Adaptive control design for a Mimo chemical reactor

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1 Automatio, Cotrol ad Itelliget Sytem 013; 1(3): Publihed olie July 10, 013 ( doi: /j.aci Adaptive cotrol deig for a Mimo chemical reactor Yaabie Abateh, Omprakah Sahu * Departmet of Chemical Egieerig, KIOT, Wollo Uiverity, Kombolcha, Ethiopia addre: op011@gmail.com(o. Sahu) To cite thi article: Yaabie Abateh, Omprakah Sahu. Adaptive Cotrol Deig for a Mimo Chemical Reactor. Automatio Cotrol ad Itelliget Sytem. Vol. 1, No. 3, 013, pp doi: /j.aci Abtract: The major diadvatage of o-adaptive cotrol ytem i that thee cotrol ytem caot cope with fluctuatio i the parameter of the proce. Oe olutio to thi problem i to ue high level of feedback gai to decreae the eitivity of the cotrol ytem. However high gai cotroller have two major problem: large igal magitude ad cloed loop itability. The olutio to thi problem i to develop a cotrol ytem that adapt to chage i the proce. Thi paper preet the deig of adaptive cotroller to a Multi Iput Multi Output (MIMO) chemical reactor. The propoed adaptive cotroller i teted by uig Math lab Simulik program ad it performace i compared to a covetioal cotroller for a differet ituatio. The paper demotrated that while the adaptive cotroller exhibit uperior performace i the preece of oie the covergece time i typically large ad there i a large overhoot. The reult from the cae tudy idicate that the ue of adaptive cotroller ca be exteded to proce with ivere repoe. For uch proce the adaptive cotroller will be uperior to the covetioal cotroller eve without parameter chage i the proce. Although the covetioal cotroller ha the maller repoe time, it i icapable of elimiatig the ivere repoe. Keyword: Proce, Cotroller, Data, Model 1. Itroductio I commo ee, to adapt mea to chage a behavior to coform to ew circumtace. Ituitively, a adaptive cotroller i thu a cotroller that ca modify it behavior i repoe to the chage i dyamic of the proce ad the character of the diturbace [1]. Adaptive cotrol ytem have bee i exitece for over thirty year, ad a wide rage of approache have bee developed []. The core elemet of all the approache i that they have the ability to adapt the cotroller to accommodate chage i the proce. Thi permit the cotroller to maitai a required level of performace i pite of ay oie or fluctuatio i the proce. There are wide rage of adaptive cotrol method curretly i ue but the objective are the ame that to provide a accurate repreetatio of the proce at all time [3]. A adaptive ytem ha maximum applicatio whe the plat udergoe traitio or exhibit o-liear behavior ad whe the tructure of the plat i ot kow. Gai chedulig i oe form of adaptive cotrol but it require kowledge about all the proce to be effective. Aother alterative i to adapt the cotroller parameter or whe a model i available to ue the model idetificatio error to tue the cotroller parameter [4]. Coequetly, tuig of the cotroller i idirect ad ecearily require a accurate model of the proce for atifactory performace. Adaptive cotrol ytem are curretly ued i may operatio ad oe of thee operatio i chemical proce. There are two mai reao why adaptive cotroller i ee chemical procee. Firt, mot chemical procee are o liear. Therefore, the liear zed model that are ued to deig liear cotroller deped o the particular teady tate (aroud which the proce i liearized).it i clear that a the deired teady tate operatio of a proce chage, the bet value of the cotroller parameter chage. Thi implie the eed for cotroller adaptatio. Secod, mot of the chemical procee are o tatioary (i.e. their characteritic chage with time). Typical example are the decay of the catalyt activity i a reactor ad the decreae of the overall heat trafer coefficiet i a heat exchager due to foulig. Thee chage lead agai to deterioratio i the performace of liear cotroller which wa deiged uig ome omial value for the proce parameter, thu requirig adaptatio of the cotroller parameter. The purpoe of thi paper i to deig ad imulate a Model Referece Adaptive cotrol (MRAC) for a multiple iput

