DESIGN OF MODEL REFERENCE ADAPTIVE CONTROLLER FOR CONICAL TANK SYSTEM

Transcription

1 14 JRT Volume 1 ue 7 SSN: DESGN OF MODEL REFERENCE ADAPTVE CONTROLLER FOR CONCAL TAN SYSTEM.ndhumath, D.Angelne Vjula, M.E., Ph.D Sr Ramarhna Engneerng College, Combatore. Abtract-The control of lqud level mandatory n roce ndutre. Many roce ndutre ue concal tan becaue t revent the accumulaton of old at the bottom of the tan. The Proortonal-ntegral (P) controller commonly ued to control the level n roce ndutre. The non-lnearty and contantly changng cro ecton of the concal tan are the mmene challenge n roce control. n th aer t rooed to obtan the mathematcal modelng of a concal tan ytem and to degn model reference adatve controller (MRAC) for controllng the level n concal tan ytem. The controller mulated ung MATLAB/ SMULN envronment and the reult confrm the effectvene of the rooed ytem than the conventonal method. ndex Term- Concal tan ytem, Model reference adatve controller. MC tuned P, Z-N tuned P.. NTRODUCTON The concal tan ytem wdely ued n many roce ndutre becaue t contrbute better dranage of the lqud old mxture, lurre. The level control of the concal tan dffcult becaue of t nonlnearty and contantly varyng cro ecton. The P and PD controller are wdely ued n many ndutral control ytem becaue of t mle tructure and robutne. Tunng of the P controller ettng the roortonal, ntegral contant. The mot common clacal controller tunng method are the Zegler Nchol (Z-N) and Cohen-Coon method. Snce t eaer than other method. nternal model control (MC) tunng offer an alternatve tunng to ncreae the controller overall erformance. n MRAC a reference model decrbe the ytem erformance. The adatve controller then degned to force the ytem (or lant) to behave le the reference model. Model outut comared to the actual outut and the dfference ued to adjut feedbac controller arameter. Therefore th technque convenent for controller degn under the requrement of the ytem. The ecton two reent the hardware decrton of the concal tan ytem. The ecton three exlan the modelng of the ytem. The ecton four rovde the P controller degn. Z-N tunng and MC tunng exlaned. The ecton fve deal wth the MRAC controller degn. The reult are obtaned and the comaron done n the ecton x. The ecton even gve the concluon and future enhancement.. HARDWARE DESCRPTON The concal tan made u of tanle teel and mounted vertcally on the tand. The water enter nto the tan from the to and leave to the reervor, whch laced at the bottom of the tan. The level of the water n the concal tan quantfed by mean of the Dfferental Preure Tranmtter (DPT). The quantfed level of water n the form of current n the range of (4- ) ma ent to the DAQ n whch ADC convert the analog data to dgtal data and feed t to the PC. The PC act a the controller and data logger. The controller conder the roce varable a feedbac gnal and fnd the manulated varable a the outut baed on the redefned et ont. The DAC module of the anulated varable to analog form nto 4- ma current gnal. The /P converter convert the current gnal to reure n the range of (3-15), whch regulate the flow of water nto the concal tan baed on the outflow rate of the tan. The bloc dagram of concal tan ytem hown n Fg.1 Fg.1. Bloc dagram of concal tan ytem. MODELNG OF CONCAL TAN PROCESS JRT 1143 NTERNATONAL JOURNAL OF NNOVATVE RESEARCH N TECHNOLOGY 68

