A Novel Gain Tuning of Anti-Windup PID Controller using Ant Lion Optimization

Transcription

1 Inenaional Jounal of Conol Theoy and Applicaion ISSN : Inenaional Science Pe Volume Numbe 6 7 A Novel Gain Tuning of Ani-Windup PID Conolle uing An Lion Opimizaion Ayyaao SLV Tummala a, Ravi Kian Inapakuhi b and P.V. Ramanaao c a,b Depamen of Elecical and Eleconic Engineeing, GMR Iniue of Technology Rajam, Sikakulam, AP, India. ayyaao. lv@gmi.og, avikian.i@gmi.og c Depamen of Elecical and Eleconic Engineeing, Nagajuna Univeiy, Gunu, AP, India. Abac: PID conolle i upeio in em of fa epone, immune o paamee vaiaion, diubance ejecion ec. Bu when conol inpu o he plan auae, he epone of he yem i ignificanly affeced and in ome cae hi may lead o inabiliy. PID conolle wih ani-windup i popoed in he lieaue ha can handle auaion in conol inpu. The challenging ak in implemenaion i he uning he paamee of ani-windup PID. To adde hi iue, a implified mehod o deign he paamee of PID wih ani-windup i popoed in hi pape. The paamee of ani-windup ae uned by An Lion opimizaion echnique (ALO). The popoed mehod i validaed fo diffeen cae udie including baic econd ode yem, peed conol of DC moo and inducion moo wih diec oque conol. The popoed deign i found o be upeio in dynamic epone in he cae udied. A Novel Gain Tuning of Ani-Windup PID Conolle i popoed uing An Lion Opimizaion. Keywod: Ani-windup PID, PI conol, An Lion opimizaion echnique, Gain uning. Inoducion PI and PID conolle ae he mo popula linea conolle due o he alien feaue like zeo eady ae eo, good dynamic epone, high diubance ejecion. Becaue of hee feaue, he applicaion of PI conolle ae va and ae no only limied o vaiable peed dive, poce conol, wind enegy conveion yem, ola powe plan, convee. PID conolle i widely ued in eveal induial applicaion. Mo of he pacical yem poe non-linea chaaceiic and hee yem ae lineaized aound an opeaing poin. Hence he conol inpu o he plan i limied o ceain ange. In ome cae he conol inpu geneaed may no be ealized in pacical cae. Conideing he cae of peed conol of choppe fed DC moo, he conol volage canno exceed inpu baey volage. Fo mo of he cae, he conol inpu i limied by plan funcioning equipmen. Conide anohe example of invee fed inducion moo, cuen inpu o he moo i eiced by device aing. Theefoe a auaion block i conneced in imulaion udie o limi he conol inpu o he plan. When auaion i e in, non-lineaiy i enfoced in plan dynamic. Thu he funcionaliy of PID 85 Inenaional Jounal of Conol Theoy and Applicaion

2 Ayyaao SLV Tummala, Ravi Kian Inapakuhi and P.V. Ramanaao conolle i deviaed fom he deied. To adde hi iue, PID conolle wih ani-wind up i popoed in he lieaue. The paamee of he PID conolle mu be deigned o impove he abiliy, anien epone of he yem and o educe eady ae eo. The uned yem mu alo be immune o lage diubance, modeling eo and paamee vaiaion[] [4]. Thee ae many echnique popoed in he lieaue o une he paamee. The unable paamee fo PID conolle ae K P, K I and K D. Ohe han convenional mehod like Ziegle Nichol mehod, Pole placemen echnique, Nyqui mehod, conolle can alo be uned by naue inpied opimizaion algoihm. The mo ecen, upeio and eaie one i uning he paamee uing An Lion Opimizaion. The anfe funcion of PI conolle i given a T PI () = K The anfe funcion of PID conolle i given a T PID () = K P P K i KI K The conol oupu of PID conolle wih ani-windup i D (.) (.) whee, e = v - u v = K Ê ˆ e K Ú e e d K Ë Á T P I D de d (.3) KD y - e K P v Acuao u Plan G() y K I - e T Figue : Ani-windup PID conolle If conolle oupu v i equal o plan inpu u i.e. unde non-auaion condiion, hi conolle wok like an odinay PID conolle and T i called a coecion faco[5] [9]. Inenaional Jounal of Conol Theoy and Applicaion 86