2 Automatio, Cotrol ad Itelliget Sytem 013; 1(3): multiple output chemical reactor [5]. The paper iclude the followig part: ectio provide a overview of model referece adaptive cotroller ad deig ad imulatio adaptive cotroller ad compario of performace of adaptive cotroller radom-adaptive (covetioal) cotroller. I the lat ectio a cae tudy which coidered the cotrol of Va de Vauee reactor will be demotrated.. Adaptive Cotrol Deig ad Simulatio Thi ectio provide three et: the firt cover the deig of model referece adaptive cotrol ad it implemetatio i imulik. The ecod ad the third compare the performace of a adaptive cotrol to a covetioal cotroller without oie ad with oie repectively..1. Baic Adaptive Cotroller Thi i to provide the implemetatio of a baic adaptive cotroller uig imulik. The firt item that mut be defied i the plat that i to be cotrolled. A CSTR with a geeral reactio A B i the ytem to be cotrolled ad the cotrol variable are cocetratio of A ad temperature of the reactor. The trafer fuctio for the two SISO ytem (cocetratio ad temperature of reactio cotrol) are obtaied a.1.1. Cocetratio Cotrol Gm We mut the determie the dampig ratio ξ ad the atural frequecy ω to give the required performace characteritic. For the cocetratio cotrol a maximum overhoot (Mp) of 5% ad a ettlig time (T) of le tha ecod are elected. We ca ue the equatio below to determie the required dampig ratio ad atural frequecy of the ytem. ξ lm ( ) p π / lm p / π ω ω 3 T ξ () (3) (4) Baed upo thee formulae we get ξ0.68 ad ω.1986 rad/. The trafer fuctio for the model i therefore Gm( ) Note that we have defied the plat we eed to develop a tadard cotroller to compare with the adaptive cotroller. The imulik diagram for thi cotroller (ad the plat) i how i figure. ω ξ + ω (5) Gm( ) S (1) Fig. Simulik covetioal cotroller Fig 1. Simulik plat implemetatio The fial tep are the to implemet the cotroller, the adaptatio law ad the lik betwee the ytem. The ext tep i to defie the model that the plat mut be matched to. To determie thi model we mut firt defie the characteritic that we wat the ytem to have. Firtly we will arbitrary elect the model to be a ecod order model of the form:

3 66 Yaabie Abateh et al.: Adaptive Cotrol Deig for A Mimo Chemical Reactor The implemetatio of the complete model referece adaptive cotrol i idetical to the previou cae except Gp1 ad Gm1 are replaced by Gp ad Gm repectively. The completed model permit the oie to be diabled, ramp fuctio oly, white oie oly or a combiatio of ramp ad white oie. The followig parameter are plotted o graph: plat output with adaptive ad with covetioal cotrol, model output, error betwee plat ad model output ad the cotroller parameter... ComparioWithout Noie Fig 3. Simulik implemetatio of Lyapuov Adaptatio Law Note that the model i complete; the firt tak we mut perform i, to compare the performace of the two cotroller for a tep iput ad o oie Fig 4. Simulik implemetatio of Cotroller Figure 6. Plat output (cocetratio) with adaptive cotrol (tep iput, o oie, Gamma0.99) Fig 5. Simulik implemetatio of a Model Referece Adaptive Cotroller b) Temperature cotrol The implified trafer fuctio model of the proce i obtaied a: Figure 7. Plat output with covetioal cotrol (tep iput, o oie, Gamma0.99) Gp ( ) (6) A referece model (ecod order) with a maximum overhot (Mp) of.5% ad ettlig time (T) of 1 ecod i choe. Ad the trafer fuctio for the model i: Gm ( ) (7) Figure 8. Plat output (temperature) with adaptive cotrol (tep iput, o oie, Gamma0.99)

