SOFT COMPUTING APPROACH TO DESIGN PID CONTROLLER FOR TANK LIQUID LEVEL CONTROL PROBLEM

Transcription

1 Journal of Engneerng Scence and Technology EUREA 4 Secal Iue January School of Engneerng, Taylor Unvery SOFT OMPUTIN APPROAH TO DESIN PID ONTROLLER FOR TANK LIQUID LEVEL ONTROL PROBLEM K. SURESH MANI, *, SARATH ANANTHASIVAM, V. RAJINIKANTH School of Engneerng, Taylor Unvery, Taylor' Lakede amu, No. Jalan Taylor', 475, Subang Jaya, Selangor DE, Malaya. Dearmen of Elecronc and Inrumenaon Engneerng, S. Joeh ollege of Engneerng, henna 6 9, Tamlnadu, Inda. *orreondng Auhor: SurehManc.Keavan@aylor.edu.my Abrac In h aer, an nvegaon ha been made o degn he be oble Prooronal Inegral Dervave PID conroller for he Hoer ye ank and Shercal ank yem. In order o denfy he omal conroller arameer, of comung cheme, uch a Parcle Swarm Omzaon, Baceral Foragng Omzaon, Frefly Algorhm, and uckoo Search are condered. In he rooed work, mnmzaon of a weghed um of Objecve Funcon OF adoed o gude he of comung echnque baed conroller degn rocedure. The qualave and quanave analy carred ou o valdae he erformance of he condered rocedure. The reul evden ha, he Brownan walk guded algorhm offer beer erformance comared o he. Keyword: Hoer ye ank, Shercal ank, PID conroller, Brownan walk, Heurc algorhm.. Inroducon Degn of arorae PID conroller wdely referred n roce ndure o enhance he quany of fnal roduc whou comromng he qualy. In he conrol leraure, a number of radonal [-4] and of comung aroach [5-7] baed PID degn rocedure are dcued by mo of he reearcher for able, unable and nonlnear yem. Even hough here ex a number of radonal unng rocedure [, 8], heurc and meaheurc algorhm baed aroache are alo condered by he reearcher n recen year [9-]. Thee of comung aroache are referred n conrol alcaon becaue of 8

2 Sof omung Aroach o Degn PID onroller for Tank Lqud Level Nomenclaure D K K d K K M Dmenon of earch Proce model Proce gan Dervave gan Inegral gan Prooronal gan Peak overhoo Selng me reek Symbol θ Proce me delay τ Proce me conan Abbrevaon BW FOPTD ITAE ITSE PID Brownan walk Fr order lu me delay Inegral me abolue error Inegral me quare error Prooronal Inegral Dervave Parcle warm omzaon mlcy, omzaon ably, and eed of reone. Due o flexbly; he of comung aroache can ealy ada wh exng clacal conroller degn rocedure. Hence, n recen day, ued a a ool o degn clacal and modfed rucured conroller for a cla of able, unable, and nonlnear roce model In h aer, of comung baed PID conroller degn rocedure dcued for hoer ank and hercal ank yem and erformance comaron reened beween algorhm, uch a Parcle Swarm Omzaon, Baceral Foragng Omzaon, Frefly Algorhm, and uckoo Search for he reference rackng and nu durbance oeraon. The aer organzed a follow: Secon reen he roblem formulaon for PID conroller degn. Proce decron dcued n Secon 3. Secon 4 reen he overvew of he heurc algorhm condered n h udy and mlemenaon. Exermenal reul are evaluaed and dcued n Secon 5. oncluon of he reen reearch work gven n Secon 6.. Problem Formulaon In order o mrove he erformance of cloed loo yem, omally uned PID conroller requred. Fgure dec he lluraon of a convenonal cloed loo conrol yem. In h, he conroller c ha o uor cloed loo ably, mooh reference rackng, and effcen durbance rejecon []. In h, c ued o mrove boh he eady ae a well a he ranen reone of. The man objecve here o make Y = R. In h framework, c connuouly adju he value of U c unl he error E zero rreecve of D. Journal of Engneerng Scence and Technology Secal Iue /5

