Design of Fractional Order PID controller for a CSTR process

Transcription

1 Internatonal Refereed Journal of Engneerng and Scence (IRJES) ISSN (Onlne) X, (Prnt) Volume 3, Issue 1 (January 014), PP Desgn of Fractonal Order PID controller for a CSTR process J.Poovarasan 1, R.Kayalvzh, R.K.Pongannan 3 1 (Department of EEE, Pondcherry Engneerng College, Pondcherry, INDIA) (Department of Instrumentaton Engg, Annamala Unversty, Annamala Nagar, Taml Nadu, INDIA) 3 (Department of EEE, Avvayar College of Engg & Tech for Women, Pondcherry, INDIA) Abstract:- Contnuous Strred Tank Reactor (CSTR) sometmes nvolves complex reactons wth hgh nonlnearty. To handle these problems, modern control strategy called Fractonal Order PID controller has been revewed. Fractonal order controller s wdely used n most areas of scence and engneerng, beng recognzed ts ablty to yeld a superor control n many dynamcal systems. For sothermal CSTR, FOPID controller s mplemented to control a nonlnear process. Ths work proposes the applcatons of a Fractonal Order PID (FOPID) controller n the area of Process Control for a CSTR Process to evaluate the use of Fractonal Order PID controller wth soft computng technques. To desgn Fractonal Order PID controller s to determne the two mportant parameters λ (ntegrator order) and μ (dervatve order). In ths artcle that the response and performance of Fractonal Order PID controller s compared wth closed loop conventonal PID controller. Keywords:- Conventonal PID, CSTR process, FOPID, Genetc algorthm, PSO I. INTRODUCTION Reacton systems nvolvng materal recycles are very usual n process ndustry. There are several types of strred reactors used n chemcal or bochemcal ndustry. CSTR s commonly used because of ts technologcal parameters [1] []. Isothermal CSTR nvolves complex reactons wth hgh nonlnearty. However ther operaton s corrupted wth varous uncertantes. Some of them arse from varyng or not exactly known parameters such as reacton rate constants, heat transfer coeffcents. In other cases, operatng ponts of reactors vary or reactor dynamcs s affected by varous changes of parameters or even nstablty of closed loop control systems. In general, PID controller produces long rse tme when the overshoot n output response decreases. In order to tackle ths problem and mprove the dynamc response of CSTR process, a Fractonal Order PID controller has been used. The desgn aspects of the controllers based on several soft computng technques. A Fractonal Order PID controller has been used to regulate the process parameters wthn a specfed tolerance lmt. A very mportant aspect of desgnng FOPID controllers s to decde upon the values of K P, K, K d, λ and μ. The Genetc algorthm and Partcle Swarm Optmzaton Algorthms are used for tunng the FOPID controller. Fractonal order dynamc systems and controllers have been ncreasng n nterest n many areas of scence and engneerng n the last few years. Controllers consstng of fractonal order dervatves and ntegrals have been used n ndustral applcatons such as power electroncs [3], system dentfcaton [4], robotc manpulators [5], etc., It should be noted that there are a growng number of physcal systems whose behavour can be compactly determned usng the fractonal order system theory and can be controlled wth Fractonal Order Proportonal-Integral-Dervatve (FOPID) controllers [6]. The present work deals wth the desgn and control of a Contnuous Strred Tank Reactor process. The contrbuton of ths work conssts manly n the desgn of K P, K, K d, λ and μ values are fndng usng Genetc algorthm and Partcle swarm optmzaton technque to desgn the Fractonal order PID controller and compared wth conventonal one. The development and mplementaton of the proposed controller was done usng MATLAB/Smulnk. II. CONTINUOUS STIRRED TANK REACTOR PROCESS The temperature control of a strred-tank heater system s reported as a classcal problem n chemcal engneerng. The complexty of the problem has been enhanced n the current study by changng smple tank to a reactor carryng out known reacton and also complete controller (both PID and FOPID) mechansm has been adopted. The analyss s extended further to stablty of the system and optmzaton of the controller parameters along wth a study on effect of reacton mechansm and other system parameters. The graphcal dagram of the CSTR process s shown n Fg.1. A contnuous strred tank reactor wth a non sothermal reacton A + B Products and wth frst order rate equaton ((-ra) = k CA) s consdered. The tank has external heatng col wth heat nput Q (kj/mn) and the tank temperature s controlled by a controller n the closed loop feedback crcut as depcted n Fgure 1. The temperature of the tank s measured at the outlet. 8 Page