3 A Novel Gain Tuning of Ani-Windup PID Conolle uing An Lion Opimizaion Thi pape deail he deign of ani-windup PID conolle by uning he paamee uing ALO algoihm[]. The ALO uned ani-windup PID conolle i compaed wih PID conolle fo econd ode yem. Lae ani-windup PI i uned fo peed conol of DC moo. The pefomance of ani-windup PI conolle i compaed wih uned PID conolle. In he lae cae, ALO uned ani-windup PI conolle i compaed wih PID conolle fo peed conol of inducion moo wih diec oque conol.. An Lion Opimizaion Algoihm ALO opimizaion i a bio-inpied heuiic algoihm inpied fom he anlion apping he an in he poce of huning hem. Anlion make inveed cone haped caviie on and wih hei jaw. Thee caviie ae ued fo apping he an. Anlion will hide ino ha ip of he cone and wai fo he an o fall in ha caviy. If he an ap in hoe caviie hen he anlion y o cach hem. Afe huning, anlion will make he channel clean fo anohe hun. The ALO algoihm imiae he behavio of an lion and an in a ap. In uch modeling an ae made o cawl ove he each pace and an lion ae made o cach hem uing ap. A andom walk i iniiaed fo hi model a an wande aound fo food andomly. Apa fom an, an lion ae alo conideed o occupy ome pace and hiding. Fo he applicaion of ALO, eveal conideaion like diffeen andom walk choen by an in he each pace, ap of an lion and ize of he caviy ae made. The ap buil by he an lion ae baed on hei fine and ae alo affeced by hei abiliy o cach. In evey ieaion each anlion hun an an and he ange of andom walk will be diminihed o a o model he liding of he an. The elocaion of he anlion depend on he fine of he an hun by i. The andom walk of an i uch ha hey updae hei poiion in each ep of opimizaion maching wih he poiion of an lion. Fo building a ap, ALO algoihm ue a oulee wheel fo elecion of fie an lion duing opimizaion which enue a highe pobabiliy fo an lion in caching he pey. Once he an fall in he ap, an lion dag he an o he epicene. Once he an eache o boom of he ap, he an lion conume i body and hen i move o a new locaion o enhance i ap o cach he ohe pey. In hi poce he be of all an lion fom each ieaion i aken a elie. In ALO algoihm, diffeen oluion (an and an lion) ae andomly geneaed. Fo evey ieaion, he poiion of he an change accoding o he an lion eleced by oulee wheel opeao. Iniially he bounday of poiion i accoding o he cuen ieaion and hen i will depend on he eleced an lion and elie. Fine of all he an will be evaluaed and he new locaion of he an lion i mached o he highe fi an lion in he peviou ieaion. The be an lion obained in cuen ieaion i compaed wih he elie and he fie of he wo i conideed a he new elie. The Anlion algoihm i given below [] I. Iniialize he maximum ieaion, populaion of anlion and an epaaely fo a given dimenion d. II. Geneae he fine value of an and anlion fom he objecive funcion. ( d ) ( d ) È YL,, L,,..., L, YL,, L,,..., L, Q OA = : : YLn,, Ln,,...., Î, ( L n d ) (.) 87 Inenaional Jounal of Conol Theoy and Applicaion

4 Ayyaao SLV Tummala, Ravi Kian Inapakuhi and P.V. Ramanaao (,,, d ) (,,, d ) È YLL, LL,..., LL YLL, LL,..., LL Q OAL = : : YLLn,, LLn,..., LL Î LL n, d epeen d h vaiable of n h anlion. L n, d epeen d h vaiable of n h an. (, n, d ) Y(L n,, L n,,..., L n, d ) epeen fine value of n h an. Y(LL n,, LL n,,..., LL n, d ) epeen fine value of n h anlion. III. The anlion wih opimum fine value i eaed a elie. while i < Max ie fo j < n (maximum # an) IV. Chooe anlion uing Roulee wheel V. Updae min-max of vaiable a given in (.3) and (.4) (.) q = q I (.3) VI. Geneae a andom walk of an uing (.5) whee, i a andom value. VII. Updae anlion poiion uing (.6) p = p I ( ) ( - ) ( - ) (.4) X( ) = È Î, S ( ) -, S ( ),..., S ( n ) (.5) end fo loop VIII. Geneae he fine value of an An i R = IX. Replace an wih anlion if f An f Anlion X. Modify elie if fine value i opimum. end while loop Diplay elie A R E ( i )> ( j ) (.6) 3. Cae Sudie and Reul Analyi Cae udy : A Second ode yem: Le u conide econd ode linea yem Inenaional Jounal of Conol Theoy and Applicaion 88