3 84 K. Sureh Manc e al. Journal of Engneerng Scence and Technology Secal Iue /5 D E U c c Y R _ Fg.. eneral cloed loo yem rucure. The cloed loo reone of he yem wh reference R and uly durbance D can be exreed a: D R Y = where he comlemenary envy funcon and envy funcon of he above loo rereened n Eq. and 3 reecvely. = = R Y T = S 3 The fnal eady ae reone of he yem for he e on rackng and he durbance rejecon reened below A A x Y y R R = = = lm lm 4 L x lm y D = = 5 where A amlude of he reference gnal and L he durbance amlude. To acheve a afacory y R and y D, neceary o ue omally uned PID arameer value. In h aer, non-neracng form of PID rucure adoed. In h rucure, a low a fler avalable wh he dervave erm o mnmze he effec of meauremen noe. The PID rucure defned below: = T T T K f d d c N 6 where K / T = K, K x T d = K d and N f = fler conan =. 3. Proce Decron Indural yem are nonlnear n naure. Mo of he real me roce loo are characerzed by an equvalen hgher order modellng equaon. Thee nonlnear rocee can be effcenly modelled a lnear rocee baed on oerang

4 Sof omung Aroach o Degn PID onroller for Tank Lqud Level regon. In he rooed work, he FOPTD model of he hoer ank yem and hercal ank yem are condered. 3.. Hoer ank Hoer ye roce model hown n Fg. a. Th yem ha concal boom oron and cylndrcal uer oron []. In h work, we condered he concal oron alone. The concal oron hghly nonlnear n naure and develong he mahemacal model baed on he workng regon a hard job. F n F n 5 cm 5 cm 5 cm F ou F ou Fg. a Hoer Tank Syem. Fg. b Shercal Tank Syem. In h aer, he mahemacal model of he hoer ank yem wh varou oerang regon dcued by Keavan e al. [] condered. In her work, he concal oron of he ank condered and four able FOPTD model are develoed baed on he dfferen oerang regon a hown n Table. Table. Proce arameer a dfferen oerang range. Inflow Range Level range % cm 3 / cm K τ θ 4 I Regon II Regon III Regon IV Regon Shercal ank The hercal ank he one of he nonlnear yem wdely dcued by he reearcher n he leraure [3, 4]. In h work, he hercal ank yem hown n Fg. b condered. The oerang regon of he hercal ank yem choen a 8 cm. A h oerang regon, 9.549% of ank flled wh he waer 9.34 L and 7.45% flled wh he ar, and he develoed mahemacal model around he correondng oerang range reened below [4] e = Journal of Engneerng Scence and Technology Secal Iue /5

5 86 K. Sureh Manc e al. In he rooed work, he concal ank oron wh a hegh of 5 cm condered for hoer ank yem and he hercal ank wh a dameer of 5 cm condered o develo he requred FOPTD model of he yem around he oerang regon. 4. Overvew of Heurc Algorhm ondered In recen year, a conderable number of heurc and mea-heurc algorhm are rooed by he reearcher o deal wh varey of omzaon roblem. In h work, well known algorhm, uch a Parcle Swarm Omzaon, Baceral Foragng Omzaon, Frefly Algorhm and uckoo Search are condered o degn he PID conroller. 4.. Parcle warm omzaon algorhm wa rooed by Kennedy and Eberhar n 995 [5]. omared o oher agen-baed ochac omzaon echnque, offer beer exloraon erformance, faer and more able convergence rae. Alo, he number of nal algorhm arameer o be agned very few comared o oher naure-nred algorhm exng n he leraure [3]. Durng he omzaon earch, each arcle remember be oon aaned o far.e., be - P,D, and alo oban he global be oon nformaon acheved by any arcle n he oulaon.e., gbe -,D. A eraon, each arcle ha oon defned by X = X, X,..., X ] and velocy defned a V = V, V,..., V ] n earch.n [,,,D dmenon D.,n [,,,D Velocy and oon of each arcle n he nex eraon can be calculaed a V, D = W *V, D * R * P, D X, D * R *, D X, D 8 X, D = X, D V, D 9 where =,,..., ; n =,,..., D; he cognve arameer ycally ; he ocal arameer ycally ; R and R are random number n he range -; and W he weghng arameer ycally.75 [3]. 4.. Brownan walk guded algorhm In he heurc algorhm baed earch, generally he ucce oward he omal oluon moly rele on he gudng rocedure. Mo of he recenly develoed naure nred omzaon earch roce guded by Lévy Flgh LF and Brownan Walk BW raegy. In h aer, BW condered o gude algorhm, uch a, and The Brownan Walk BW a ubdffuve non-markovan roce, whch follow a auan drbuon wh zero mean and me-deenden varance. In h work, he BW recenly dcued by Raja e al. [6] adoed. Journal of Engneerng Scence and Technology Secal Iue /5