2 Level(cm) 14 JRT Volume 1 ue 7 SSN: MATHEMATCAL MODELNG The cro ecton of the concal tan hown n Fg.. Fg..Concal tan where Q n - nflow rate n lh Q o - outflow rate n lh R- Maxmum radu of the tan n cm H- Maxmum heght of the tan n cm r- radu of the tan tan at teady tate n cm h- heght of the tan tan at teady tate n cm Accordng to ma balance equaton Accumulaton =nut-outut dv Qn Q (1) The volume of the concal tan can be exreed a equaton () dh A Qn Q () Where A the Area of the Tan A r (3) So the heght of the tan, dh Where Q h n h 3 (4) v Above equaton (4) Non lnear form, Lnearaton done ung Taylor ere method Lnearaton of Q n h, f h h f Q Q f h, Q f h Q h Q (5) 3 Lnearaton of h, h 3 h 3 3 h 5 h h (6) Now alyng teady tate value y= (h-h ) andu=(q- Q ). The aroxmate lnear model obtaned a, dy y U 5 h 3 5 h (9) Above equaton mle that the concal tan ytem frt order ytem. The teady tate heght h = cm condered. Correondng gan and tme contant value are calculated. The tranfer functon exreed n equaton (1).578 G ( ) (1) Ung the above Tranfer functon et ont wll not be reached exactly. Offet error wll be reent n the ytem. So, ntead of analytcal modelng Bloc box modelng done. V. (8) BLOC BOX MODELNG loc box modelng ued to obtan the arameter of the tranfer functon of the FOPDT model by lettng the reone of the actual ytem and that of the model to meet at two ont, whch decrbe the two arameter τ and t d. The loo made oen and a te ncrement (3 lh) gven n nflow rate then readng are noted tll the ytem reache the teady tate value. The exermental data are aroxmated to a Frt Order Plu Dead Tme (FOPDT) model to obtan the oen loo arameter of the concal tan roce. The reone hown n Fg (7) Fg.3. Oen loo reone of concal tan ytem The tranfer functon aroxmated ung roce reacton curve method exreed by equaton (11). JRT 1143 NTERNATONAL JOURNAL OF NNOVATVE RESEARCH N TECHNOLOGY 69

3 14 JRT Volume 1 ue 7 SSN: e G( ) V. P CONTROLLER DESGN (11) The P controller cont of roortonal and ntegral term. The roortonal term change the controller outut roortonal to the current error value. Large value of roortonal term mae the ytem untable. The ntegral term change the controller outut baed on the at value of error. So, the controller attemt to mnmze the error by adjutng the controller outut. The mot common clacal controller tunng method are the Z-N and Cohen-Coon method. The Z-N method can be ued for both cloed and oen loo ytem, whle Cohen-Coon tycally ued for oen loo ytem. V. ZEGLER NCHOLS TUNNG Z-N oen loo tunng formula for P controller gven n the equaton.9 (1) t d (13) The calculated P gan arameter are, = 36.4 =.11 V. NTERNAL MODEL CONTROL TUNNG nternal model control tunng alo referred a Lambda tunng method offer a robut alternatve tunng amng for eed. Lambda tunng a form of nternal model control (MC) that endow a P controller wth the ablty to generate mooth, non-ocllatory control effort when reondng to change n the et ont. The MC baed tunng arameter for P controller can be obtaned by determnng the controller equaton. Otherwe drectly the arameter can be calculated by ung the formulae t d (14) (15) Aumng =5 ec, The calculated P gan arameter are, = =.4 V. MODEL REFERENCE ADAPTVE CONTROLLER A tunng ytem of an adatve control wll ene thee arametrc varaton and tune the controller arameter n order to comenate for t. The arametrc varaton may be due to the nherent non-lnearty of the ytem uch a concal tan. n a concal tan the cro ecton area vare a a functon of level whch n turn lead to arametrc varaton. The tme contant and gan of the choen roce vary a a functon of level. n MRAC a reference model decrbe the ytem erformance. The adatve controller then degned to force the ytem (or lant) to behave le the reference model. Model outut comared to the actual outut and the dfference ued to adjut feedbac controller arameter. MRAC ha two loo: an nner loo (or regulator loo) that an ordnary control loo contng of the lant and the regulator, and an outer (or adataton) loo that adjut the arameter of the regulator n uch a way a to drve the error between the model outut and lant outut to zero. Bloc dagram of MRAC hown n Fg.4. Fg.4. Bloc dagram of MRAC trategy Tracng error, y y e (16) m The cot functon, 1 J e (17) d J e e (18) JRT 1143 NTERNATONAL JOURNAL OF NNOVATVE RESEARCH N TECHNOLOGY 63