2 Desgn of Fractonal Order PID controller for a CSTR process 1. Modelng of Isothermal CSTR The Contnuous Strred Tank Reactor wth sngle nput and sngle output s shown n Fg. 1. Here sothermal seres-parallel reacton (Van der Vusse reacton) s consdered to study the steady state and dynamc behavour of CSTR. The two reactons are: A BC A D (1) A Cyclopentaddene, B Cyclopentenol, C Cyclopentanedol, D Dcyclopendtadene Fgure 1: Isothermal CSTR The desred product n the reacton s spces B, the ntermedate product n the prmary reacton, whch ncreases the dffculty to control. The rates of formaton of A and B are assumed to be: r A 1 A 3cA k c k () rb k1ca k cb (3) Where k1, k, k3are the reacton rate constants. The feed stream conssts of pure A. The mass balances for A and B are gven by the followng Eq. (4) & (5): d(ca) F (CAf CA) K1CA K3CA (4) dt V d(cb) F CB K1CA KCB (5) dt V The steady state equatons are: C As Fs Fs Fs K1 K1 4K3 V V V (6) K K 3 3 K1CAs CBs (7) Fs K V These modellng equatons assume a constant volume. The equatons for C C and C D are neglected because C B s not dependent on them. The manpulated nput n ths system s dluton rate. The parameters of the reactor are gven n Table I. Parameter Table I: CSTR parameters. Value K 1 50h -1 K 100h -1 K 3 C Af 1/6 mol/lter mn 10gmol/lter 9 Page

3 Desgn of Fractonal Order PID controller for a CSTR process These results lead to the steady-state response of the CSTR as shown n the Fg.. For an sothermal CSTR steady state nput-output can be obtaned by relatng dluton rate and concentraton of component B. Fg. : Steady-State response of the CSTR The Complexty nvolved n conventonal modellng of CSTR ncreases due to the presence of nonlneartes lke nput multplcty, gan sgn change, asymmetrc response and transformaton from mnmum to non- mnmum phase behavour and tme lag n measurng nstruments forcng to make many assumptons, sacrfcng the accuracy due to the neglgence of uncertanty. Inaccuracy n the modellng due to varous assumptons gves degraded performance of controller. In the present work soft computng technques are used to develop better and more effcent non lnear model of CSTR. III. FRACTIONAL ORDER PI D CONTROLLER The most common form of a fractonal order PID controller s the PI λ D μ controller nvolvng an ntegrator of order λ and a dfferentator of order μ where λ and μ can be any real numbers. The transfer functon of such a controller has the form U(S) 1 GC(s) kp ki kds,(, 0) (8) E(S) S Where Gc(s) s the transfer functon of the controller, E(s) s an error, and U(s) s controller s output. The ntegrator term s 1 s λ, that s to say, on a sem-logarthmc plane, there s a lne havng slope -0 λ db/decade. The control sgnal u(t) can then be expressed n the tme doman as u(t) k e(t) k D e(t) k D e(t) (9) p I D Fg. 3 show the block-dagram confguraton of FOPID. Clearly, selectng λ = 1 and μ = 1, a classcal PID controller can be recovered. The selectons of λ = 1, μ = 0, and λ = 0, μ = 1 respectvely corresponds conventonal PI & PD controllers. All these classcal types of PID controllers are the specal cases of the fractonal PI λ D μ controller gven by (7). Fg. 3 Block dagram confguraton of Fractonal Order PID controller It can be expected that the PI λ D μ controller may enhance the systems control performance. One of the most mportant advantages of the PI λ D μ controller s the better control of dynamcal systems, whch are descrbed by fractonal order mathematcal models [8]. Another advantage les n the fact that the PI λ D μ controllers are less senstve to changes of parameters of a controlled system. 10 Page

