03, TextRoad Publcaton ISSN 090-4304 Journal of Basc and Appled Scentfc Research www.textroad.com PI-Controller Adjustment Usng for a Laboratory Scale Contnuous Strred Tan Heater Mohammad Ahmad, Mohammadsoroush Sohelrad* Department of Electrcal Engneerng, Bandarabbas Branch, Islamc Azad Unversty, Bandarabbas, Iran ABSTRACT In ths paper, a PI type controller s tuned to control the level and temperature of a Contnuous Strred Tan Heater (CSTH). The PI parameters are adjusted by usng Partcle Swarm Optmzaton () method. A laboratory scale CSTH s consdered as plot to show the proposed method. The effectveness of the proposed method llustrates by a comparson between the -PI controller and two other PI controllers whch are desgned and optmzed by Zegler-Nchols (Z-N) and Genetc Algorthms (GA). The smulaton results confrm the valdty of the as the proposed method to adjust the PID type controller n compare wth the ZN-PI and GA-PI controllers. KEY WORDS: Partcle Swarm Optmzaton, Genetc Algorthm, Zegler-Nchols, PI Controller, CSTH, Interactng System.. INTRODUCTION Interactng systems are used more commonly than no nteractng systems n the ndustry. These systems are utlzed to have a constant temperature, perfect mxture and plan densty. A laboratory sze Contnuous Strred Tan Heater (CSTH) n seres wth a Feedng Tan and a crculaton pump can be defned as an nteractng system for educatonal purposes. By usng a system whch conssts of these three elements a wde varety of control problems and ssues such as nonlnearty, lnearzaton, coupled and decoupled loops, tme delay and others, can be studed and solved. Hence nteractng systems have hgh sgnfcance n process control systems for theoretcal and practcal studes and analyss [- ]. PID controller s a mechansm whch efforts to reduce the dfference between measured varable and reference value of a process by calculatng and dong desred acton that can modfy the performance. Ths regulaton s done by changng n three parameters whch are nown as K P, K I and K D respectvely. PI controller n comparson wth the other control devces and algorthms plays a ey role n the ndustry and control purposes [3, 4, 5, 6]. It s nown as the frst and sometmes the best soluton for the control problems and overcomes all other advanced controllers. In spte of so many advantages such as the capablty to be used n most processes control systems, straghtforward and uncomplcated n use and smple mplementaton, sometmes the other controllers can be more useful than PI controllers [6].In most cases the man problem orgnates from the PI parameters desgn. Tradtonally, ths problem has been solved by a relatvely smple tral and error method. Durng the prevous decades more systematc approaches such as Zegler-Nchols and Cohen- Coon have been presented [6]. Control practtoners show much more nterest to Zegler-Nchols tunng formula n compare wth the other tunng rules. Some researchers use Evolutonary Computaton (EC) methods to desgn a PID controller. [7,8,9] apples GA to adjust a PID controller. In [0] a fuzzy-genetc method s appled for auto tunng of a PID controller. Ths paper s amed to show an applcaton of Partcle Swarm Optmzaton (), by tunng a PIcontroller for a laboratory scale CSTH such that the output llustrates the preferred propertes. can converge to the optmum values much faster than the other optmzaton methods. Moreover, the optmum values whch are found by have the less cost n compare to the other optmzaton methods. Smulaton results prove these facts and ndcate that the -PI controller has an mproved performance ndex n compare to the GA and ZN methods. The scentfc contrbutons of ths paper are: ) the fast convergence of n order to fnd the optmum values n compare to the other algorthm. ) Show the less cost of functon 3) repeatablty of the for optmzaton process. Apart from ths ntroductory secton, ths paper s organzed as follows. The plant under study s descrbed n secton. The tunng methodology s explaned n secton 3 and PI controller adjustment s developed n secton 4. As a fnal secton, the smulaton results are presented and dscussed n secton 5. *Correspondng Author: Mohammadsoroush Sohelrad, Department of Electrcal Engneerng, Islamc Azad Unversty, Bandarabbas, Iran. Emal:sohel.phd@gmal.com 3
Sohelrad and Ahmad, 03. PLANT MODEL: A two tans CSTH control rg s consdered as the plot system and shown n Fgure. The lqud flows n a loop from upper to the lower tan by effect of gravty and from the lower to the upper tan usng the pump []. Fgure. Process control rg [] The schematc dagram of the process control rg s shown n fgure. The amount of lqud flows n and of tan s controlled by valve and valve respectvely []. F Process Tan T Heatng H A T col F T F T 3 T 3 H Connectng Tan Fgure.Process control rg dagram []. Tan has an electrc heater whch controls the lqud temperature. The man am s to control the level and temperature of the lqud (dstlled water) n tan by controllng the lqud nlet flow and the heatng power. The bloc dagram of the CSTH whch conssts of the transfer functons of the systems shown n fgure 3 []. 4
