Model Optimization Identification Method Based on Closed-loop Operation Data and Process Characteristics Parameters

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1 Senor & Tranducer 204 by IFSA Publhng, S. L. Model Optmzaton Identfcaton Method Baed on Cloed-loop Operaton Data and Proce Charactertc Parameter Zhqang GENG, Runxue LI, 2 Xangba GU College of Informaton Scence and Technology, Bejng Unverty of Chemcal Technology, Bejng Chna. 2 Snopec Engneerng, Bejng 00029, Chna 2 Tel: , fax: E-mal: guxb@nopec.com Receved: 9 October 203 /Accepted: 9 January 204 /Publhed: 3 January 204 Abtract: Output noe trongly related to nput n cloed-loop control ytem, whch make model dentfcaton of cloed-loop dffcult, even undentfed n practce. The forward channel model choen to olate dturbance from the output noe to nput, and dentfed by optmzaton the dynamc charactertc of the proce baed on cloed-loop operaton data. The charactertc parameter of the proce, uch a dead tme and tme contant, are calculated and etmated baed on the PI/PID controller parameter and cloed-loop proce nput/output data. And thoe charactertc parameter are adopted to defne the earch pace of the optmzaton dentfcaton algorthm. PSO-SQP optmzaton algorthm appled to ntegrate the global earch ablty of PSO wth the local earch ablty of SQP to dentfy the model parameter of forward channel. The valdty of propoed method ha been verfed by the mulaton. The practcablty checked wth the PI/PID controller parameter turnng baed on dentfed forward channel model. Copyrght 204 IFSA Publhng, S. L. Keyword: Model optmzaton dentfcaton, Cloed-loop operaton data, Proce charactertc parameter, PSO, SQP, PID tunng.. Introducton Sytem dentfcaton one of the method and theore for modelng, whch bae on extractng the proce nformaton from the data of nput and output. For mot of ndutry procee, the ytem a part of the feedback ytem, and whch not allowed to be cut off under the conderaton of the economc and ecurty. The cloed-loop dentfcaton therefore neceary. The tradtonal method of ytem dentfcaton are ued for open-loop ytem, on the one hand, the ame output wll be obtaned even wth the dfferent nput, o the le nformaton wll be got from the proce. On the other hand, the noe n the output cloely related wth the nput through feedback, all of thee make the etmaton error larger wth tradtonal etmaton method and the ytem undentfed. Many effectve method are developed for ytem parameter etmaton of the cloe-loop ytem [-6], and can be dvded nto three categore: The ndrect dentfcaton (ID): Ignore the feedback and dentfy the open-loop ytem ung meaurement of the nput and output. Artcle number P_79

2 The drect dentfcaton (DI): dentfy ome cloed-loop tranfer functon and determne the open-loop parameter ung the knowledge of the controller. The jont proce dentfcaton (JPI): Regard the nput and output jontly a the output from a ytem drven by ome extra nput or et-pont gnal and noe. Ue ome method to determne the open-loop parameter from an etmate of th augmented ytem. Regardng ID and JPI, the parameter for the feedback controller mut be known before the ytem tet, and one of the meaurable gnal mut be ncluded. Th make the method lmted n real ndutral applcaton. The DI method regard the cloed-loop ytem a an open one. Whle th not ueful for cloed-loop ytem a dcued above. Many method [7-0] are ued to optmze the ytem parameter n D. I. Pan [4] developed a method to dentfy the ytem ung NLJ baed on a mplex method. The ID method dvded nto two tep: frt, generatng good etmaton of the loop entve baed on extenve cloed-loop data, and then the loop entvte are ued to factor the plant dynamc by nvere flterng. Many method had been propoed for multvarable ytem wth thee approache, whch have ome attractve propect, the nvere flterng tep could be dauntng for relatvely larger multvarable ytem. Nkhl [] developed an approach named trut regon SQP to optmze parameter, whch wll get better reult f the good ntal pont gven. In addton, Jn [3] dentfed the parameter of model wth partcle warm optmzaton (PSO) algorthm. NLJ and other method of DI earch the bet ytem parameter wthout the nformaton of gradent, whch made low peed n optmzaton proce. SQP take advantage of the nformaton, but entve to the ntal pont. PSO work a an ntellgence npred method that can get better reult n earch pace, however, t not a good dea to let the warm earch n the whole pace. Emprcal lterature revew how that mot reearche defne the earch pace ubjectvely baed on ther experence, rather than extractng proce nformaton from the nput and output data of the proce ndutry. In th paper, we mulated the dynamc charactertc of the proce object wth the forward channel, o the dentfcaton of the proce telf tranfer to dentfy the parameter of forward channel model. We take full advantage of the proce nput and output data and the PI/PID controller parameter to determne the earch pace of the forward channel parameter. At the meantme, a compoted earch method combne PSO wth SQP adopted, whch further make full ue of the global earch ablty of PSO and local earch ablty of the SQP. 2. Proce Object Model Baed on Forward Channel In the context of mot practcal ndutral object, they can be approxmated by applyng Second Order Sytem Plu Delay (SOSPD) model or Frt Order Sytem Plu Tme Delay (FOSPD) [3]. Take SOSPD model a example, the model tranfer functon gven by: - Ke G () ( T)( T ), () 2 The tme delay can be replaced by frt-order or econd-order Pade approxmaton [4]. Th paper ue forward channel to mulate the dynamc charactertc of the ytem, enurng output noe and nput are ndependent to get the dynamc charactertc of ytem. A hown n Fg., the model block dagram how that n the whole proce of dentfcaton, ytem dentfcaton can be conducted a long a we capture the output of the controller a well a the actual output of the ytem, and th wll not brng up any nterference to the orgnal ytem, and guarantee the afety of the actual ndutral operaton. Fg.. Identfcaton model baed on forward channel. 3. Proce Object Informaton Extracton Baed on Cloed-loop Data 3.. Tme Delay Etmaton Baed on Cloedloop Data Snce the delay tme contant an mportant proce varable parameter, the determnaton of t value of great gnfcance to the accuracy of dentfcaton. A hown n Eq. 2, the cro correlaton functon between output u of controller and output y of ytem ued to olve delay tme τ [2]. = max E[y()u(- )]= max u ( - ) y ( ), (2) n = 2

3 When elect utable δ=τ, the value of the cro correlaton functon wll be maxmzed, therefore the etmaton value of delay tme can be obtaned Etmaton of Stable Cloed-loop PI/PID Sytem Proce Parameter For the table cloed-loop ytem wth PI/PID controller, the tradtonal optmzaton tunng rule wll be appled. Wth the quanttatve relatonhp among the tme contant of proce object, proportonal gan K c of controller, ntegraton tme T, and dfferental tme Td, revere calculaton can be ued to obtan the tme contant of proce ytem object and the etmaton of proportonal gan. Th paper ue Mnmum IAE-Shnkey (996) page-48 and Mnmum IAE-Shnkey (996) page-9 [3] to conduct revere calculaton for PI and PID controller relatvely, obtanng tme contant of proce object and proce proportonal etmated value. The equaton are hown n Eq. 3 and Eq. 4. For PI Controller: For PID Controller: 2* T T= 2.29*3.5, T 2= *T T K= 0.2* T * Kc T =2.5*Td, T2= *T T K = T d * K c (3) (4) where T and T 2 refer to the tme contant, K refer to the proce gan n Eq., T refer to ntegraton tme, Td refer to dfferental tme, and Kc refer to the gan of controller. 