5 A Novel Gain Tuning of Ani-Windup PID Conolle uing An Lion Opimizaion G () = w xw w Hee he objecive i o une he paamee K P, K I and K D fo PID conolle. Conain: K P K I K D x =.8 and w = (3.) To une he paamee of PID conolle, an objecive funcion i fomulaed in uch a way ha eady ae eo, eling ime, ie ime and peak ovehoo i educed. whee, y i a efeence oupu, y i he meaued oupu, y p i he peak value of he oupu. ( ) Ú F = min y - y d yp - y (3.) PI and PID conol paamee ae uned uing ALO algoihm. The paamee obained fo PID conolle afe uning ae given below K P = 9.9, K I =.49 and K D = 3.66 The anien epone of he plan i hown in Figue ().When compaed o PI conolle, PID conolle i upeio in em of peak ovehoo, eling ime, Figue (3) how he conol inpu o he plan wihou auaion (acuao). The conol effo i vey high which may no be poible in eal-ime condiion. Hence hee i a need o limi he conol inpu o he plan. To adde hi iue a auaion block i added o imulaed yem o limi he conol inpu o ±5. oupu y.5.5 PID PI conol inpu 4 x ime in Figue : Oupu of econd ode yem.5.5 ime in Figue 3: Conol inpu The epone how ha peak ovehoo, ie ime and eling ime ae inceaed unde auaed condiion. Thi i becaue when he conol inpu o he plan canno exceed auaion limi and hi inoduce nonlineaiy in o he yem. In ome cae hi may lead o inabiliy. To adde hi iue, PID conolle i eplaced wih ani-windup PID conolle. Thee ae many deign of PID conolle wih ani-windup. Ou of hee he convenional mehod, Tacking Back calculaion cheme i adoped hee. The anfe funcion of ani-windup PID conolle i given in ecion-i. The deign of ani-windup PID conolle include elecion of K P, K I, K D and T. 89 Inenaional Jounal of Conol Theoy and Applicaion

6 Ayyaao SLV Tummala, Ravi Kian Inapakuhi and P.V. Ramanaao The limi of PID conolle ae eleced ame a befoe. The ange of coecion faco i eleced a [. ]. Thu he numbe of paamee o be uned i fou. Following he AnLion opimizaion algoihm given in ecion, he objecive funcion (3.) i minimized and he coeponding uned paamee ae given below. K P = 9.9, K I =.49, K D = 3.66 and T = wihou auaion wih auaion oupu y ime in Figue 4: Oupu of he yem Figue (5) how he pefomance of he yem wih ani-windup conolle. The oupu ele fae wih le peak ovehoo fo PID wih ani-windup..4. PID wih Ani-windup PID oupu y Cae Sudy-: Speed Conol of DC moo: ime in Figue 5: Oupu wih ani-windup conolle Hee he objecive i o une he paamee K P, K I and K D fo PID conolle. Conain: K P K I K D To une he paamee of PID conolle, an objecive funcion i fomulaed in Eq.(3.3) o miigae eady ae eo, eling ime, ie ime and peak ovehoo. Ê * - ˆ * wmax w F = F = min ÁÚ w - w d * (3.3) Ë w Inenaional Jounal of Conol Theoy and Applicaion 9

7 A Novel Gain Tuning of Ani-Windup PID Conolle uing An Lion Opimizaion V S ω - PID wih Ani-windup i a Hyeii conolle DC Choppe DC Moo ω ω The open loop anfe funcion of DC moo i: Figue 6: Speed conol of DC moo T() = Ka J B ( L R ) K (3.4) ( ) a a a In hi ecion, we wan o analyze he pefomance of DC moo wih ani-windup PID conolle. The objecive of hi ecion i o deign a peed conolle fo DC moo. The DC moo opeae unde cloed loop condiion opeaing wih vaiable load and i peed i egulaed uing duy aio of ep-down choppe which i deived fom he conolle. Acual peed w i ened and i compaed wih i efeence value w *. Thi peed eo i given o a peed egulao which geneae efeence amaue cuen i a * and hi cuen efeence i given o hyeei cuen conolle wih hyeei band of ± A. Iniially PID conolle i eleced a peed conolle. Wih PID conolle, peak ovehoo i.83%. Thi i becaue a he ime of aing he aing cuen i limied o 3A. To enhance he pefomance of peed conolle, PID conolle i eplaced wih PI conolle wih ani-wind up. The majo challenge in he deign of ani-windup i elecion of T. Figue (7) how he epone of he yem wih diffeen value of T. 5 peed in ad/ ime in Figue 7: Vaiaion of peed wih coecion faco Thu hee i a need o elec a pope value of T. The value of coecion faco i uned uing ALO algoihm. Figue (8) how he pefomance of he conolle wih ani-windup. The peed ovehoo i daically educed a he ime of aing. Unde unning condiion ince he conol cuen i le han 3A, he conolle i imila o PI conolle. A load oque of 3Nm i added a. and becaue of hi peed i educed and again Inenaional Jounal of Conol Theoy and Applicaion

