DESIGN OF MULTILOOP CONTROLLER FOR THREE TANK PROCESS USING CDM TECHNIQUES

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1 DESIGN OF MULTILOOP CONTROLLER FOR THREE TANK PROCESS USING CDM TECHNIQUES N. Kngsb 1 nd N. Jy 2 1,2 Deprtment of Instrumentton Engneerng,Annml Unversty, Annmlngr, , Ind ABSTRACT In ths study the controller for three tnk mult loop system s desgned usng coeffcent Dgrm method. Coeffcent Dgrm Method s one of the polynoml methods n control desgn. The controller desgned by usng CDM technque s bsed on the coeffcents of the chrcterstcs polynoml of the closed loop system ccordng to the convenent performnce such s equvlent tme constnt, stblty ndces nd stblty lmt. Controller s desgned for the three tnk process by usng CDM Technques; the smulton results show tht the proposed control strteges hve good set pont trckng nd better response cpblty. KEYWORDS Coeffcent dgrm method, three tnk, multloop, CDM-PI 1. INTRODUCTION Most of the processes ndustry n power plnts, refnery process, rcrfts nd chemcl ndustres re multvrble or mult-nput mult-output (MIMO) nd control of these MIMO processes re more complcted thn SISO processes. The strteges re used to desgn controller for the Sngle nput nd sngle output (SISO) process cnnot be ppled for Mult nput nd mult output (MIMO) process becuse of the more ntercton between the two loops. The dfferent methods hve been presented n the lterture for control [1] of MIMO process. Proportonl-ntegrl-dervtve (PID) or Proportonl-Integrl (PI) bsed controllers re used very commonly to control three tnk systems. Generlzed synthess method used to tunng the controller prmeters. Generlly the two types of control schemes re vlble to control the MIMO processes. The frst control scheme or multloop control scheme, where sngle loop controller re used to n the form of dgonl mtrx s one.. The second scheme s [3] multvrble controller known s the centrlzed controller. Mtrx s not dgonl one. In ths pper, the Coeffcent Dgrm Method (CDM) cn be used to desgn controller for MIMO process. Now the CDM s well estblshed pproch to desgn controller, whch provdes n outstndng tme domn chrcterstcs of closed loop systems. Bsclly the CDM s bsed on pole ssgnment, whch cn locte of the closed-loop system re used to obtned the predetermned vlues. Although t hs been used to demonstrte the desgn bsed on CDM. It hs some robustness nd s possble to see tht of the smooth response wthout oscllton n chnge n the model of the process exsts. 2. COEFFICIENT DIAGRAM METHOD The CDM desgn procedure s quet esly understndble, effcent nd useful. Therefore, the coeffcents of the CDM controller polynomls whch cn be determned more esly thn the PID DOI: /jsc

2 controller strteges. The CDM desgn procedure effcent desgn method (CDM) s possble to desgn very good controllers wth less effort nd esy when compred wth the other method, under the condtons of stblty, tme domn performnce nd robustness. The trnsfer functon of the numertor nd denomntor of the system re obtned ndependently ccordng to stblty nd response requrements.. Generlly the order of the controller desgned by CDM s lower thn the order of the plnt. when usng the PI controller for the frst order plnt, the order of the controller s equl to the order of the plnt, nd for the second order plnt, the order of the controller s lower thn the order of the plnt equl to one.the prmeters re stblty ndex γ equvlent tme constnt nd stblty lmt γ * whch represent the desred performnce. The bsc block dgrm of the CDM desgn for sngle-nput-sngle-output system s shown n Fg. 1.Where y s the output sgnl, r s the reference sgnl, u s the controller sgnl nd d s the externl dsturbnce sgnl. N(s) nd D(s) re to be numertor nd Denomntor of the plnt trnsfer functon. A(s) s the denomntor polynoml of the controller trnsfer functon, F(s) nd B(s) re clled the reference numertor nd the feedbck numertor polynomls of the controller trnsfer functon. The CDM controller structure they re smlr to ech other. It hs Two Degree of Freedom (2DOF) control structure becuse of two numertors n controller trnsfer functon. The system output s gven by N(s)F(s) A(s)N(s) y (s) = r + d (1) P(s) P(s) n P(s) =A(s) D(s) +B(s) N(s) = s = 0 (2) Where P(s) s the chrcterstcs polynoml of the closed loop system. The CDM desgn prmeters wth respect to the chrcterstc polynoml coeffcent whch re equvlent tme constnt τ, stblty ndex γ nd stblty lmt γ re defned s τ = 1 0 (3) 2 γ, 1 = = ~(n-1), γ 0 = γn (3b) * γ = + (3c) From equton (3-3c), the coeffcents nd the trget chrcterstc polynoml P trget (s) s gven by = τ 1 j j = 1 γ j 0 = Z 0 (4) P trget(s) = 0 (5) n = j= 1 ( τs) + τs + 1 γ j j 12