6 Sof omung Aroach o Degn PID onroller for Tank Lqud Level The followng formulae are condered Brownan drbuon = α / B = A. βπ A = βγ β n π where A he random varable, β he aal exonen, α he emoral exonen, and Γ β a amma funcon. A dealed decron of BW dcued n [6-8]. Fgure 3 how he exloraon race made by a BW guded ngle agen n a D dmenonal earch ace. When eraon ncreae, all he agen n he algorhm wll converge oward he omal value of he conroller arameer n he earch unvere. - Kd K K Fg. 3. Search race made by a ngle agen n Brownan drbuon Baceral foragng omzaon algorhm wa develoed n by mmckng he foragng behavour of E. col bacera. In he rooed work, he enhanced algorhm dcued n [4] condered. The nal algorhm arameer are agned a follow: Number of E.ol bacera = N N c = N ; N = N re 3 N ; Ned 4 N ; Nr = N ; Ped = d aracan = W aracan = N ed N Nr N ; and hreellan = W reellen = N ; N c. N In algorhm, omzaon accuracy and convergence rae deend on he chemoax oeraon and can be exreed a n Eq. [4]. θ j, k, l = θ j, k, l 3 T where θ j, k, l how h bacerum a j h chemoacc, k h reroducve and l h elmnaon-deral e; he e ze n he random drecon, and a random vecor of ze {-, }. In he rooed work, Eq. modfed a hown below: θ j, k, l = θ j, k, l B 4 T Journal of Engneerng Scence and Technology Secal Iue /5

7 88 K. Sureh Manc e al. where he ymbol rereen he enry we mullcaon, and B he Brownan walk oeraor Frefly algorhm Frefly algorhm a naure nred meaheurc algorhm nally rooed by Yang [9]. I develoed by relcang he flahng llumnaon aern generaed by he frefly. Th bolumnecence wh vared flahng aern ued o eablh communcaon beween wo neghbourng nec, o earch for ray and alo o fnd mae []. The overall erformance exloraon me, eed of convergence, and omzaon accuracy of he deend on he OF, whch monor he earch. For a mnmzaon roblem, lumnance of a frefly condered baed on he followng relaon lumnance = /OF. A dealed exlanaon abou avalable n leraure [7-]. In, he lgh neny a a arcular dance d from he lgh ource X obey he nvere quare law. The lgh neny of a frefly I, a he dance d ncreae nerm of I / d. The movemen of he araced frefly oward a brgher frefly j can be deermned by he followng oon udae equaon; X = X β γ d j e X j X α. gnrand- ½ B 5 where X udaed oon of frefly, X nal oon of frefly, β γ d j e X j walk oeraor. X he aracon beween frefle, and B he Brownan uckoo earch echnque wa nally rooed by Yang and Deb [9]. I baed on he breedng rck of arac cuckoo. algorhm ha he followng aumon [7] Each cuckoo lay an egg and deo n an arbrarly choen ne The ne wh good urvved egg wll be aroved over o he nex generaon. uckoo egg normally hache everal day before han he ho egg. The cuckoo chck grow qucker and exel he ho egg. In a earch unvere, he number of ho ne fxed. The ho brd dcover he cuckoo egg wh a robably a [,]. When he egg dcovered, ho brd may elmnae from ne, or mly abandon he ne and buld a new ne. In, durng he omzaon earch, he new oluon deend on he old oluon X X and he earch gudng rocedure. manly In h work, he followng exreon are condered o fnd he new oluon X = X α B 6 Journal of Engneerng Scence and Technology Secal Iue /5