Fgure 3.Process bloc dagram [] The system constants and ntal condtons and also the symbol are gven n the appendx. [].By usng the decouplng blocs the CSTH has been consdered as a system wth two blocs whch formed a nonnteractng system.in fact, system has been changed from a MIMO to two SISO to remove the couplng effects among the two systems whch are level system and temperature system[]. The level system transfer functon s: G (s) = 4577.8 s + () And the temperature system transfer functon s defned as: G (s) = 80.7 s +.00034.57 s + 0.047 s + (.53 0 )( e. ) () 3. DESIGN METHODOLOGY: As mentoned n the frst secton, a PI controller s amed to control the CSTH system. s used to obtan the parameters of ths PI controller. The structure of the PID controllers whch s defned n (3) s formed by three parameters. PI Controller = K + K S (3) A. Partcle Swarm Optmzaton (): was proposed by Eberhart and Kennedy n 995. The socal behavor a group of brds, and also the decson mang procedure of human bengs are the man thought behnd ths algorthm. s smlar to the GA n the ntalzaton s step whch has to start wth a populaton; but, wors wthout evoluton operators such as crossover or mutaton. The populaton n s called partcles whch ncludes the values of varables and also s not encoded n the form of bnary. The partcles moveover the objectve surface wth an ntal velocty and then try to update ther veloctes and postons after each teraton based on ther local and global best postons as mentoned n (4) and (5) []: v v c rand pbest s c rand gbest s (4) where: v s s v (5) v = present velocty of agent at teraton, = new velocty of agent at teraton, C = adjustable cogntve acceleraton constants,c = adjustable socal acceleraton constant, s = present poston of agent at teraton, pbest = personal best of agent, 5
Sohelrad and Ahmad, 03 gbest = global best of the populaton. For (5): s denotes the poston of agent at the next teraton +, The velocty vector s updated by the for each partcle then the new velocty adds the postons or values of the partcle. Velocty updates procedures are affected by two factors: one s the best global poston whch s defned as the lowest cost found by a partcle and the other s the best local poston whch s defned as the lowest cost n the current populaton. The man advantages of are the ease of mplementaton and also the mnmum amount of parameters whch are needed to tune. The s capable to fnd the best solutons for the cost functons whch have many local mnmum [].Fgure 4.llustrates the general flowchart for the technque. Start Intalzaton of prelmnary condton for each agent STEP Calculaton of cost of each searchng pont STEP Revson of each searchng pont STEP3 NO Termnaton crtera met? YES Stop Fgure 4. Steps n [] B. Descrpton of the Tunng Methodology: The SISO system and ts related tunng algorthm whch s used n ths paper s shown n fgure 5. The steps for tunng were mentoned n prevous secton. The velocty and postonal algorthms defne the search wthn the soluton space. Followng each teraton, the mpact of each agent s poston wthn the search space s evaluated accordng to the cost functon. R (s) E (s) U (s) Y(s) C (s) P (s) + - Compute performance Crteron for each agent Fgure 5.Postonng of the wth n a SISO system 6
The mnmzaton of the cost functon provdes a global quantfcaton of overall system performance. The parameters used for the all smulatons usng the are gven n Table.. Table. Parameters Parameter Value Maxmum Iteratons 50 Maxmum Velocty (Vmax) Cogntve Acceleraton (c) Socal Acceleraton (c) Weght ( W ) 0.9 4. PI-CONTROLLER TUNING USING : In ths secton, the algorthm s used to tune the parameters of the proposed PI controllers. The PIcontroller has two parameters whch are symbolzed by K P and K. Because of the order of the CSTH system, two PI controllers are suffcent for the control purposes. Therefore n two control loops wth two PI - controllers, there are four parameters whch need to be tuned and found by usng the. The optmum values of K P and K are perfectly calculated usng. In optmzaton methods, t s essental to defne a performance ndex to fnd the optmum values. In ths paper, the performance ndex s defned as (6) whch s nown as the Integral of the Absolute Error (IAE). IAE e t dt 0 In IAE, t s defned as the smulaton tme. It s clear that a controller whch shows the lowest IAE value would be selected as the most effcent controller. To fnd the optmum values for the parameters, the tres to mnmze the performance ndex whch s the IAE. In order to attan better performance, the optmum number of teraton, the amount of partcles and also the partcle sze are chosen as 4, 50 and respectvely. These parameters have been determned by a tral and error method to fnd the optmum values for ths partcular problem. It should be mentoned that for ths study, the algorthm s run 50 tmes and then the optmum values are selected. The optmum values presented n the Table. Table. -PI Optmum Values PI Parameters K p K Iteraton Cost Level.73. 4 8.59 Temperature 4.5.33 34 0.8 5. RESULT AND DISCUSSION: In ths secton, the results from the proposed -PI controller whch s appled to the CSTH are presented and dscussed. In order to compare and llustrate the effcency of the based scheme, two other PI- controllers whch are adjusted by ZN and GA are desgned and tuned for CSTH. Table 3, summarzes the optmum values of the parameters for both the ZN-PI and GA-PI controllers. Table 3. ZN-PI Controller Optmum Values PI Parameters K p K Iteraton Cost ZN Level.5.9-9.3 Temperature 4.78.08-5.07 (6) The level system step response s shown n Fgure 6. GA Level.9.4 43 8.83 Temperature 4.53.4 45 3.8 7