3 Fg.1: Bsc block dgrm of CDM 3.CONTROLLER DESIGN USING CDM Mny of the processes n ndustry re descrbed s Frst order process wth tme dely (FOPTD) Gp (s) = Kp θs e τ p s + 1 (6) Where k p s process gn s tme constnt nd s tme dely. Snce the trnsfer functon of the process s of two polynomls, one s numertor polynoml N(s) of degree m nd other s the denomntor polynoml D(s) of degree n where m n, the CDM controller polynoml A(s) nd B(s) of structure shown n Fg 1re represented by A (s) = p q l 0 s ndb(s) = k 0 S (7) = = The controller to be relzed for the condton p q must be stsfed. For better performnce the degree of controller polynoml chosen s mportnt. The controller polynoml for FOPTD process wth numertor Tylor s pproxmton s chosen s A(s) = s B(s) = k 1 s +k 0 (8) (8b) The determnton of the coeffcent of the controller polynoml n CDM pole-plcement method s used. The feedbck controller s chosen by pole-plcement technque then feed forwrd controller s determned so s to mtch the closed loop system stedy-stte gn. Hence, polynoml dependng on the prmeters k nd l s obtned. Then, trget chrcterstc polynoml P trget(s) s obtned by plcng the desgn prmeters nto Eqn 5. Equtng these two polynomls s obtned, whch s known to be Dophntne equton. A(s) D(s) + B(s) N(s) = P trget (s) (9) Solve these equtons the controller coeffcent for polynoml A(s) nd B(s) s found.the numertor polynoml F(s) whch s defned s pre-flter s chosen to be F(s) = P(s)/N(s) S=0 = P (0)/N (0) (10) 13

4 Ths wy, the vlue of the error tht my occur n the stedy-stte response of the closed loop system s reduced to zero. Thus, F(s) s computed by F(s) = P(s)/N(s) S=0 = 1/k p (11) 4. CDM-PI CONTROLLER The trnsfer functon model of conventonl PI controller s G c (s) = kc (1+ ) (12) The controller gn kc nd ntegrl tme T re relevnt wth polynoml coeffcent s k 1 =kc nd k 0 =kc/t. By pplyng the CDM, the vlues of k1 nd K 0 cn be clculted s follows: 1) To fnd the equvlent tme constnt 2) The stblty ndex γ 1 = 3, γ 2 = 4.5 re used. 3) From the Eqn.(2), derve the chrcterstc polynoml wth the PI controller stted n Eqn (12) nd equtes to the chrcterstc polynoml obtned from Eqn(14). Then the prmeters k1nd K 0 of the PI controller re obtned. 4) Chose the pre-flter B(s) = K 0 nd G f (s) s feed forwrd controller G f (s) = F(s) k 1 = 0 = (13) B(s) k 1 s + 1 T s THREE TANK PROCESS Fg.2: Equvlent block dgrm of CDM The three-tnk process tken for study [6] s shown n Fg 2. The controlled vrbles re the level of the tnk1 (h1) nd level of the tnk3 (h3)nd Mnpulted vrbles re n flow of tnk1 (fn1) nd n flow of tnk3 (fn3). The stedy stte opertng dt of the Three-tnk system s gven n Tble1. The mterl blnce equton for the bove three-tnk system s gven by dh1 fn1 Az1 = 2g(h1 h2) (14) dt s1 s1 dh2 AZ1 Az3 = 2g(h1 + h2) 2g(h2 h3) (15) dt s2 s2 14

