ann Unverty of Technology- Combtore, Combtore 64 47, Tml Ndu, Ind (e-ml: deeppg@ gml.com). G. Sugumrn Senor Engneerng Reerch Fellow wth the Deprtment of Electrcl nd Electronc, Ann Unverty of Technology- Combtore, Combtore 64 47, Tml Ndu, Ind (e-ml: urugu@ gml.com). order model from hgher order lner ytem. Ech of thee method h both dvntge nd ddvntge when tred on prtculr ytem. Severl method hve been developed for degnng PID controller. Zegler et l., [7] hve propoed the frequency repone method by ung nformton from the Nyqut curve of the ytem. The method only utble for ytem wth monotonc tep repone. Hng et l., [8] hve reexmned the Zegler-Nchol method nd propoed new tunng formule, n whch ettng pont weght for ytem wth PID controller re ntroduced. Zhung et l., [9] propoed n optml degn of PID controller bed on the mnmzton of n ntegrl crteron. Yeung et l., [] preented the grphcl method for common contnuou tme nd dcrete tme compentor. Vrou method re developed by employng frequency repone mtchng technque for degnng the controller. Rttn et l., [] propoed method bed on complex curve fttng nd nvolve the mtchng of frequency repone of cloed loop ytem wth the reference model. Tchuner [] h propoed the jury tblty condton derved from Routh nd Fuller tble. The dgtl controller degn method propoed by Inook et l., [3] bed on ere expnon of pule trnfer functon. Agurre [4] ntroduced method for the degn of contnuou tme controller by mtchng combnton of tme moment nd Mrkov prmeter of the cloed loop ytem. The mn purpoe of the pproch to reduce the exceve overhoot of the ytem to be compented. To enhnce the cpblte of trdtonl PID prmeter tunng technque, everl ntellgent pproche hve been uggeted to mprove the PID tunng, uch thoe ung Genetc Algorthm (GA) [5] nd the Prtcle Swrm Optmzton (PSO) [6]. Wth the dvnce of computtonl method n the recent tme, optmzton lgorthm re often propoed to tune the control prmeter n order to fnd n optml performnce [7]. In th pper mple lgebrc cheme propoed to degn PID controller for Lner Tme Invrnt Contnuou Sytem (LTICS). Adjunct Polynoml cheme ued for dervng the bc econd order ytem from the orgnl hgher order ytem, nd to obtn fne tuned econd order ytem depctng the orgnl chrctertc of the ytem, Modfed Prtcle Swrm Optmzton (MPSO) lgorthm propoed. Pole-zero cncellton method employed for ntlze the PID gn vlue. Mtlb multon procedure re ued to obtn the optml PID gn vlue. The robutne Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 949 cholr.wet.org/37-689/9

2 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/9 of the propoed cheme compred wth generl PSO bed formulted econd order model. II.DESCRIPTION OF THE PROBLEM A. PID Controller Trnfer Functon The tndrd block dgrm of PID controller hown n Fg.. PID controller cn be mthemtclly repreented [8], t de( u( K P e( + e( τ ) dτ + Td () T d( Fg. Generl block dgrm of PID controller Where u( nd e ( denote the control nd error gnl of the ytem. K P the proporton gn, T nd Td repreent the ntegrl nd dervtve tme contnt repectvely. The correpondng PID controller trnfer functon G c ( gven, Gc ( K P + + Td () T Equton () cn be rewrtten, K I Gc ( K P + + K D (3) K I nd K D re repreent the ntegrl nd dervtve gn vlue of the controller. B. Hgher Order Trnfer Functon Conder n n th order lner tme nvrnt contnuou ytem repreented by, n A N( (4) D( n Where, N( the numertor polynoml nd D( the denomntor polynoml. Alo A nd repreent the contnt coeffcent of the -term of the numertor nd denomntor of G (. Equton (4) repreented the hgher order contnuou ytem trnfer functon. C. Lower Order Trnfer Functon To fnd m th lower order model for the contnuou ytem R m (, where m < n n the followng form repreented by (5), uch tht the formulted lower order model retn the chrctertc of the orgnl ytem nd pproxmte t repone cloely poble for the me type of nput. R m m B m N ( ( (5) m m D ( b Where, N m ( nd D m ( re the numertor polynoml nd denomntor polynoml of the formulted lower order model repectvely. Alo B nd b repreent the contnt coeffcent of the -term of the numertor nd denomntor of R m (. Equton (5) repreented the lower order trnfer functon. The mn objectve of the degn tht to tune the gn ( K P, K I nd K D ) of the PID controller for dered output. For reduce the computtonl complexte nd dffculte of mplementton, the hgher order of the ytem reduced nto lower econd order ytem. PID controller tuned wth repect to the degn pecfcton for formulted econd order model. Further the cloed loop repone of the new lower order model ttched wth PID controller obtned, whch depct the chrctertc of the orgnl hgher order ytem repone wth PID controller. III.OVERVIEW OF PARTICLE SWARM OPTIMIZATION The prtcle wrm optmzton (PSO) technque ppered promng lgorthm for hndlng the optmzton problem. PSO populton-bed tochtc optmzton technque, npred by ocl behvor of brd flockng or fh choolng [9]. PSO npred by the blty of flock of brd, chool of fh, nd herd of nml to dpt to ther envronment, fnd rch ource of food, nd vod predtor by mplementng n nformton hrng pproch. PSO technque w nvented n the md 99 whle ttemptng to multe the choreogrphed, grceful moton of wrm of brd prt of oco cogntve tudy nvetgtng the noton of collectve ntellgence n bologcl populton. The velocty of prtcle nfluenced by three component nmely, nertl momentum, cogntve nd ocl. The nertl component multe the nertl behvor of the brd to fly n the prevou drecton. The cogntve component model the memory of the brd bout t prevou bet poton, nd the ocl component model the memory of the brd bout the bet poton mong the prtcle. Mthemtcl model for PSO follow [9], Velocty updte equton gven by V+ ω V + C r ( Pbet S ) + C r ( gbet S ) (6) Poton updte equton gven by S S V (7) Ech prtcle tre to modfy t velocty nd poton nd bed on (6) nd (7) nd reche the trget. Where, V Velocty of prtcle Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 95 cholr.wet.org/37-689/9

3 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, S Current poton of the prtcle ω Inert weght C Cognton ccelerton coeffcent C Socl ccelerton coeffcent Pbet Own bet poton of prtcle gbet Globl bet poton mong the group of prtcle r, r Unformly dtrbuted rndom number n the rnge [ to ] IV.MODIFIED PARTICLE SWARM OPTIMIZATION Step5 Step6 Step 7 Step 8 vlue Select the prtcle ndvdul wort vlue,.e. Prtcle too wy from the trget Updte prtcle ndvdul bet (pbe, globl bet (gbe, prtcle wort (Pwor n the velocty equton (8) nd obtn the new velocty Updte new velocty vlue n the equton (7) nd obtn the poton of the prtcle Fnd the optml oluton wth mnmum ISE by the updted new velocty nd poton Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/9 In th new propoed modfed PSO hvng better optmzton reult compre to generl PSO by plttng the cogntve component of the generl PSO nto two dfferent component. The frt component cn be clled good experence component. Th men the brd h memory bout t prevouly vted bet poton. Th mlr to the generl PSO method. The econd component gven the nme by bd experence component. The bd experence component help the prtcle to remember t prevouly vted wort poton. To clculte the new velocty, the bd experence of the prtcle lo tken nto conderton []. The new velocty updte equton gven by V + ω V + Cg r (Pbet S ) + Cb r (S Pwort ) + C r3 (gbet S ) (8) Where, C g Accelerton coeffcent, whch ccelerte the prtcle towrd t bet poton C b Accelerton coeffcent, whch ccelerte the prtcle wy from t wort poton P wort Wort poton of the prtcle r, r, r 3 Unformly dtrbuted rndom number n the rnge [ to ] The poton re updted ung (7). The ncluon of the wort experence component n the behvor of the prtcle gve the ddtonl explorton cpcty to the wrm. By ung the bd experence component; the prtcle cn byp t prevou wort poton nd try to occupy the better