4 Desgn of Fractonal Order PID controller for a CSTR process IV. GENETIC ALGORITHM Evaluaton of performance crtera s manly based on measures of the system error. The system error s defned as the dfference between the desred response of the system and ts actual response. In the present work, GA based optmzaton technque s used to tune the PID and Fractonal Order PID controller parameters mnmzng the Integral Square Error. The technque uses genetc algorthm to tune the PID and FOPID parameters for a mnmum performance ndex for each operatng regon of the CSTR process. The transfer functon of the PID controller s gven by 1 d GC(S) KC KI KD (10) S dt V. PARTICLE SWARM OPTIMIZATION PSO s an evolutonary computatonal technque based on the movement and ntellgence of swarms lookng for the most fertle feedng locaton. A swarm s an apparently dsorganzed collecton (populaton) of movng ndvduals that tend to cluster together, whle each ndvdual seems to be movng n a random drecton. PSO uses a number of agents (partcles) that consttute a swarm movng around n the search space lookng for the best soluton [9-11]. Each partcle s treated as a pont n an n-dmensonal space and adjusts ts flyng accordng to ts own flyng experence, as well as the flyng experence of other partcles. Each partcle keeps track of ts coordnates n the problem space, whch are assocated wth the best soluton (ftness) that has been acheved so far. Ths value s called pbest. Another best value called gbest s that obtaned so far by any partcle n the neghbours of the partcle. The PSO concept conssts of changng the velocty (or acceleraton) of each partcle toward ts pbest and the gbest poston at each tme step. Each partcle tres to modfy ts current poston and velocty accordng to the dstance between ts current poston and pbest, and the dstance between ts current poston and the gbest. At each step n, by usng the ndvdual best poston, pbest, and global best poston, gbest, a new velocty for the th partcle s updated by, V x(v (n 1) r (pbest P (n 1)) r (gbest P (n 1))) (11) 1 1 Fg. 4. Block dagram confguraton of controller wth soft computng technques VI. SIMULATION RESULTS A controller s robust f t results n actual closed loop behavor that does not devate unacceptably from the nomnal closed-loop behavor whch n turn, corresponds to nomnal process behavor. The smulnk model of the proposed system shown n Fgs.5 and 6. The Nomnal Response of proposed controller for CSTR process for step nput, waveform for set pont change of 0% ncrement and decrement at tme perod of 100 & 00 sec and waveform for lne dsturbance of 5% ncrement and decrement at tme perod of 100 & 00 sec are shown n Fgs. 7,8 and 9 respectvely. The Performance and analyss of CSTR process wth PID and FOPID usng GA and PSO algorthms shown n table II A m B m C m 0 1 For sothermal CSTR nomnal plant s gven by 11 Page

5 Level n cm Level n cm Desgn of Fractonal Order PID controller for a CSTR process Transfer functon model s gven by z T.F z 1.586z Fg.6. Smulnk of FOPID controller wth CSTR Process GA PID PSO PID -0.4 GA FOPID PSO FOPID Tme n sec Fg.7. Nomnal Response of proposed controller for CSTR process for step nput GA PID PSO PID GA FOPID PSO FOPID Tme n sec Fg.8. waveform for set pont change of 0% ncrement and decrement at tme perod of 100 & 00 sec. 1 Page