5 dh3 fn3 Az3 Az2 = + 2g(h2 h3) + 2gh3 (16) dt s3 s3 s3 Tble.1 Stedy stte opertng prmeters of three tnk process h1, h2, h3 n m 0.7,0.5,0.3 fn1 nd fn3 n ml/sec 100 Outflow coeffcent (Az1, Az2, Az3) Are of tnk (S1-S3)n m Accelerton due to grvty n m/sec e-5,3.057e-5,2.307e-5 Fg.3: Schemtc dgrm of three tnk process 6. SIMULATION RESULTS AND DISCUSSION In ths work, the coeffcent dgrm method bsed control system s consdered for the three tnk system under nomnl opertng condtons. The mn objectve of ths process s to control the level of Tnk1 nd Tnk3. The coeffcent dgrm method s desgned bsed on the thorough knowledge of the three tnk process. Also the PI controller prmeters for the nterctng three tnk process re obtned by utlzng drect synthess method. The controller prmeters of three tnk system re obtned by usng drect synthess method for the closed loop system. The controller settngs for loop1 Kc1= , T1= nd for loop2 Kc2=1.4589, T2= The mult loop CDMPI controller s obtned wth tme constnt =10 nd found to be Kc1=2.1720, T1=0.111nd tmeconstntτ=15 Kc2= T2= for loop 1 nd loop2 respectvely. The open loop response of the process s shown n Fg.4.The closed loop response of the three tnk process for set pont chnge n tnk1 from ts opertng vlue of 0.7m to 1m s shown n Fg.5 nd ts correspondng effect of ntercton n tnk3.fg. 6 shows the closed loop response of tnk3 for set pont chnge of 0.3 m to1.0 from ts opertng vlue nd ts correspondng effect of ntercton n tnk1 nd ther vlues re tbulted n Tble 2. Wth sme opertng condtons, smultons runs re crred out for drect synthess bsed three tnk processes for comprtve study. The smulted servo responses re stored n Fg.7 nd Fg 8. The performnce ndces re clculted n terms of settlng tme, Integrl Squre Error (ISE) nd Integrl Absolute Error (IAE) nd vlues re 15

6 chrted n Tble 2. From the tble t s observed tht ntellgent fuzzy control system gves stsfctory performnce thn the PI controller. The servo nd regultory responses re plotted n Fg.9 to 12.The servo trckng nd regultory responses re plotted n Fg. 13 to 16. The performnces of these controllers re evluted nd tbulted n Tble 6. From the tble, t s clerly ndctes tht the control ugmented the control system s consderbly reduced the effect of lod dsturbnce n the process vrble compred to the PI controller. Fg 4. Open loop Response of the three tnk process Fg5. Closed loop response of three tnk process wth set Pont chnge n Tnk-1(Conventonl PI-Controller) Fg6. Closed loop response of three tnk process Wth set pont chnge ntnk-3(conventonl PI-Controller) 16

7 Fg7.Closed loop response of three tnk process wth set pont chnge n Tnk-1(CDM-PI) Controller Fg8. Closed loop response of three tnk process Wth set pont chnge n tnk-3(cdm-pi) Controller Fg9. Servo trckng response of three tnk process n Tnk-1(Conventonl PI-Controller) Fg10.Servo trckng response of three tnk process n Tnk-3(Conventonl PI-Controller) 17

8 Fg11. Servo trckng response of three tnk process n Tnk-1(CDM-PI) Controller Fg12.Servo trckng response of three tnk process n Tnk-3(CDM-PI) Controller Fg13. Servo trckng nd Regultory response of three tnk process n Tnk-1Conventonl PI-Controller Fg14. Servo trckng nd Regultory response of three tnk process ntnk-3conventonl PI-Controller) 18

