Predictive control of a solar air conditioning plant with simultaneous identification

P edic i e con ol o a sola ai condi ioning plan wi h simul aneous iden ifica ion A.N´ u˜ nez-Reyes and C.Bo dons Abs ac — This pape p esen s he applica ion o a p edic i e con olle wi h simul aneous iden ifica ion o a sola ai con- di ioning plan . The ime a ying na u e o he p ocess makes necessa y an adjus men o he con olle pa ame e s o he a ying ope a ional condi ions. The main no el y wi h espec o classic adap i e MPC scheme is o penalize he iden ifica ion e o in he cos unc ion used o con ol. The beha iou o he con olle is illus a ed by simula ions and expe imen al esul s. The in eg a ion o iden ifica ion and con ol a oids he edious iden ifica ion p ocedu e ha is necessa y be o e he s a -up o any p edic i e con olle . This new adap i e MPC scheme shows i s e ec i eness in con olling he ou le empe a u e in he sola he mal plan . I. INTRODUCTION Model P edic i e Con ol (MPC) has de eloped conside- ably o e he las yea s, bo h wi hin he esea ch con ol communi y and in indus y [1]. This success can be a ibu ed o he ac ha MPC is, pe haps, he mos gene al way o posing he p ocess con ol p oblem in he ime domain. MPC o mula ion in eg a es op imal con ol, s ochas ic con ol, con ol o p ocesses wi h dead ime, mul i a iable con ol and u u e e e ences when a ailable. Ano he ad an age o MPC is ha because o he fini e con ol ho izon used, cons ain s and, in gene al nonlinea p ocesses which a e equen ly ound in indus y, can be handled. Howe e , one o he majo d awbacks o his ype o con ol s a egy is he need o ob ain a dynamic model o he plan . Mos o he success o comme cial p edic i e con o- lle s such as Dynamic Ma ix Con ol DMC [2] comes om i s abili y o use a s ep esponse model o he plan , which can be easily iden ified wi h expe imen al es s. Howe e , he iden ifica ion phase needs a lo o expe ise and ime o pe o m he expe imen s and his is usually done only once, a he p ocess s a -up. The model is no upda ed equen ly e en i p ocess dynamics changes along ime. Model upda ing is pa icula ly impo an in p ocesses wi h changing ope a ing condi ions, whe e he p ocess pa- ame e s a e con inually e ol ing. In p ocesses in ol ing mass anspo a ion (as he one con olled in his wo k), he cha ac e is ic ime cons an and delay a e a ec ed by flow changes, gi ing ise o a p ocess dynamics ha changes du ing a iable ope a ing egimes. This wo k was pa ially suppo ed by Spanish Minis y o Science and Technology unde g an DPI2004-07444-C04-01 and by HYCON Ne wo k o Excellence, con ac numbe FP6-IST-511368 A.N´ u˜ nez-Reyes and C.Bo dons a e wi h Dp o. de Ingenie ´ ıa de Sis emas y Au om´ a ica. Escuela Supe io de Ingenie os. Uni e sidad de Se illa. Camino de los Descub imien os s/n. 41092 Se illa. Spain (ampa o,bo dons)@ca uja.us.es Model unce ain y and dis u bances a e impo an con- ce ns in MPC and ha e been ho oughly s udied in ecen yea s. The main app oaches o he subjec appea in he fields o adap i e con ol and obus con ol. The e is a lo o wo k done in obus MPC, wi h significan con ibu ions in he min-max en i onmen which, in spi e o hei heo e ical impo ance, a e di ficul o be implemen ed in p ac ice [3]. Adap i e MPC has also been widely s udied by a numbe o au ho s, o example [4] [5]. The applica ion o a sel - uning con olle wi h a ecu si e leas squa es iden ifica ion algo i hm gi es ise o a solu ion ha is easily implemen able bu shows nume ical p oblems when he exci a ion anishes [6]. A supe iso y le el is needed which makes he p ocedu e mo e complex. This can be sol ed wi h he me hodology p oposed by Shouche e al. [7], Model P edic i e Con ol and Iden ifica ion MPCI, which is an adap i e MPC scheme ha employs he pe sis en exci a ion condi ion [8] o gua an ee iden ifiabili y. The main d awback o his me hod is ha he use o he pe sis en exci a ion condi ion de e io a es he con ol pe o mance. Al hough he iden ifica ion capabili ies o he me hod a e e y good, he ac ha he con ol signals a e calcula ed in o de o gua an ee exci a ion gi es poo con ol ea u es. In addi ion, he e a e no epo s o applica ions o eal plan s. The me hod p esen ed he e ies o o e come his p oblem. Sola he mal plan s a e usually di ficul o con ol because he ene gy sou ce (sola adia ion) is no manipulable [5] and is con inually changing. This makes cons an flow changes necessa y o e e ence acking, p o oking sudden p ocess dynamics changes. Lo s o con ol s a egies ha e been applied o hese plan s, anging om classical PIDs oMPC [9]. In his pape , a me hod ha uses p edic i e con ol and iden ifica ion simul aneously has been es ed on a sola ai condi ioning plan . The p oposed me hod