8 Ayyaao SLV Tummala, Ravi Kian Inapakuhi and P.V. Ramanaao 5 PI PI wih ani-windup peed in ad/ ime in Figue 8: Speed oupu wih ani-windup conolle egained o efeence peed wihin.5. Bu hee i no effec of coecion faco on hi becaue he conol cuen equied unde load change condiion i le han 3A acual cuen efeence cuen 5 cuen in A ime in Figue 9: Amaue cuen Cae udy-3: Speed Regulaion of Inducion moo: The dynamic of inducion moo ae given by [].The noaion ae ame a given in lieaue. V S Swiching Table Volage Souce Invee Inducion Moo ω Volage ω - ω PID wih Ani-windup τ e Toque and Flux Hyeei Compaao Flux & Toque Eimao Cuen * ψ Figue : Speed conol of inducion moo Inenaional Jounal of Conol Theoy and Applicaion 9

9 A Novel Gain Tuning of Ani-Windup PID Conolle uing An Lion Opimizaion dw npm = d JL TL ( yaib - yaia )- (3.5) J dy a R = - R ya - d L L M ia npwy b (3.6) dy b R = - R yb d L L M ib npwy a (3.7) di a = d di b = d MR LL MR LL y y a b npm Ê MR LR ˆ wy b - ia u LL Á a Ë LL L (3.8) npm Ê MR LR ˆ - wy a - ib u LL Á b Ë LL L (3.9) The meaued peed w i compaed wih he efeence value w * and peed eo i fed o peed egulao. The oupu of he peed egulao i a efeence oque e *. Flux and Toque eimao eimae flux and oque fom ao volage and cuen. Thee efeence oque and efeence fluxe ae given o Toque and hyeei compaao. Figue () how he peed epone wih PID conolle and PI conolle wih ani-windup. Reul how ha he peed change unde udden change in load oque condiion i low wih ani-windup conolle. 4. Concluion Figue : Speed epone of Inducion moo The funcionaliy of PID conolle i deviaed fom he deied when conol inpu o he plan auae. Thi lead o inoducion of conolle wih ani-windup. In adiional mehod, coecion faco i eleced a a andom value which effec he pefomance of he conolle. A i i difficul o une he ani-windup conolle paamee, we popoed he deign of ani-windup PID conolle paamee uing An Lion opimizaion echnique. The pefomance of ALO uned ani-windup conolle i evaluaed on diffeen yem. In cae of econd ode yem, ALO uned ani-windup PID conolle oupefom ani-windup PID conolle. In he econd cae ALO uned ani-windup PI conolle oupefom PID conolle. In he hid cae, ALO uned ani-windup PID conolle howed upeio pefomance compaed o PID conolle. 93 Inenaional Jounal of Conol Theoy and Applicaion

10 Ayyaao SLV Tummala, Ravi Kian Inapakuhi and P.V. Ramanaao Refeence [] K. H. Ang, G. Chong, and Y. Li, PID conol yem analyi, deign, and echnology, IEEE Tan. Conol Sy. Technol., Vol. 3, No. 4, pp , 5. [] [3] [4] [5] [6] [7] [8] [9] [] [] Y. Li, K. H. Ang, and G. C. Y. Chong, PID conol yem analyi and deign, IEEE Conol Sy., Vol. 6, No., pp. 3 4, 6. K. J. Åöm and T. Hägglund, The fuue of PID conol, Conol Eng. Pac., Vol. 9, No., pp , Nov.. G. P. Liu and S. Daley, Opimal-uning PID conol fo induial yem, Conol Eng. Pac., Vol. 9, No., pp ,. J. W. Choi and S. C. Lee, Aniwindup aegy fo PI-ype peed conolle, IEEE Tan. Ind. Elecon., Vol. 56, No. 6, pp , 9. H.-B. Shin and J.-G. Pak, Ani-Windup PID Conolle Wih Inegal Sae Pedico fo Vaiable-Speed Moo Dive, IEEE Tan. Ind. Elecon., Vol. 59, No. 3, pp ,. F. Cupeino, E. Mininno, D. Nao, B. Tuchiano, and L. Salvaoe, On-line geneic deign of ani-windup unucued conolle fo elecic dive wih vaiable load, IEEE Tan. Evol. Compu., Vol. 8, No. 4, pp , 4. J. M. Gome da Silva J. and S. Tabouiech, Ani-windup deign wih guaaneed egion of abiliy: an {LMI}-baed appoach, Vol. 5, No., pp , 3. L. Zaccaian and A. R. Teel, A common famewok fo ani-windup, bumple anfe and eliable deign, Auomaica, Vol. 38, No., pp ,. S. Mijalili, The An Lion Opimize, Adv. Eng. Sofw., Vol. 83, pp. 8 98, 5. T. S. L. V Ayyaao, G. I. Kihoe, and M. Rambabu, Adapive Conol of Sauaed Inducion Moo wih Unceain Load Toque, In. J. Recen Tend Eng. Technol., Vol. 3, No. 4, pp. 6,. Inenaional Jounal of Conol Theoy and Applicaion 94