4. The Identfcaton Method for Forward Channel Model Baed on Cloed-loop Proce Informaton Contrant 4.. PSO-SQP Algorthm PSO wa developed by Kennedy n 995 [4]. It ued n electrc, energy and optmzaton [5-7]; Smlar to other warm ntellgence optmzaton algorthm, uch a genetc algorthm, each partcle repreent a poble oluton, and ha two charactertc parameter ncludng poton and velocty. Uually the functon value of t poton refer to the partcle ftne value, and t ued to evaluate qualty of the current partcle poton. The PSO algorthm frt randomly ntalze a group of partcle n the earch pace, and then update the poton and velocty accordng to the optmal poton of both ndvdual and entre populaton baed on Eq. 5 and Eq. 6, untl the atfactory oluton are found or the maxmze teraton number of optmzaton ha been reached. V w* V C* rand()*( pbet x) C2* rand ()*( gbet x) (5) x x V, (6) 2 D V where =[ V, V... V ] refer to the velocty of partcle, and repreent the next drecton and tep 2 length; X =[X,... D X X ] refer to the current poton of partcle,pbet and gbet repreent the found optmal poton of ndvdual partcle and entre populaton relatvely. w mean weght,t manly ued to carry out the tradeoff between global and local optmzaton capacte.c and C 2 refer to acceleratng factor,and they relatvely repreent the change of local and global approxmaton rate. rand() refer to the random value among [0,]. Sequental Quadratc Programmng (SQP) method a local optmzaton method, propoed by Wlon n 963 [3, 8]. It convert the orgnal problem nto QP ub-problem, partcularly utable for nonlnear programmng problem. Th paper ue PSO to conduct global optmzaton. When the global optmal convergence threhold le than a certan threhold, SQP wll be ued for local optmzaton wthn global optmum. The algorthm decrpton hown a follow:. Intalze the velocty and poton of partcle, and calculate each partcle ndvdual optmum and the global optmum of whole warm. 2. Updatng velocty and poton wth regard to Eq. 2 and Eq. 3, a well a updatng on partcle ndvdual optmum and global optmum of the warm. 3. Determne whether the convergence threhold of partcle global optmum le than a certan et value. If ye, conduct SQP for local exploraton by ettng the global optmum a the ntal pont, and ntal optmzaton range a boundary. Otherwe, go to tep Determne whether the termnaton condton of optmzaton ha been reached. If ye, then termnate. Otherwe, go to tep Ftne Functon A t requre forward channel to obtan the dynamc charactertc of ytem whle conductng 3

4 ytem dentfcaton, functon f(x)= t yydt - ' therefore elected a the objectve functon. Durng the begnnng tage, a Pade perform a delay approxmaton, the devaton of ytem dentfcaton large, but t relatvely mall. However, n the late proce, the approxmaton devaton gettng maller, and t ntead, gettng larger. Therefore, t good to conduct dentfcaton on forward channel, o a to obtan the dynamc charactertc of ytem. In addton, functon f(x)= yy - p dt play a ftne functon whle tunng the ytem, th further help enure mall dcrepancy of ytem. Addtonally, n actual ndutral practcal, the decay rato of ytem output uually controlled at a certan rato between 4: to 0:, thereby th contrant added n when tunng the ytem Contrant Condton Formaton of Forward Channel Model Optmzaton Identfcaton Baed on Proce Informaton In order to make the obtaned forward channel model to match actual proce object, t neceary to get the etmate value of the forward channel through extractng the proce nformaton from cloed-loop data, and then approprately expand them to form an effectve optmzaton earch pace. Therefore contrant (7) ued to get earch pace though expandng the extracted proce parameter, and et them a the optmzaton earch range for the forward channel model parameter to be dentfed. /a*x a*x, (7) _etmate x _etmate For the actual ndutral applcaton, the proportonal gan K c of controller and K of proce object are uually requred to atfy the contrant of 0 K c* K 3.5 [6]. Wth combnaton of the above two proportonal gan of the proce