8 Sof omung Aroach o Degn PID onroller for Tank Lqud Level where α > he ucceedng e Imlemenaon Heurc algorhm baed PID conroller unng rocedure deced n Fg. 4. For a gven roce model, he algorhm fnd he omal K, K and K d value from he earch unvere D by mnmzng he objecve funcon. In he leraure, a number of objecve funcon are exng o uor heurc algorhm baed PID degn ak. In h work, OF framed by conderng he me doman conran M, and and he error ITAE, and ITSE a reened below: J mn = w M w w3 ITAE w4 ITSE 7 [ r - y ] d 5 5 ITAE = e d = 8 [ r - y ] d 5 5 ITSE = e d = 9 where he weghe are agned a w = w = w 3 = w 4 =. Inal arameer ITAE, ITSE Heurc Algorhm M, R _ e K K K d PID U c Nonlnear Syem Y Fg. 4. Sof comung baed PID conroller unng. Pror o he omzaon earch, neceary o agn he arameer for he heurc algorhm. The nal algorhm arameer condered n he rooed work reened n Table. The algorhm allowed o exlore he earch unvere unl he OF value mnmzed. Th rocedure reeaed me and he average value of he conroller arameer choen a he be oble conroller arameer value. Table. Inal arameer of heurc algorhm condered. Parameer Maxmum Number of 5 Ieraon Poulaon of agen N 5 Search dmenon D 3 Song crera J mn Number of ral Performance meaure M,, ITAE, ITSE value Journal of Engneerng Scence and Technology Secal Iue /5

9 9 K. Sureh Manc e al. 5. Reul and Dcuon The heurc algorhm baed conroller unng rocedure demonraed ung a,,, and algorhm ung Hoer ank and Shercal ank roce model. In order o erform a far comaron, all he algorhm are agned wh he ame nomnal arameer a hown n Table. 5.. Hoer ank model Inally, he rooed conroller degn rocedure mlemened ung he Hoer ank model dcued n Secon 3.. For h ank, Keavan e al. [] develoed four FOPTD model baed on four oerang regon. Inally, he FOPTD model of I regon condered and he conroller unng rocedure execued. The of comung aroach connuouly adju he value of K, K, and K d unl he objecve funcon J mn reache a mnmal value. Durng he omzaon earch, he baed aroach converge a 49 h eraon, baed earch converge a 73 rd eraon, baed earch converge a 55 h eraon and baed earch converge a 64 h eraon. From hee reul, noed ha, offer faer convergence comared o he alernave condered n h udy. The conroller arameer obaned ung he of comung echnque hown n Table 3. The erformance of he conroller eed wh an uny reference nu and an nu durbance of 5% of reference nu.5 nroduced a econd. The roce reone and he correondng conroller reone are reened n Fg. 5 and 6 reecvely. orreondng erformance meaure value, uch a M,, ITAE and ITSE are reened n Table 3. From h, one can oberve ha, he rooed mehod uor mooh reference rackng and effecve nu durbance rejecon oeraon. Table 3. onroller value and erformance meaure value for I Regon. Mehod K K K d M ITAE ITSE Proce ouu Reference Tme ec Fg. 5. Proce ouu reone wh I Regon model. Journal of Engneerng Scence and Technology Secal Iue /5

10 Sof omung Aroach o Degn PID onroller for Tank Lqud Level onroller ouu Tme ec Fg. 6. onroller ouu reone wh I Regon model. Smlar rocedure reeaed for oher FOPTD model of he Hoer ank yem and he reul are clearly reened n Table 4, 5, and 6 and Fg. 7 o. From hee reul, noed ha, he BW baed,, and algorhm offer beer reul comared wh he baed conroller. Table 4. onroller value and erformance meaure value for II Regon. Mehod K K K d M ITAE ITSE Table 5. onroller value and erformance meaure value for III Regon. Mehod K K K d M ITAE ITSE Table 6. onroller value and erformance meaure value for IV Regon. Mehod K K K d M ITAE ITSE Journal of Engneerng Scence and Technology Secal Iue /5

