Adaptive System Control with PID Neural Networks

Transcription

1 Adaptve System Control wth PID Neural Networs F. Shahra a, M.A. Fanae b, A.R. Aromandzadeh a a Department of Chemcal Engneerng, Unversty of Sstan and Baluchestan, Zahedan, Iran. b Department of Chemcal Engneerng, Unversty of Ferdows, Mashhad, Iran. In ths paper, PID neural wor, whch s an adaptve controller, has analyzed and compared wth two other conventonal PID algorthms through computer smulaton and expermental study. Cancellaton and pole placement are the two selected conventonal algorthms. In the smulaton study, the effects of factors such as non-mnmum phase behavor and model changes on the performance of schemes are nvestgated. In the expermental study, performance of controllers on pressure control of two seral tans s nvestgated. Smulaton and expermental results demonstrate that PID neural wor can be tuned easly and has better performance n compare wth two conventonal schemes especally n the case of non-mnmum phase behavor and model msmatch. However, t has slower dynamc n compare wth cancellaton algorthm. Introducton PID controller s the most common control algorthm s used wdely n chemcal process as could be seen n Desbourough et al. 00 and also Astrom et al. 00. Ths s because of ts good performance as long as a smple structure, n the case that t tunes well. By now, a lot of tunng schemes have been devsed such as Atherton et al. 999 Martns et al. 000 but performance of ths controller degrades durng the tme due to process non lnearty or process tme varyng parameters, so t must be retuned. Retunng such a controller beng performed through a tral and error procedure whch s a tme consumng tas and requres a sllful operator. In an adaptve PID, controller parameters automatcally and contnuously tuned n accordance wth changes of the process parameter so as explaned n Wdrow et al. 985 t could be a soluton to ths problem. In recent years, artfcal neural wors have been progressed a lot. Ther ablty to estmate every nonlnear functon wth at least one hdden layer wth suffcent neurons has been proved as reported n Hornc et al These models are data drven and extensvely used n smulaton and control of nonlnear process such as wors done by Hecht 989 and Tsen et al So n wors le Martns et al. 000, Junghu et al. 004, Andras et al. 004, desgners try to use neural wors to modfy PID controllers. Furthermore, smplcty s one of the mportant features of PID controllers so desgners try to eep ths characterstc. In schemes suggested by Wdrow et al. 985 and Junghu et al. 004 wth no maor changes n conventonal PID structure, try to use capablty of neural wors. The frst scheme uses predcton capablty of neural wors and the second one for taclng sever

2 nonlnearty of process. PID neural wor PIDNN whch s proposed by Hualln et al. 000 s a new nd of wors and ts hdden layer neurons smply wor as PID controller terms through ther actvaton functons thus t smultaneously utlzes advantages of both PID controller and neural structure. In ths paper, performance of ths drect controller whch performs an adaptve control through onlne learnng process has been studed and compared wth two other conventonal adaptve PID controllers. In the rest of the paper, after bref revew of selected schemes, ther performance analyzed and compared through computer smulaton and then by expermental study and fnally concluson s gven. Compared Schemes Structures PID neural wor As t s shown n fgure, ths controller has a smple feed forward neural wor whch conssts of -3- structure, so t has three layers. Fgure. Structure of PIDNN There are two proportonal neurons n nput layer wth followng actvaton functon. ne for recevng system settng and other for recevng process output. < > In the hdden layer three neuron of dfferent type of proportonal, ntegral and dervatve neuron exst. The actvaton functon for ntegral neuron s as followed. < + > and the actvaton functon for dervatve neuron s as followed. < > 3 In the hdden layer, the neurons nputs are w 4

3 Table. Desgn parameter for dfferent schemes Scheme Desgn parameter PIDNN α learnng rate Cancellaton φ m phase margn Pole placement p desred pole locaton Where s the number of neuron n hdden layer and s the number of neuron n nput layer. Fnally hdden layer s comprsed of one proportonal neuron whch produces controller output whle ts neuron nput s 3 w 5 o o Where s the number of neuron n hdden layer and o s the output layer s sngle neuron. Learnng of ths wor s done through onlne bac-propagaton algorthm. bectve functon for ths algorthm s as follow and the am of the PIDNN s to mnmze ths obectve functon. N J [ r y ] N 6 Where N s the total number of samplng ntervals. Conventonal schemes By now, several schemes for adaptve tunng of PID controller have been proposed as reported n Astrom et al Shahroh et al. 000 compared four adaptve schemes for tunng of PID controller. Wth regard to the result of ths wor, two schemes among them named as cancellaton by Banyacz 985 and pole placement by Torro 985 have been analyzed as a conventonal schemes n ths study. In the frst scheme, the process dynamc s modeled wth a second order model and the controller parameters are desgned to cancel the process model poles and acheve the desred phase margn. In the second scheme, the process model poles are cancelled, however the controller gan s adustment to place the closed loop pole at the desred locaton. These two models are ndrect controller, so they need an algorthm for dentfcaton of the process parameter. For ths purpose a recursve least square RLS wth varable forget factor and proposed by Fortescue et al. 98 has been used. Computer Smulaton Results In ths secton, the performance of the three mentoned algorthm nvestgated through computer smulaton. Effects of process model change and non-mnmum phase behavor are nvestgated. There s one desgn factor n accordance wth table for each algorthm. The values of these parameters are so selected to mnmze the sum of absolute error IAE as follow. IAE e t. dt 7 The sequence of model changes and ther correspondng tme ntervals are gven n table. The frst two models are of second order wth dfferent delay tme and the followng two models are of frst order wth dfferent delay tme. The ffth model s a non-