object, contrant (8) therefore ued to confrm the optmzaton range of controller proportonal gan K. mpact on the effect of optmzaton. The lnear decreae weght adopted n th paper, where the parameter n th paper ue w max =0.9, w mn =0.4, and C =C 2 = Data Length To enure the data ued n cloed-loop dentfcaton fully repreent the actual proce object dynamc charactertc, the electon of approprate data length of great mportance [5, 9]. Regardng engneerng experence, the electon of data length can be condered to ue the formulaton 50 N or 50T. Baed on the above two N T T 50 50T opton, th paper ue N=max(, ) to T T decde data length The Optmzaton and Identfcaton Method Ung Forward Channel Model Baed on Cloed-loop Proce Informaton Contrant In order to mprove the veratlty of forward channel cloed-loop model dentfcaton method baed on forward channel, the SOSPD model elected a the model to be dentfed. Ealy to fnd that, through the table cloed-loop proce nformaton that baed on PI/PID control, combned wth Eq. 2 ~ 4, the etmaton of tme contant T and T 2, gan K and delay tme contant τ, of the forward channel model can be ealy obtaned. By further ung contrant (7) and (8), the optmzaton range of the forward channel can alo be decded. Next, comprehenvely ntegrate the PSO global optmzaton ablty wth SQP local earch capablty, and conduct parameter dentfcaton on forward channel model, o a to obtan proce object dynamc charactertc. The flow chart hown n Fg 2. [max(0,/ * ),mn(3.5/, * )] a K c _ etmate K a K c _ etmate () The Optmzaton Parameter of PSO The weght w of PSO play the role of balancng the partcle local and global earch capablte. When the weght large, the populaton ha trong global optmzaton ablty. Smlarly, the partcle warm perform trong local earch ablty whle the weght mall. Learnng factor C, C 2 repreent the learnng ablty of partcle from ndvdual optmum and global optmum repectvely. It ha a great Fg. 2. The dentfcaton method for forward channel model optmzaton baed on cloed-loop proce nformaton contrant. 4

5 5. Smulaton 5.. The Valdty of Method In order to tet and verfy the valdty of the propoed method, the followng proce object elected: -6 e G () (20)(4 ) By ung PI controller and t tranfer functon gven a follow: Gc() Kc( ) T Conductng mulaton reearch wth the propoed method Etmaton of Proce Object Tme Delay Whle conductng the dentfcaton of ytem dynamc charactertc, elect Kc=.286, T= a [3]. Smlarly, when decdng the delay tme, et amplng nterval T=0.2, and elect the ampled data wth t= 0 to 200 T. Regardng δ wthn 0 to 400 T. The varaton curve of n u (- ) y () hown n Fg. 3, where δ at the = peak equal 57 T, that.4, therefore the etmaton of delay tme τ_etmate equal.4. alo further obtan the oluton range of proce object parameter, whch can be ued a the PSO- SQP optmzaton range a well Optmzaton Identfcaton for Forward Channel Regardng the extracted proce object parameter, we ue contrant (7) and contrant (8) to obtan the followng optmzaton contrant: T T K Regardng delay, t can ue frt-order or econdorder Pade approxmaton. Wth propoed cloedloop dentfcaton method baed on forward channel, we can get forward channel model. Here the tme delay approxmated by frt-order Pade approxmate: G ( ) * (8.467 )(3.933) 9.47 In order to verfy the valdty of the model, the output correlaton curve of real object model and forward channel model hown n Fg. 4, whch how that the forward channel obtaned by propoed cloed-loop dentfcaton method can tmulate the dynamc charactertc of real proce object. Fg. 3. Correlaton coeffcent regardng tme delay Acquton of Proce Object Parameter Regardng the acquton of proce object parameter, we ue known controller parameter and Eq. 3 to conduct revere oluton, thu we got the etmaton value T _etmate=8.8377, T 2 _etmate=9.488, K_etmate= We can Fg. 4. Comparon for forward channel and orgnal ytem output The Applcablty of Forward Channel Identfcaton Model In order to further verfy the valdty of the dentfed forward channel, we conder ung PI/PID parameter tunng to verfy the dentfed forward channel applcablty. 5