Sohelrad and Ahmad, 03.4. Process Out Put 0.8 0.6 0.4 0. ZN GA Step 0 4 6 8 0 4 6 8 0 4 Tme (sec) Fgure 6.Level System Response The temperature system step response n shown n Fgure 7..6.4. Process Output 0.8 0.6 0.4 0. GA ZN Setp 0 5 0 5 0 5 30 35 40 Tme (sec) The results ndcate that generates better responses n compare to the GA and ZN. From Table and3 t s clear that the s able to tune the PI parameters not only n lower cost whch s 8.59 for level system and 0.8 for the temperature system but also n fewer amounts of teratons 4 and 38. The cost values for the GA are 8.83 and 3.8 whch are greater than the ones. The ZN tunng methods show the worst responses n compare to the other ones. The cost values for the ZN method are 9.3 for the level system and 5.07 for the temperature system. From fgures 5 and 6 t can be concluded that system shows better response to the controller whch s tuned by rather than the GA or ZN methods.the results are summarzed n Table 4. Table 4. PI-Controller Optmum Values PI Parameters K p K Iteraton Cost ZN Level.5.9-9.3 Temperature 4.78.08-5.07 GA Fgure 7.Temperature System Response Level.9.4 43 8.83 Temperature 4.53.4 45 3.8 Level.73. 4 8.59 Temperature 4.5.33 34 0.8 8
6. CONCLUSION In ths paper, two PI controllers has been successfully tuned to control a laboratory contnues strred tan heater by usng partcle swarm optmzaton algorthm. The smulaton results verfed that the -PIcontrollers are able to dsplay the stablty and robust performance wth a mnmum of the cost. Moreover, the results ndcated that the performance of the -PID controller s much better than the ZN and GA-PI type controllers for both level and temperature systems. The PI controllers are one of the most used controllers n the engneerng and appled systems; hence the paper s results can be used for the CSTH systems n ndustry and practcal matters. APPENDIX: System parameters and values [0] Symbol Defnton Intal Values Tan cross-sectonal area. 0.85 0.45 m Tan cross-sectonal area. 0.85 0.335 m Ppe cross-sectonal area. 0.03459 m Ppe L Ppe Cp h h m,,3 f f,3 t t t 3 Ppe length. REFERENCES [] F. Lu, J. Chen, A Desgn of Constraned Fuzzy Controller for CSTRs, IEEE Internatonal Conference on Systems, Man and Cybernetcs, 004. [] Fen Wu, LMI-based Robust Model Predctve Control Evaluated on an Industral CSTR Model, Proceedngs of the 997 EEE Internatonal Conference on Control Applcatons, Hartford, CT. October 997. [3] C. Smth, and A. Corrpo, Prncples and Practce of Automatc Process Control, Wley & sons.new Yor, 997. [4] D. Xaosong, D. Popovc, and G. Schulz-Eloff, Real tme demtfcaton and control of a contnuous strred tan reactor wth Neural Networ, IEEE, Hyderabad, Inda, 995. [5] G. Lghtbody, and G. Irwn, Nonlnear Control Structures Based on Embedded Neural System Models, IEEE Transactons On Neural Networs, VOL. 8, May 997. [6] C. Madhuranthaam, A. Elamel, and H. Budman, Optmal tunng of PID controllers for FOPTD, SOPTD and SOPTD wth lead processes, IEEE Control Systems Magazne, December 006. [7] F. Banch, R. Mantz, and C. Chrstansen, Multvarable PID control wth set-pont weghtng va BMI optmzaton, IEEE Control Systems Magazne, September 007. [8] M. Mohammad, UPFC Controller Desgn for Power System Stablzaton wth Fuzzy-PIBased Genetc Algorthm, J. Basc. Appl. Sc. Res., (0)575-584, 0. [9] M. G. Dozen, A. Gholam, M. Kalantar Speed Control of DC Motor Usng Dfferent Optmzaton TechnquesBased PID Controller, J. Basc. Appl. Sc. Res., (7)6488-6494, 0. [0] K. Âström, T. Hägglund, Revstng the Zegler Nchols step response method for PID control, Journal of Process Control, Lund, Sweden, 004. [] M.S. Sohelrad, M.M.B. Isa, M. Hojabr and S.B.M. Noor, Modelng, Smulaton an Control of a Laboratory scale Contnuous Strred tan Heater, Journal of Bascs and Appled scentfc Research,May, 0. [] J. Kennedy, R. Eberhart, andy. Sh, Swarm Intellgence, Morgan Kaufmann, San Francsco, CA, 00..67 m Lqud (water) densty. 00 g/m 3 Lqud heat capacty. Tan lqud level. Tan lqud level. Tan,,3 nlet and out let lqud mass flow rate. Tan nlet lqud volumetrc flow rate. Tan, outlet lqud volumetrc flow rate. Tan nlet lqud temperature. Tan outlet lqud temperature. Tan outlet lqud temperature. 486 J/g/C 0.07 m 0.8 m - 0.0003 m 3-3 C 30 C 7 C 9