6 Level n cm Desgn of Fractonal Order PID controller for a CSTR process GA PID PSO PID GA FOPID PSO FOPID Tme n sec Fg.9. waveform for lne dsturbance of 5% ncrement and decrement at tme perod of 100 & 00 sec. Table.II Performance and analyss of CSTR process wth PID and FOPID usng GA and PSO algorthms CONTROLLER Proportonalty Integral Dfferental Lamda Cost Mue () & ALGORITHM Gan (K p ) Gan (K ) Gan (K d ) () (ISE) GA PID PSO PID GA FOPID PSO FOPID VII. CONCLUSION It s generally not possble to derve an accurate model of a process or plant especally wth nonlneartes. If a relable model s not avalable, t s qute dffcult to desgn a controller producng desred outputs. When the data set does not represent the whole operatng range adequately, the model to be obtaned wll not be as robust. Tradtonal modellng technques are rather complex and tme consumng when we ncorporate entre dynamcs of the process. However, soft computng technques namely Genetc Algorthm and Partcle Swarm Optmzaton have been used to obtan best model parameters. In the present work, modellng of CSTR was carred out usng the above soft computng technques. The model formulated captures the nonlnearty present n the CSTR. The model thus developed can be used n desgnng model based control schemes, such as PID and FOPID controllers whch offers robust controller performance. REFERENCES [1]. Anton A. Kss, Costn S. Bldea, Alexandre C. Dman, Pet D. Iedema, State ultplcty n PFR separator recycle polymerzaton systems, Chemcal Engneerng Scence 58, Elsever, 003, pp []. Mohd Fuaad Rahmat, Amr Mehd Yazdan, Mohammad Ahmad Movahedand Somayeh Mahmoudzadeh, Temperature control of a contnuous strred tank reactor by means of two dfferent ntellgent strateges, nternatonal journal on smart sensng and ntellgent systems vol.4, no., June011, pp [3]. A.J. Calder on, B.M. Vnagre, V. Felu, Fractonal order control strateges for power electronc buck converters, Sgnal Processng, 86(), 006, [4]. M. Schlegel, M.ech, Fractal system dentfcaton for robust control - the moment approach, Proceedngs of the 5th Internatonal Carpathan Control Conference, 004, 004. [5]. N.M. Fonseca Ferrera, J.A. Tenrero Machado, Fractonal-order hybrd control of robotc manpulators, 11 th Internatonal Conference on Advanced Robotcs, 003, [6]. I. Podlubny, Fractonal-order systems and PI λ D µ controllers, IEEE Transactons on Automatc Control, 44(), 1999, [7]. B.M. Vnagre, C.A. Monje, A.J. Calder on, J.I. Suarez, Fractonal PID controllers for ndustry applcaton: a bref ntroducton, Journal of Vbraton and Control, 13(),007, [8]. C.A.Monje, Y.Q.Chen, B.M.Vnagre,D.Xue, V.Felu, Fractonal order systems and controls, ISSN , Sprnger London Dordrecht Hedelberg newyork, 010 [9]. F.L. Lews, D.M. Dawson, C.T. Abdallah, Control of Robot Manpulators, New York, Macmllan, Page

7 Desgn of Fractonal Order PID controller for a CSTR process [10]. J. Kennedy, R.C. Eberhart, Y. Sh, Swarm Intellgence, New York, Morgan Kaufmann, 001. [11]. R.C. Eberhart, J. Kennedy, A new optmzer usng partcle swarm theory, Proceedngs of the Sxth Internatonal Symposum on Mcro Machne and Human Scence, pp , [1]. B. Wayne Bequette, Process control: Modellng, Desgn and Smulaton, Sprnger-Verlag London Lmted, 009, pp , AUTHOR BIOGRAPHY J.Poovarasan was born n Pondcherry, Inda. He has obtaned M.E (Electroncs and Instrumentaton) from Annamala Unversty, Chdambaram n 004. Currently he s pursung hs Ph.D n Annamala Unversty, Chdambaram n the Department of Electroncs and Instrumentaton. Hs areas of nterest are power converters, controllers desgn and applcatons. R.Kayalvzh was born n Chdambaram, Inda, on She has obtaned B.E (Electrcal and Instrumentaton) and M.E (Power Systems) n 1984 and 1988 respectvely from Annamala Unversty. She completed Ph.D n same unversty on ntellgent control strateges. She has put n a total servce of more than 5 years. Her research nterests are n DC -DC converter modellng, smulaton and mplementaton. R. K. Pongannan obtaned B.E. Degree from CIT, Combatore, Inda, n 1995, M.E. degree from the PSG Tech, Combatore, n 004 and Ph.D from Jawaharlal Nehru Technologcal Unversty Hyderabad, Inda, n 010. Currently, He s a Professor/EEE, Avvayar College of Engg & Tech for Women, Pondcherry, Inda. He s the author or coauthor of more than 30 papers n nternatonal journals and conferences. He s a Revewer for IEEE TRANSACTIONS ANDINDER SCIENCE JOURNALS. Hs research nterests nclude power electroncs & drves. 14 Page