6 5.2.. Tunng Model Baed on Forward Channel The block dagram of the cloed tunng model baed on forward channel model hown n Fg. 5. Fg. 5. PI/PID controller parameter tunng model baed on forward channel Optmzaton Tunng of PI/PID Parameter Through dentfcaton, the parameter of forward channel can be obtaned. Wth Eq. 3 and Eq.4, we can get the etmaton value of controller parameter. Then, we ue contrant (7) and (8) to obtan the value range of controller parameter and further ue PSO-SQP algorthm to get the PI/PID controller tunng parameter baed on forward channel. The ytem output correlaton curve of forward channel before and after PI controller parameter tunng hown n Fg. 6. And Fg. 7 how the real proce output correlaton curve wth PI controller parameter orgnal and optmal reult obtaned from tunng baed on forward channel model. The controller parameter and ytem performance ndex before and after optmzaton tunng hown n Table and Table 2 repectvely, the orgnal parameter et a [3], whch can be regard a experence value. Regardng Fg. 7 and Table 2, the ytem output curve after forward channel tunng, how better compared wth orgnal controller control performance. Fg. 7. Correlaton curve of orgnal ytem before and after tunng. Table. Comparon PI parameter of before and after tunng. Controller Parameter Proportonal Gan P Integraton Tme T Orgnal Controller Parameter Controller Parameter of after Tunng Table 2. Comparon of PI controller performance ndex. Performance Index Orgnal After Tunng Overhoot/% Re Tme/ Adjutment Tme/ From above, we have already verfed the propoed method valdty and applcablty on cloed-loop table loop nvolved wth PI controller. We need further verfy the method applcablty on cloed-loop table ytem wth PID controller. Whle ung PID controller, t tranfer functon : G c + Td ()=K c (+ )( ) T T d + N Fg. 8 how the ytem output curve of before and after tunng, and Table 3 dplay the comparon of control performance ndex. Through Fg. 8 and Table 3, we can ee that the control effect of both ytem dentfcaton and tunng method baed on forward channel ha been mproved compared wth orgnal controller parameter. Table 3. Comparon of PID controller performance ndex. Fg. 6. Correlaton curve of forward channel before and after tunng. Performance Index Orgnal Sytem Overhoot/% Re Tme/ Adjutment Tme/ After Tunng Sytem

7 Fg. 8. Correlaton Curve of orgnal ytem before and after PID parameter optmzaton tunng. Fg. 9. Comparon for forward channel and orgnal ytem output The Ant-Jammng of Identfcaton Method At the proce object output, we add n colored noe of 5 %-0 % to teady-tate value, and ue the propoed dentfcaton method and the tunng method above to verfy the valdty and avalablty of the dentfcaton method. Fg. 9 how the comparon of ytem dentfcaton output and orgnal ytem actual output, a well a ther charactertc output conderng the noe added n. Fg. 0 how the comparon of ytem charactertc output though adoptng the controller parameter after tunng baed on forward channel model and that of the orgnal controller parameter. From Fg. 9 and Fg. 0, t can be een that the propoed dentfcaton method ha a certan ant-jammng capablty. 