4 Table. Smulated process model samplng perod s 3 seconds. Sequence of apply Samples Contnuous model s + 40s 3 e s s + 40s s e s + 0s s 0.5 s e 3s s + mnmum phase model. The smulaton results are llustrated n fgure. As can be seen, PIDNN has much more better response n compare wth two conventonal schemes and ths s owng to the fact that t has a neural wor structure and has more robust performance as explaned n Schaloff 997. Addtonally, t needs less tral and error procedure to be tuned. a PIDNN, α 0^-5 b Cancellaton, φ m 58 c Pole placement, p 0.6 Fgure. Closed loop response

5 Expermental Results As a result of smulaton study none of two conventonal schemes act better than PIDNN. Therefore n the expermental study, PIDNN s only compared wth cancellaton scheme. Process arrangement could be seen n fgure 3. In ths process, the second tan pressure y s controlled by nput ar flow rate to the frst tan u. Fgure 3. Expermental set up If RLS does not mae good estmaton of process model cancellaton scheme performance degrade so n the begnnng of the process some Pseudo Random Bnary Sequence PRBS n the form of open loop for 0 samplng nterval s appled to the algorthm to help RLS to estmate process model. As t s shown n fgure 4, both schemes have satsfactory response but PIDNN has better performance especally n the begnnng of the control sesson. That s owng to the fact that RLS algorthm n cancellaton schemes does not mae good estmatons of process parameters despte of applyng PRBS. Furthermore cancellaton scheme has larger overshoots n compare wth PIDNN response although n the followng steps t gets better and PIDNN shows slower response. Ths s because of ts tranng algorthm whch s n the form of bac propagaton wth fx learnng rate. a PIDNN, α 0^-5 b Cancellaton, m φ 70 Fgure 4. Expermental response

6 Concluson In ths paper, PIDNN has compared wth two conventonal schemes. Results show PIDNN has better performance n compare wth cancellaton and pole placement algorthm n the case of model msmatch and also processes wth non-mnmum phase behavor. PIDNN requres less tral and error for tunng and has more robust performance. But t has slower dynamc n compare wth cancellaton algorthm. References Andras, A., Meszaros, A. and Azevedo, S. F., 004, n-lne tunng of a PID controller based on plant hybrd modellng, Computers and Chemcal Engneerng, 8, Astrom, K. J. and Hagglund, T., 00, The future of PID control, Control Engneerng Practce, 9, Astrom, K. J. and Haggland, T., 988, Automatc Tunng of PID Controllers, Instrument Socety of Amerca, Research Trangle Par. Atherton, D. P., 999, PID controller tunng, Computng & Control Engneerng, Banyacz, C. S., Hetthessy, J. and Kevczy, L., 985, An adaptve PID regulator dedcated for mcroprocessor-based compact controllers, IFAC Symp. Ident. & Syst. Para. Est., 99, New Yor. Desbourough, L. and Mller, R., 00, Increase customer value of ndustral control performance montorng-honeywell s experence, AIChE J., Symposum Seres Number 38, 98. Fortescue, T.R., et. al., 98, Implementaton of self-tunngs regulators wth varable forgettng factors, Automatca, 7, 83. Hecht, R., 989, Theory of bac-propagaton neural wors, IEEE Proceedngs of the Internatonal Conference on Neural Networs,, 593. Hornc, K., Stnchcombe, M. and Whte, H., 989, Multlayer feed-forward neural wors are unversal approxmator, Neural Networs,, 359. Hualln, S. and P, Y., 000, PID neural wors for tme-delay systems, Computers and Chemcal Engneerng, 4, Junghu, C. and Huang, T. C., 004, Applyng neural wors to on-lne updated PID controllers for nonlnear process control, Journal of Process Control, 4, -30. Martns, G. F. and Coelho, M. A. N., 000, Applcaton of feed-forward artfcal neural to mprove process control of PID-based control algorthms, Computers and Chemcal Engneerng, 4, Schaloff, R. J., 997, Artfcal Neural Networs, McGraw-Hll, New Yor. Shahroh, M. and Fanae, M. A., 000, Comparson of Four Adaptve PID Controllers, Scenta Iranca, 7, Torro, S. and Shah, S. L., 985, Adaptve PID Control, Proc. Amer. Cont. Conf., 3, Tsen, A. D., Jang, S. S. and Wong, D. S. H., 996, Predctve control of qualty n batch polymerzaton usng hybrd ANN models, AICHE, 4, Wdrow, B. and Streans, S. D., 985, Adaptve sgnal processng, Prentce Hall.