poton. The lgorthmc tep for the modfed PSO follow Step Select the number of prtcle, generton, tunng ccelertng coeffcent C g, C b, nd C nd rndom number r, r, r 3 to trt the optml oluton erchng Step Intlze the prtcle poton nd velocty Step 3 Select prtcle ndvdul bet vlue for ech generton Step 4 Select the prtcle globl bet vlue,.e. prtcle ner to the trget mong ll the prtcle obtned by comprng ll the ndvdul bet V.STEPS FOR MPSO BASED MODEL ORDER FORMULATION TECHNIQUE A. Adjunct Polynoml Scheme The djunct polynoml cheme ued to obtn the pproxmte econd order model for the gven hgher order ytem. Th cheme h the followng tep Step Conder n n th order lner tme nvrnt contnuou ytem repreented by the trnfer functon n generl form, N( D( n n An + An n n n + n A + A + + Step Clculte the trnent gn (TG) nd tedy tte gn (SSG) for the gven hgher order ytem n equton (9) An TG () (9) n A SSG () Step 3 For mplcty the pproxmte lower order model to be formulted ung djunct polynoml method gven by A + A R( () + + Step 4 Sclng the equton (), A + A R ( (3) + + Step 5 To mntn the TG nd SSG ung the equton () nd () n equton (3) ( ) ( TG) + SSG R ( (4) + + Step 6 The coeffcent of the pproxmted econd order model R( by equton (4) gve nput to modfed PSO. The MPSO ued to erch the better vlue of ( / ) nd ( / ) Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 95 cholr.wet.org/37-689/9

4 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, B. Modfed Prtcle Swrm Optmzton Modfed PSO lgorthmc tep re ppled fter the pproxmte econd order model R( obtned, hown n the equton (4), by ung the modfed prtcle wrm optmzton lgorthm the formulted lower order model chevng the objectve mnmum ISE nd follow the contrnt. The flowchrt for the propoed model order formulton cheme hown n Fg.. nd get the cloed loop repone wth the ntl vlue of the controller prmeter. Step 8 Fnd the optmum vlue for the controller prmeter whch tfy the requred pecfcton Step 9 By pplyng the optmum vlue, ccde th controller wth the orgnl ytem. Step Obtn the cloed loop repone of the reduced order ytem wth the controller. Step Obtn the cloed loop repone of the orgnl ytem wth the controller. VII.NUMERICAL EXAMPLE Let u conder lner tme nvrnt contnuou ytem repreented n the form of trnfer functon gven n [], Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/9. Fg. Flowchrt for model order formulton of lner tme nvrnt contnuou ytem VI.GENERAL ALGORITHM FOR DESIGNING THE PID CONTROLLER Step Red the open loop trnfer functon of the gven hgher order ytem Step Form the cloed loop trnfer functon Step 3 Obtn the tep repone of the cloed loop ytem Step 4 Check the repone for the requred pecfcton. Step 5 If the pecfcton re not met, get the reduced order model by ung propoed MPSO bed formulton technque nd degn controller for the reduced order model. Step 6 Obtn the ntl vlue of the prmeter KP, KI nd KD by pole zero cncellton. Step 7 Ccde the controller wth the reduced order model (5) Step- Clculte the trnent gn (TG) nd tedy tte gn (SSG) for the gven hgher order ytem n (5). 35 TG SSG.6 (6) 96 Step- Applyng Adjunct polynoml cheme, [Appendx] to n (5) to get pproxmted econd order model R(, Step-3 On clng (7), R ( (7) R ( (8) Step-4 To mntn TG nd SSG, ue the Equton (4) the reult R( become R ( (9) Step-5 The MPSO lgorthm now nvoked to erch the vlue of term (.773) nd the contnt term (.56) of the denomntor n R( repreented by (9), o the chrctertc of econd order model mtche the gven hgher order ytem gven by (5). MPSO determne better reduced econd order model wth the let ntegrl qure error. The trnfer functon of the reduced econd order model obtned ung MPSO cheme, Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 95 cholr.wet.org/37-689/9