4 Level(cm) Level(cm) Level(cm) 14 JRT Volume 1 ue 7 SSN: where e denote the model error and θ the controller arameter vector. γ denote the adataton gan. ntead of θ the P controller arameter P, are condered. So the, 1 e a a 1 b b Smlarly Parameter, 1 e X. a a 1 b b b b U U c c Y Y SMULATON RESULTS (19) () The cloed loo reone obtaned for Z-N tuned P. Both the ervo and regulator oeraton are obtaned. n the ervo oeraton only et ont tracng done. n the regulator oeraton, the urbance can be corrected automatcally and dered level obtaned. The cloed loo reone of Z-N tuned P hown n Fg Fg.6 Reone of MC tuned P controller n MRAC a reference model decrbe the ytem erformance. Model outut comared to the actual outut and the dfference ued to adjut feedbac controller arameter. The Servo and Regulatory reone hown n Fg Tan level Set ont 1 Tan level Set ont 1 Tan level Set ont Model outut Fg.5. Reone of Z-N tuned P controller The nternal Model Control tunng ued to obtan the cloed loo reone. Both ervo and regulator oeraton are obtaned a hown n Fg Fg.7 Reone of MRAC To Comare the Controller acton varou arameter uch a re tme, ea tme, ea overhoot and ettlng tme are taen. Comaron of Z-N tuned P, MC tuned P, MRAC for et ont 1 cm hown n Table. TABLE : Quanttatve Comaron of Z-N tuned P, MC tuned P, Adatve P controller for etont=1cm Controller Settlng Re AE JRT 1143 NTERNATONAL JOURNAL OF NNOVATVE RESEARCH N TECHNOLOGY 631