11 9 K. Sureh Manc e al.. Proce ouu Reference Tme ec Fg. 7. Proce ouu reone wh II Regon model..8 onroller ouu Tme ec Fg. 8. onroller Ouu reone wh II Regon model.. Proce ouu Reference Tme ec Fg. 9. Proce ouu reone wh III Regon model. Journal of Engneerng Scence and Technology Secal Iue /5

12 Sof omung Aroach o Degn PID onroller for Tank Lqud Level onroller ouu Tme ec Fg.. onroller ouu reone wh III Regon model.. Proce ouu Reference Tme ec Fg.. Proce ouu reone wh IV Regon model. onroller ouu Tme ec Fg.. onroller ouu reone wh IV Regon model. Fgure 3 reen he comaron of ITAE and ITSE for he Hoer ank yem regon I o IV. From h reul, oberved ha, comared wh he, he BW guded algorhm offer reduced error value. Parcularly, BW guded algorhm ouerform he alernave condered n h udy. I offer beer ITAE and ITSE value comared wh, and. Journal of Engneerng Scence and Technology Secal Iue /5

13 94 K. Sureh Manc e al. 4 5 ITAE ITSE 4 ITAE ITSE Error 8 6 Error 3 4 a I Regon ITAE ITSE 6 5 b II Regon ITAE ITSE 8 4 Error 6 4 Error 3 c III Regon d IV Regon Fg. 3. Error comaron for Hoer ye model. 5.. Shercal ank model The rooed conroller degn rocedure hen mlemened on he FOPTD model of hercal ank yem dcued n Secon 3.. Durng he conroller degn roce, he rocedure condered n Secon 5. reeaed wh he hercal ank model. The average earch eraon a follow, converge a 53 rd eraon, baed earch converge a 7 h eraon, converge a 8 nd eraon and converge a 94 h eraon Fnal conroller arameer condered n h udy hown n Table 7. The erformance of he PID conroller for hercal ank yem eed for reference rackng and nu durbance rejecon oeraon. The nu durbance value of.5 nroduced a 5 econd a deced n Fg. 4 and 5. The roce reone and he correondng conroller reone reened n Fg. 4 and 5 reecvely. orreondng erformance meaure value are reened n Table 7. The BW guded offer beer M and comared wh he, and. Fgure 6 how he aemen of ITAE and ITSE for he hercal ank yem. From h, noed ha, even hough he earch eraon large, reul n rovdng le error value when comared o oher mehod. Journal of Engneerng Scence and Technology Secal Iue /5

14 Sof omung Aroach o Degn PID onroller for Tank Lqud Level Table 7. Performance meaure value for hercal ank yem. Mehod K K K d M ITAE ITSE Proce ouu.5 Reference Tme ec Fg. 4. Proce ouu reone of hercal ank roce. onroller ouu Tme ec Fg. 5. onroller ouu reone of hercal ank roce. 7 6 ITAE ITSE 5 Error 4 3 Fg. 6. Error value of hercal ank roce. Journal of Engneerng Scence and Technology Secal Iue /5