9 Fg15. Servo trckng nd Regultory response of three tnk process n Tnk1 (CDM-PI) Controller Fg16. Servo trckng nd Regultory response of three tnk process n Tnk-3(CDM-PI) Controller Controller scheme PI Controller CDM-PI Controller Tble.2 Performnce nd evluton of the controllers Controller Prmeters LOOP-1 LOOP-2 ts ISE IAE ts ISE IAE

10 7. CONCLUSION Interntonl Journl on Soft Computng (IJSC) Vol. 5, No. 2, My 2014 In ths work the Multloop CDM-PI controller s desgned for three tnk process nd compred wth the conventonl PI controller desgned by Synthess tunng method through smulton. The ts, ISE nd IAE re tken s performnce ndces. The superorty of the CDM-PI control s nlyzed nd clerly shows tht more potentl dvntges of usng CDM-PI control for three tnk process. The control technque hs good set pont trckng wthout ny offset wth better settlng tme. The comprson of these bove two controllers clerly shows tht CDM-PI controller s superor resultng n smoother controller output wthout osclltons whch would lke ncrese the ctutor lfe. 8. REFERENCES [1] S.Abrhm Lncon., D.Svkumr., J.Prksh Stte nd Fult Prmeter Estmton Appled To Three-Tnk Bench Mrk Relyng On Augmented Stte Klmn Flter., ICGSTACSE Journl, Volume 7, Issue 1, My [2] M.Zhung nd D.P. Atherton (1994), PID controller desgn for TITO system, IEEP process controls Theory Appl., Vol. 141 no.2pp [3] A. Nderlnsk (1971), A heurstc pproch to the desgn of lner multvrble ntegrtng control system, Automtc, vol.7, [4] P.J. Cwthrop (1987), Contnuous-Tme self-tunng Control, Vol.1-Desgn, Reserch Studes Press, Letchworth, UK. [5] Q.G. Wng, B. Zou, T.H. Lee ndq. B (1996), Auto tunng of multvrble PID controllers from decentrlzed rely feedbck, Automtc, vol.33, no.3, pp [6] S. Mjh (2001), "SISO controller for TITO systems", presented t the Int. Cn on Energy. Automton nd nformton Tech. [7] S.Skogestd, I.Postlehwte (1996), Multvrble Feedbck Control Anlyss nd Desgn, John Wley & Sons Chchester. [8] S.Mnbe (1998), Coeffcent Dgrm Method, Proceedngs of the 14th IFAC Symposum on Automtc Control n Aerospce, Seoul. [9] KAstrom nd T. Hgglund (1995), PID Controllers: Theory Desgn nd Tunng, Instrument Socety of Amerc, 2nd Edton. [10] I. Ky (1995), Auto tunng of new PI-PD Smth predctor bsed on tme domn specfctons, ISA Trnsctons, vol.42 no.4, pp [11] S.Mnbe (1994), A low cost nverted pendulum system for control system educton, Proc. of the 3rd IFAC Symp. On dvnces n control Educton, Tokyo. [12] A.Desbens, A. Pomerlu nd D. Hodoun (1996), Frequency bsed tunng of SISO controller for two by-two processes, IEE Proc. Control Theory Appl., Vol.143, pp [13] M.Senthlkumr nd S. Abrhm Lncon (2012), Desgn of stblzng PI controller for coupled tnk MIMO process, Interntonl Journl of Engneerng Reserch nd Development, Vol.3 no. 10: pp [14] S.E Hmmc, I. Ky nd M.Koksl (2001), Improvng performnce for clss of processes usng coeffcent dgrm method, presented t the 9th Medterrn conference on control, Dubrovnk. [15] S.E. Hmmc (2004), Smple polynoml controller desgn by the coeffcent dgrm method, WSEAS Trns. on Crcuts nd Systems, v.3, no.4, pp [16] S.E. Hmmc nd M. Koksl (2003), Robust controller desgn for TITO systems wth Coeffcent Dgrm Method s, CCA 2003 IEEE Conference on Control Applctons. [17] W.L Luyben (1986), Smple methods for tunng SISO controllers n multvrble systems, Ind. Eng. Chem. Process Des. Dev