6. Concluon The propoed forward channel optmzaton dentfcaton method baed on cloed-loop operaton data. The proce charactertc nformaton contrant are etmated ealy from cloed-loop proce data and cloed-loop table PI/PID controller parameter. And the optmzaton earch pace of the relatve parameter n the forward channel kllfully defned by etmated proce charactertc nformaton. It therefore effectvely help undertand the optmzaton proce of global traveral and local earch. The obtaned forward channel better to ft wth the dynamc charactertc of cloed-loop ytem. The mulaton reearch how the effectvene of th propoed method, and PI/PID controller tunng reult by ung the dentfed forward channel model qute well. It verfe the applcablty of the propoed cloed-loop model optmzaton dentfcaton method. Regardng the ndutry proce, for a large number of applcaton of PI/PID control loop, t can help enure the proce ytem afety, and ha a wde range of ndutral practcal applcaton propect. Fg. 0. Charactertc curve of before and after orgnal ytem tunng. Acknowledgement The work upported by Natonal natural cence foundaton of Chna (637466), the HI-Tech Reearch and Development Program of P. R. Chna (2007AA04Z70) and The Natural Scence Foundaton of Nngbo (202A6000). Reference []. Pan Ldeng, Pan Yangdong, Sytem dentfcaton and modelng, t ed., Chemcal Indutry Pre, 2004, pp [2]. Wang Wehe, Wang Png, Identfcaton method and applcaton of econd order plu tme delay model, Journal of Control and Intrument n Chemcal Indutry, Vol. 9, No. 37, 200, pp [3]. Jn Qbng, Wu Dengfeng, An dentfcaton method of cloed-loop baed on PSO optmzaton, Journal of Control and Intrument n Chemcal Indutry, Vol. 2, No. 37, 200, pp [4]. Ma Junyng, Luo Yuanhao, Development of a knd of oftware to dentfy the parameter of PID model and the flter parameter of a cloed-loop PID ytem wth NLJ, Journal of Bejng Unverty of Chemcal Technology, No.4, 2004, pp [5]. T. Hagglund, Automatc on-lne etmaton of backlah n control loop, Journal of Proce Control, No. 7, 2007, pp [6]. Zhang Suofeng, L Png, Tunnng of PID parameter baed on mproved partcle warm optmzaton 7

8 algorthm, Journal of Indutral Intrumentaton & Automaton, No. 2, 202, pp [7]. Urban Forell, Lennart Ljung, Cloed-loop dentfcaton revted, Journal of Automatca, No. 35, 999, pp [8]. Zhang Wedong, Xu Xaomng, Quanttatve performance degn for nteractng proce wth tme delay, Journal of Automatca, No. 35, 999, pp [9]. N. N. Parkh, S. C. Patwardhan, R. D. Gud, Cloed loop dentfcaton of quadruple tank ytem ung an mproved ndrect approach, IFAC Proceedng Volume (IFAC-Paper Onlne), Vol. 8, Iue PART, 202, pp [0]. M. Shamuzoha, Moonyong Lee, IMC-PID controller degn for mproved dturbance rejecton of tmedelayed proce, Journal of Indutral & Engneerng Chemtry Reearch Ind. Eng. Chem. Re., Vol. 46, No. 7, 2007, pp []. Nkhl Arora, Lorenz T. Begler, A trut regon algorthm for equalty contraned parameter etmaton wth mple parameter, Journal of Computatonal Optmzaton and Applcaton, Vol. 28, Iue, 2004, pp [2]. Alexander Horch, A mple method for detecton of tcton n control valve, Journal of Control Engneerng Practce, Vol. 7, No. 0, 999, pp [3]. Adan O Dwyer, Handbook of PI and PID controller tunnng rule, Imperal College Pre, [4]. J. Kennedy, R. Eberthart, Partcle warm optmzaton, n Proceedng of the IEEE Internatonal Conference on Neural Network, Petth, VA, 27 November December 995, Vol. 4, pp [5]. Elangehwaran Pathmanathan, Rodazl Ibrahm, Vjanth Sagayan Arvadam, CO2 Emon Model Development Employng Partcle Swarm Optmzed - Leat Squared SVR (PSO-LSSVR) Hybrd Algorthm, n Proceedng of the 4 th Internatonal Conference on Intellgent and Advanced Sytem, ICIAS 202, 202, Vol., pp [6]. Sun Y., Xong H. Job-hop chedulng problem baed on partcle warm optmzaton algorthm, Senor & Tranducer, Vol. 6, Specal Iue, November 202, pp [7]. S. Svagamaundar, D. Svakumar, Etmaton of valve tcton ung partcle warm optmzaton, Senor & Tranducer, Vol. 29, Iue 6, 202, pp [8]. Xu Wenxng, Geng Zhqang, Chao partcle warm optmzaton algorthm ntegrated wth equental quadratc programmng local earch, Journal of Control and Decon, No. 4, 202, pp [9]. T. Hagglund, A control-loop performance montor, Journal of Control Engneerng Practce, Vol. 3, No., 995, pp Copyrght, Internatonal Frequency Senor Aocaton (IFSA) Publhng, S. L. All rght reerved. ( 8