5 14 JRT Volume 1 ue 7 SSN: Z-N tuned P Controller MC tuned P Controller MRAC Comaron of Z-N tuned P,MC tuned P, MRAC for et ont 3 cm hown n Table. Table : Quanttatve Comaron of Z-N tuned P, MC tuned P, Adatve P controller for etont=3cm Controller Settlng Re AE Z-N tuned P Controller MC tuned P Controller MRAC A hown n above table n MRAC the ntegral Abolute Error (AE) reduced when comared to the P controller. The ettlng tme alo reduced n MRAC whch mean t gve the fater reone. X. CONCLUSON AND FUTURE ENHANCEMENT Concal tan ytem hghly nonlnear becaue of t varable cro ecton. The Conventonal P controller and Model Reference Adatve Controller are mlemented n mulaton. MRAC gve the better erformance. P controller and Model Reference Adatve Controller are to be mlemented for real tme to control the Level of Concal Tan ytem. Adataton Gan n MRAC to be Otmzed ung Otmzaton Technque. REFERENCES [1] Abhhe Sharma and Nthya Venatean (13), Comarng P controller Performance for Non Lnear Proce Model, nternatonal Journal of Engneerng Trend and Technology, Vol.4, No.3, [] Anand, S., Awn, V. and umar, S.R. (11), Smle Tuned Adatve P Controller for Concal Tan Proce, Recent Advancement n Electrcal, Electronc and Control Engneerng, [3] Angelne Vjula,D., Devarajan,N., (14), Degn of Decentraled P Controller ung Model Reference Adatve Control for Quadrule Tan Proce, nternatonal Journal of Engneerng and Technology, Vol.5, No.6, [4] Anna Joeh and Samon aac, J. (13), Real Tme mlementaton of Model Reference Adatve Controller for a Concal Tan, nternatonal Journal of Theoretcal and Aled Reearch n Mechancal Engneerng, Vol., No.1, [5] Bhuvanewar, N.S., Uma, G. and Rangawamy, T.R. (9), Adatve and Otmal Control of a Non-Lnear Proce ung ntellgent Controller,Aled oft comutng, Vol.9, No.1, [6] Boonrmuang,P.,Numomran,A.,angwanrat,S., (9), Degn of P Controller ung MRAC Technque for Coule-Tan Proce, nternatonal Scence ndex,vol.3, No.11, [7] Ganeh Ram, A.,Abraham Lncoln, S. (13), A Model Reference-baed Fuzzy Adatve P Controller for Nonlnear Level Proce Sytem', nternatonal Journal of Reearch and Revew n Aled Scence,Vol.14, No., [8] George Stehanooulo (1984) Chemcal Proce Control, Prentce-Hall ublcaton, New Jerey, Eatern Economy Eon. [9] ala, H., Aravnd, P. and Valluvan, M. (13), Comaratve Analy of dfferent Controller for a Nonlnear Level Control Proce, Proceedng of EEE Conference on nformaton and Communcaton Technologe, [1] eavan, E. and Raeh umar, S. (13), PLC baed Adatve PD Control of Non Lnear Lqud Tan Sytem ung Onlne Etmaton of Lnear Parameter by Dfference Equaton,nternatonal Journal of Engneerng and Technology, Vol.5, No., [11] Marhana, D. and Thruathmurugan, P. (1), Degn of Zegler Nchol Tunng Controller for a Non-lnear Sytem, Proceedng of nternatonal Conference on Comutng and Control Engneerng, JRT 1143 NTERNATONAL JOURNAL OF NNOVATVE RESEARCH N TECHNOLOGY 63

6 14 JRT Volume 1 ue 7 SSN: [1] Mchael L. Luyben and Wllam L. Luyben (1997), Eental of Proce Control, McGraw-Hll ublcaton, Sngaore, nternatonal Eon. [13] Nthya, S., Svaumaran, N., Balaubramanan, T. and Anantharaman, N. (8), Model baed Controller Degn for a Shercal Tan Proce n Real Tme,nternatonal Journal of Smulaton, Sytem, Scence and Technology, Vol. 9, No.3, [14] Nthya Venatean,Anantharaman, N. (1), Controller Degn baed on Model Predctve Control for a Non-Lnear Proce, Mechatronc and t alcaton (SMA), EEE,Vol.5, No.1,.1-6. [15] Panaj Swarnar,Shalendra Jan,Nema,R.., (11), Effect of Adataton Gan n Model Reference Adatve Controlled Second Order Sytem, Engneerng, Technology & Aled Scence Reearch,Vol.1, No.3, [16] Praah, R., Anta, R. (11), Neuro- P Controller baed Model Reference Adatve Control for Nonlnear Sytem, nternatonal Journal of Engneerng, Scence and Technology,Vol.3, No.6, [17] Satheeumar, J., Satheehumar., Poongod, P., Rajaearan,., (1),Modellng and mlementaton of LabVEW Baed Non-lnear P Controller for Concal Tan, Journal of Control & ntrumentaton Vol.1, No.1,.1-9. [18] Ratharan Duraamy, Svaumar Dahnamurthy, (1), An Adatve Otmzaton Scheme for Controllng Ar Flow Proce wth Satfactory Tranent Performance, Maejo nternatonal Journal of Scence and Technology Vol.3, No., [19] Sowmyal, P., Srvgneh, N., Svaumaran, N. and Balaubramanan, G. (1), A Fuzzy Control Scheme for Nonlnear Proce, Proceedng of nternatonal Conference on Advanced Engneerng Scence and Management, JRT 1143 NTERNATONAL JOURNAL OF NNOVATVE RESEARCH N TECHNOLOGY 633