5 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/ R ( () Step-6 Performnce pecfcton re condered wth repect to the cloed loop repone of the compented ytem to unt tep nput. The degn pecfcton re choen () Overhoot % () Settlng tme econd () Overhoot % Step-7 The cloed loop trnfer functon of the unty feedbck ytem wth cn be repreented, T ( () + the output repone of T( not tble wthn the pecfed degn pecfcton. So the PID controller ccded to the forwrded pth to djut the repone. Step-8 Applyng pole- zero cncellton method to ntlze the (KP, KI nd KD) vlue, KP 3.34, KI 3.43 nd KD Step-9 Ung the multon procedure the ntl prmeter re tuned to get unt repone of the compented ytem to meet the requred pecfcton re, KP 4.634, KI 3.5 nd KD.5. The trnfer functon of the degned PID controller follow, G c ( () Step- The cloed loop trnfer functon of the PID controller repreented by G c ( n equton () ttched to the econd order model repreented by R( n equton () obtned, T c ( (3) Step- The cloed loop trnfer functon of the PID controller repreented by G c ( n equton () ttched to the orgnl hgher order ytem repreented by n equton (5) obtned, ' T c ( (4) ' The unt tme repone of, T c ( nd T c ( re repreented by equton (5), (3) nd (4) re hown n Fg.3, Fg.4, nd Fg.5 repectvely. The compron of the unt tme repone pecfcton re gven n Tble. A m p ltu d e A m p ltu d e Unt Step Repone of the Eghth Order Sytem Tme (ec) Fg. 3 Unt tep repone of the eghth order ytem Unt tep repone of the econd order ytem wth PID controller Tme (ec) Fg. 4 Unt tep repone of the MPSO bed econd order ytem wth propoed PID controller A m p ltu d e Unt tep repone of the eghth order ytem wth the PID controller Tme (ec) Fg. 5 Unt tep repone of the eghth order ytem wth propoed PID controller Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 953 cholr.wet.org/37-689/9

6 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, TABLE I COMPARISON OF UNIT TIME RESPONSE SPECIFICATIONS Specfcton detl Orgnl Reduced Orgnl PSO bed MPSO bed ytem order ytem ytem wth reduced order reduced order propoed PID ytem wth ytem wth controller propoed PID propoed PID controller controller Re tme (ec) Settlng tme (ec) % Pek overhoot Pek tme (ec) Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/9 VII.DISCUSSION Durng MPSO lgorthm proce vrou prmeter re ued, number of generton5, number of prtcle4. For uccefully mplement the MPSO, the vlue of the prmeter nert weght (w).5, ccelertng fctor C g,c b nd C re chooe by.5.the MPSO lgorthm w coded n Intel Pentum proceor 4.,.8 GHz, 56 MB RAM nd t took econd by CPU for complete the multon. Fg.3 gve the unt tep tme repone the gven eght order lner tme nvrnt contnuou ytem, t exceed the dered degn pecfcton. For chevng the dered output repone wthout computtonl dffculte, MPSO technque nvoked to fnd the better econd order ytem. Formulted econd order ytem bed on MPSO technque effectvely depct the orgnl chrctertc of the hgher order ytem. Cloed loop repone of the propoed PID controller wth formulted econd order ytem gven n Fg.4. Fg. 5 repreent the cloed loop repone of the hgher order ytem wth propoed controller. Tble how tht the propoed modfed prtcle wrm optmzton gve the better ytem repone for the hgher order ytem. From Fg.4 nd Fg.5 t oberved tht the formulted lower order ytem depct the chrctertc of the orgnl hgher order ytem effectvely nd updte the wort experence of the prtcle n the velocty equton gve better optml oluton compred wth the generl PSO model. VIII. CONCLUSION The qulty of formulted lower order model judged by degnng the PID controller. PID controller of the formulted lower order ytem effectvely control the orgnl hgh order ytem. The mn dvntge of the propoed method tht t ey of mplementton nd let elped tme. The propoed pproch cn lo be ued for degnng dcrete PID controller. Th cn lo extended for other evolutonry technque nd hybrd method nd lo t extended for further degn of compentor well tte vrble controller nd oberver for tblzton proce. APPENDIX Conder n n th lner tme nvrnt contnuou hgher order ytem repreented