4 Automatio, Cotrol ad Itelliget Sytem 013; 1(3): thi i a igificat improvemet. Further icreae i the adaptatio gai doe ot reult i a improvemet of the ytem..3. Compario with Noie (Compario with Ramp Noie) The ext logical tep i to compare the performace of the two cotroller i the preece of oie i the form of ramp igal, (lope1). The adaptatio gai ha bee retored to Figure 9. Plat output temperature) with covetioal cotrol (tep iput, o oie, Gamma0.99 Lookig at thee graph oe of the major diadvatage of adaptive cotrol i immediately apparet. It take the adaptive cotroller early 0 ecod to match perfectly the output of the referece model. However the covetioal cotroller i matched withi ecod. The overhoot of the adaptive cotroller i alo exceive (of the order of 50%) while the covetioal cotroller ha a overhoot of below 3%. Oe method of addreig thi problem i to icreae the adaptatio gai (Gamma). For example, icreaig the adaptatio gai to 100 give the repoe how i figure 10 ad 11. Figure 1. Plat output (cocetratio) with adaptive cotrol (tep iput, ramp oie, Gamma0.99) Figure 10. Plat output with adaptive cotrol (tep iput, o oie, Gamma100) Figure 13. Plat output (cocetratio) with covetioal cotrol (tep iput, ramp oie, Gamma0.99) Figure 11. Plat output with adaptive cotrol (tep iput, o oie, Gamma100) Figure 14. Plat output (temperature) with adaptive cotrol (tep iput, ramp oie, Gamma0.99) Thi ha improved the overhoot to below 10% ad the ettlig time i ow le tha 10 ecod. While ot perfect

5 68 Yaabie Abateh et al.: Adaptive Cotrol Deig for A Mimo Chemical Reactor dx ( x + CBS ) + k 1 x 1 ( u + k ) u x dt (9) Figure 15.Plat output (temperature) with covetioal cotrol (tep iput, ramp oie, Gamma0.99) The ituatio begi to how the actual advatage of adaptive cotrol. I thi cae the covetioal cotroller i icapable of maitaiig eve a table ytem. O the other had the adaptive cotrol maage to maitai tability. However large overhoot ad offet ad log ettlig time are preet. There i alo a large teady tate error. A before icreaig the adaptatio gai to 100 reduce the overhoot to below 10%, the ettlig time to below 5 ecod ad the teady tate error to zero. Thi i how below i figure. Where, C AS ad C BS deote the effluet cocetratio of compoet A ad B at teady tate, repectively. The tate variable x 1 ad x are deviatio variable defied by x 1 C A -C AS ad x C B -C BS ; u i the maipulated variable give by uf/v u, where uf/v. the cocetratio of A i the feed tream, deoted by C Af ad i equal to 10mol/L. The reactor volume, V, i 7L ad the rate cotat are k mi-, k mi- ad k L.mol-1.mi-1. It i kow that the proce i at teady tate with F 4 L/mi, C AS 3mol/L ad C BS mol/l iitially. The cotrol objective i to regulate the cocetratio of B, x, by maipulatig the dilutio rate, Here; it i aumed that the origial oliear characteritic are ukow ad oly the proce omial trafer fuctio G ( ) p ( ) (10) I kow ad i available for deig. The repoe for tep chage i the iput i how i figure 17 Figure 17. Repoe for a tep chage i the iput Figure 16. Plat output (cocetratio) with adaptive cotrol (tep iput, ramp oie, Gamma100).3.1. Cae Study Up to ow, we have take a geeral reactio A B. So it i eetial to coider a pecific reactio to demotrate the propoed adaptive cotrol cheme to a great exitet. Thi cae tudy coider the cotrol of the Va de Vue reactor, the reactio cheme coitig of the followig reactio: A B C A D A yclopetaddiee, B Cyclopeteol C Cyclopetaediol, D dicyclopetadiee The actual proce dyamic are decribed by ( C x ) ( u + k + kc ) x k dx 1 uc dt x Af AS A (8) For the adaptive cotrol ytem, a referece model (ecod order) with maximum overhoot (5%) ad ettlig time of ecod i choe ad the trafer fuctio for the model i: G P ( ) (11) Cotroller ettig for the o-adaptive cotroller i doe uig Ziegler-Nichola techique ad the bet cotroller parameter are foud to be Kc3, τi1 ad τd Uig the above iformatio the performace of the two cotroller are compared for differet ituatio..4. Compario without Noie Firt, the performace of the two cotroller without oie are compared. The repoe for a tep chage (0.1) i the iput are how i figure 18. ad figure 19.