15 96 K. Sureh Manc e al. 6. oncluon In h aer, PID conroller unng rooed for hoer ye ank and hercal ank yem ung,, and. The erformance of he rooed rocedure valdaed ung radonal roce meaure, uch a M,, ITAE, and ITSE. The reul how ha he -baed aroach offer a faer convergence when comared wh, and rooed BW guded and. However, even hough here a devaon n he erformance meaure value, BW guded algorhm offer overall ueror reul han uned conroller for boh he hoer ye ank and hercal ank yem. Reference. O Dwyer, A. 9. Handbook of PI and PID conroller unng rule. 3 rd Ed.. Imeral ollege Pre, London.. Johnon, M.A.; and Morad, M.H. 5. PID conrol: new denfcaon and degn mehod. Ed.. Srnger, London, UK. 3. Vjayan, V.; and Panda, R... Degn of a mle eon fler for mnmzng overhoo for low order rocee. ISA Tranacon, 5, Vjayan, V.; and Panda, R... Degn of PID conroller n double feedback loo for SISO yem wh e-on fler, ISA Tranacon, 54, Baha, M.; and Belarb, K.. Neural able adave conrol for a cla of nonlnear yem whou ue of a uervory erm n he conrol law. Journal of Engneerng Scence and Technology, 7, Beheer, A.H.. Wnd drven nducon generaor regulaon ung an yem aroach o Takag Sugeno fuzzy PID conrol. WSEAS Tranacon on Syem and onrol, 6, Manc, S.K.; Sarah, A.; and Rajnkanh, V. 4. Refned double earch omzaon mehodology o degn PID conroller for unable yem. Auralan Journal of Bac and Aled Scence, 8, Lu,.P.; Yang, J.-B.; and Whdborne, J.F. 8. Mulobjecve omzaon and conrol. Prnce Hall, New Delh, Inda. 9. Koeewaran, R.; Svakumar, L. 4. Lévy guded frefly algorhm baed unng of decenraled PI conroller of nonlnear mulvarable yem-coal gafer. Proceedng of Advance n onrol and Omzaon of Dynamcal Syem I, 3, Koeewaran, R.; Svakumar, L. 4. Performance evaluaon of omal PI conroller for ALSTOM gafer durng coal qualy varaon. Journal of Proce onrol, 4, Laha, K.; Rajnkanh,V.; and Surekha, P.M. 3. -Baed PID conroller degn for a cla of able and unable yem. ISRN Arfcal Inellgence, Vol. 3, Arcle ID 54367, age.. Keavan, S.M.; Padmeh, TVN.; and Shyan,.W. 4. onroller unng for nonlnear hoer roce ank a real me analy. Journal of Journal of Engneerng Scence and Technology Secal Iue /5

16 Sof omung Aroach o Degn PID onroller for Tank Lqud Level Engneerng Scence and Technology, EUREA 3 Secal Iue Augu, Rajnkanh, V.; and Laha, K.. Tunng and reunng of PID conroller for unable yem ung evoluonary algorhm. ISRN hemcal Engneerng, Vol., Arcle ID , age. 4. Rajnkanh, V.; and Laha, K.. onroller arameer omzaon for nonlnear yem ung enhanced bacera foragng algorhm. Aled omuaonal Inellgence and Sof omung, Volume, Arcle ID 464, age. 5. Kennedy, J.; and Eberhar, R Parcle warm omzaon. In Proceedng of IEEE nernaonal conference on neural nework, Sr Madhava Raja, N.; Sureh Manc, K.; and Rajnkanh, V. 3. Frefly algorhm wh varou randomzaon arameer: an analy. Proceedng of he 4h Inernaonal onference on Swarm, Evoluonary, and Memec omung SEMO '3, B. K. Pangrah, P. N. Suganhan, S. Da, and S. S. Dah, Ed., Lecure Noe n omuer Scence, Vol. 897, Yang, X.-S. 8. Naure-nred meaheurc algorhm. Lunver Pre, UK 8. Sr Madhava Raja, N.; Rajnkanh, V.; and Laha, K. 4. Ou baed omal mullevel mage hreholdng ung frefly algorhm. Modellng and Smulaon n Engneerng, Vol. 4, Arcle ID , 7 age 9. Yang, X.-S.; and Deb, S. 9. uckoo earch va Lévy flgh. Proceeng of World ongre on Naure & Bologcally Inred omung NaBI 9, IEEE Publcaon, USA, -4.. Koeewaran, R.; and Svakumar, L. 4. Omal unng of decenralzed PI conroller of nonlnear mulvarable roce ung archval baed mulobjecve arcle warm omzaon. Modellng and Smulaon n Engneerng, Vol. 4, Arcle ID 5476, 6 age. Journal of Engneerng Scence and Technology Secal Iue /5