by t trnfer functon n n 3 A n + A n A3 + A + A + A n n 3 n + n (5) The Adjunct Polynoml cheme for obtnng the pproxmted lower order model from the gven hgher order ytem follow: A Frt order: + Second order: Thrd order: (n-) th order: A + A + + A + A + A n n 3 An + An A + A n n n + n (6) (7) (8) (9) Equton (6) through (9), gve the lower order model formulted ung djunct polynoml cheme from the gven hgher order ytem. Bed on the requrement, utble lower order model cn be elected nd operte. It hould be noted for hgher order ytem of order n, (n-) lower order model could be formulted. Th method of electon of pproxmte lower order model help to et the ntl vlue of opertng prmeter to be ued n the Modfed Prtcle Swrm Optmzton proce. REFERENCES [] G. J. Slv, A. Dtt, New reult on the ynthe of PID controller, IEEE Trncton on Automtc Control, Vol. 47, No., pp. 4-5,. [] C. F. Chen nd L. S. Shen, A novel pproch to lner model mplfcton, Interntonl Journl of Control Sytem, Vol. 8, pp , 968. [3] V. Zln, Smplfcton of lner tme-nvrnt ytem by moment pproxmton, Interntonl Journl of Control Sytem, Vol., No. 8, pp , 973. [4] P. O. Gutmn, C. F. Mnnerfelt nd P. Molnder, Contrbuton to the model reducton problem, IEEE Trn. Auto. Control, Vol. 7, pp , 98. [5] R. Prd nd J. Pl, Stble reducton of lner ytem by contnued frcton, Journl of Inttuton of Engneer IE(I) Journl, Vol. 7, pp. 3-6, October, 99. Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 954 cholr.wet.org/37-689/9

7 World Acdemy of Scence, Engneerng nd Technology Interntonl Journl of Electrcl nd Informton Engneerng Vol:5, No:8, Interntonl Scence Index, Electrcl nd Informton Engneerng Vol:5, No:8, wet.org/publcton/9 [6] S. Mukherjee, Stkh nd R. C. Mttl, Model order reducton ung repone-mtchng technque, Journl of Frnkln Int., Vol. 34, pp , 5. [7] J. G. Zegler, N. B. Nchol, Optmum ettng for utomtc controller, Trncton of the AMSE, Vol. 64, pp , 94. [8] C. C. Hng, K. J. Atrom nd W. K. Ho Refnement of the Zegler- Nchol tunng formul, IEEE Proceedng of Control Theory nd Applcton, Vol. 38, No., pp. -8, 99. [9] M. Zhung, D. P. Atherton Automtc tunng of optmum PID controller, IEEE Proceedng of Control Theory nd Applcton, Vol. 4, No. 3, pp. 6-4, 993. [] K. S. Yeung, K. Q. Chd nd D. X. Ten, Bode degn chrt for contnuou- tme nd dcrete- tme compentor, IEEE Trncton on Educton, Vol. 38, No. 3, pp. 5-57, 995. [] K. Rttn, Dgtlzton of extng contnuou control ytem, IEEE Trn. Auto. Control, Vol. 9, pp. 8-85, 984. [] J. Tchuner, A Generl Formulton of the Stblty Contrnt for Smpled Dt Control Sytem, IEEE Proceedng, Vol. 5, pp. 63-6, 963. [3] H. Inook, G. Obnt nd M. Tkehm, Degn of dgtl controller bed on ere expnon of pule trnfer functon, Journl of Dynmc ytem, Meurement nd Control, Vol. 5, No. 3, pp. 4-7, 983. [4] L. A. Agurre, PID tunng bed on model mtchng, IEEE Electronc Letter, Vol. 8, No. 5, pp. 69-7, 99. [5] A. Vrek, T. Urbcc nd B. Flpc, Genetc Algorthm n Controller Degn nd Tunng, IEEE Trncton on Sy. Mn nd Cyber, Vol. 3, No.5, pp , 993. [6] Z. L. Gng, A prtcle wrm optmzton pproch for optmum degn of PID controller n AVR ytem, IEEE Trncton on Energy Converon, Vol.9, No., pp , 4. [7] J. Zho, T. L, J. Qn, Applcton of prtcle wrm optmzton lgorthm on robut PID controller tunng, Advnce n Nturl Computton - Sprnger, pp , 5. [8] M. Gopl, Control ytem prncple nd degn, Tt McGrw Hll Publcton, New Delh, 997. [9] R. C Eberhrt nd Y. Sh, Prtcle Swrm Optmzton: Development pplcton nd reoure, Proceedng Congre on Evolutonry Computton IEEE ervce, NJ, Kore,. [] S. N. Deep nd G. Sugumrn, MPSO bed model order formulton technque for SISO contnuou ytem, Interntonl Journl of Engneerng nd Appled Scence, Vol. 7, No. 3, pp. 5-3,V. [] Krhnmurthy nd V. Sehdr, Model reducton ung Routh tblty crteron, IEEE Trn. Auto. Control, Vol. 3, pp , Aug.978. Interntonl Scholrly nd Scentfc Reerch & Innovton 5(8) 955 cholr.wet.org/37-689/9