6 Automatio, Cotrol ad Itelliget Sytem 013; 1(3): Figure 18. Plat output with adaptive cotroller (tep iput, o oie,γ0.5) Figure 1. Plat output with adaptive cotroller (tep iput, ramp oie, γ0.5) Figure 19. Plat output with covetioal cotroller (tep iput, o oie) Lookig at thee two graph, the advatage of adaptive cotroller ca be ee a it elimiate the ivere repoe. Although the covetioal cotroller ha the maller repoe time ( ecod) compared to the adaptive cotroller (7 ecod), it i icapable of elimiatig the ivere repoe. The repoe time for the adaptive cotroller ca be decreaed at a cot of iitial ocillatio. Figure 0 how the effect of icreaig the adaptatio rate to Figure. Plat output with covetioal cotroller (tep iput, ramp oie) From the above two figure it ca be ee that the covetioal cotroller i icapable of maitai eve tability. Although there i a large teady tate error, the adaptive cotroller give a better plat repoe. But the teady tate error ca be elimiated by icreaig the adaptatio rate. Thi i how i the ext figure. Figure 0. Plat output with adaptive cotroller (tep iput, o oie,γ0.75).4.1. Compario with Ramp Noie The ext tak to be doe i to compare the performace whe there i a diturbace or a chage i the proce parameter. The repoe for a tep chage i the iput with a ramp oie (lope0.1) are how i the ext two figure. Figure 3. Plat output with adaptive cotroller (tep iput, ramp oie, γ0.75) 3. Cocluio The ue of multiple model ad adaptive cotroller are attractive epecially whe the proce i kow to traitio to ukow operatig tate. It i alo ituitive that a fixed parameter cotroller (covetioal cotroller) may ot provide atifactory cloed loop cotrol. The o adaptive

7 70 Yaabie Abateh et al.: Adaptive Cotrol Deig for A Mimo Chemical Reactor model ca provide peed wheever it parameter are cloe to thoe of the proce while the adaptive model ca provide accuracy becaue it parameter are permitted to adapt. The paper ha aimed to provide a udertadig of how to implemet a adaptive cotroller ad to compare a adaptive cotroller with a covetioally deiged cotroller i variou ituatio. The paper demotrated that while the adaptive cotroller exhibit uperior performace i the preece of oie the covergece time i typically large (greater tha 10 ecod) ad there i large overhoot. Thee two problem are due to the adaptive cotroller failig to adapt fat eough to force the plat to match the model. Icreaig the adaptatio rate improve the performace of the adaptive cotroller at the cot of icreaed ocillatio. Oe iteretig obervatio i that the preece of oie icreae the time required for the adaptive cotroller to coverge. The probable reao for thi i that the preece of the oie provide the adaptive cotroller with more of igal to proce. The reult from the cae tudy idicate that the ue of adaptive cotroller ca be exteded to proce with ivere repoe. For uch proce the adaptive cotroller will be uperior to the covetioal cotroller eve without parameter chage i the proce. Although the covetioal cotroller ha the maller repoe time, it i icapable of elimiatig the ivere repoe. Referece [1] B.Waye Bequette, proce dyamic modellig, aalyi ad imulatio; Precetice Hall:NJ,1998 [] G. Stephaopolu, Chemical proce cotrol; pretice Hall of Idia private limited, New Delhi, 00. [3] William L.Luybe Proce Modelig, Simulatio ad Cotrol for Chemical Egieer;MCGraw-Hill,Ic.,1990 [4] C.T. Che; Direct Adaptive Cotrol of Chemical Proce Sytem; Idutrial Egieerig Chemical Reearch 001, 40, [5] R.Gudala,, K.A.Hoo, Multiple Model Adaptive cotrol Deig for a MIMOchemicalreactor,Idutrial Egieerig Chemical Reearch 38, , 000. [6] D. Tyer, M. Sorouh, Adaptive Temperature Cotrol of Multi Product Jacketed, Reactor..Idutrial Egieerig Chemical Reearch , [7] I. Mcmau, Adaptive Cotrol; A QUT Avioic project, Queelad Uiverity of Techology; 00. [8] A. Rajagola, G. Wahegto; Simulik Tutorial, Ohio State Uiverity, 00. [9] M. Kozek, Mraclab-a Tool for Teachig Model Referece Adaptive Cotrol; Viea Uiverity of Techology, 000.