makes use o a cos unc ion ha includes acking e o and con ol e o (as any p edic i e con olle ) as well as he iden ifica ion e o in a pas ece- ding ho izon. This is a combina ion o he con ol p oblem and he iden ifica ion p oblem in jus one cos unc ion. This me hod is in he amewo k o he dual con ol [10]. The p oblem is no oo cos ly and has been implemen ed on an indus ial low-cos SCADA. The pape is o ganized as ollows. In sec ion II a desc ip- ion o he sola plan is p esen ed. Sec ion III desc ibes he p oposed con ol s a egy, which is es ed unde simula ion and compa ed o a sel - uning MPC in sec ion IV. The esul s o applying he p oposed con olle o he eal plan a e shown in sec ion V and finally he conclusions a e d awn. P oceedings o he 44 h IEEE Con e ence on Decision and Con ol, and he Eu opean Con ol Con e ence 2005 Se ille, Spain, Decembe 12-15, 2005 MoIB20.5 0-7803-9568-9/05/$20.00 ©2005 IEEE 1355 II. PLANT DESCRIPTION The sola ai condi ioning plan is loca ed in Se ille (Spain). I is used o cool he Labo a o ies o he Sys em Enginee ing and Au oma ic Con ol Depa men o he Uni- e si y o Se ille. I consis s o a sola field ha p oduces ho wa e which eeds an abso p ion machine gene a ing chilled wa e and injec s i in o he ai condi ioning sys em, achie ing a cooling powe o 35 kW. Accumula ion sys em B1 Sola sys em VM1 CC1 CC2 CC3 CC4 Tac I T o Accumula ion sys em Fig. 1. Plan desc ip ion The sola plan can be analyzed as an ai condi ioning ins alla ion ha uses he mal ene gy o p oduce cold ai . A comple e desc ip ion o he plan can be ound in [9]. The o e all con ol objec i e is o supply chilled wa e o he ai dis ibu ion sys em a he equi ed empe a u e. This is accomplished by con olling he empe a u e o he ho wa e supplied by he sola field. Since he p ima y ene gy (sola adia ion) is no manipulable, he desi ed empe a u e is achie ed by ac ing on he ci cula ing flow. The sola con ibu ion, in addi ion o adia ion seasonal and daily cy- clic a ia ions, is also dependen on a mosphe ic condi ions such as cloud co e , humidi y, and ai anspa ency. I is impo an o main ain a cons an ou le empe a u e as he sola condi ions change, and he only means a ailable o achie ing his is ia adjus men o he fluid flow. The con ol p oblem add essed in his pape is he e- gula ion o he sola field ou le empe a u e (T o). Figu e 1 shows he main componen s o he plan , which a e he ollowing: a) Sola sys em, composed o a se o fla sola collec o s. The p ima y sou ce o ene gy is sola adia ion which is used by he sola collec o s o inc ease he empe a u e o he ci cula ing wa e . The sola field is composed o 151 m2o fla collec o s which wo k wi hin he ange o 60 o 100 ◦Cand supply a nominal powe o 50 kW. b) Accumula ion sys em, composed o wo 2500-li e anks wo king in pa allel. This sys em ac s as a bu e , s o ing ho wa e o be used in ansien si ua ions whe e he sola adia ion does no allow he desi ed empe a u e o be ob ained a he end o he ho wa e ci cui . The objec i e o he con ol sys em is o main ain he ou le oil empe a u e T o a a desi ed le el in spi e o dis u bances such as changes in he sola i adiance le el (caused by clouds), mi o eflec i i y o inle wa e em- pe a u e. This is accomplished by a ying he flow o he fluid h ough he field manipula ing he h ee-way al e (VM1). The field exhibi s a a iable delay ime ha de- pends on he con ol a iable (flow). The ans e unc ion o he p ocess a ies wi h ac o s such as i adiance le el o wa e inle empe a u e. The main enance o a cons an ou le empe a u e h oughou he day as he sola condi ions change equi es a wide a ia ion in he ope a ional flow le el. This leads o subs an ial a ia ions in he gene al dynamic pe o mance and in pa icula , om he con ol iewpoin , gi es ise o a sys em ime delay which a ies significan ly. The con olle pa ame e s need o be adjus ed o sui he ope a ing condi ions, and he p oposed me hod o e s one app oach which can accommoda e such a equi emen . The p oposed con ol s a egy is implemen ed on a small- size Dis ibu ed Con ol Sys em (DCS) as a ou ine ha communica es h ough he s anda d in e ace OLE o P ocess Con ol (OPC). OPC acili a es he in e ope abili y be ween au oma ion and con ol applica ions. III. CONTROL STRATEGY This sec ion is dedica ed o desc ibing he p oposed con- ol s a egy. The p edic i e con olle wi h simul aneous iden ifica ion on-line is based on Gene alized P edic i e Con ol (GPC), ha consis s o applying a con ol sequence ha minimizes a mul is age cos unc ion ha conside s bo h acking e o and con ol e o . Fo con ol pu poses a simple, linea model is equi ed which ela es changes in fluid flow o changes in ou le empe a u e. In his sec ion he heo e ical de elopmen o n-o de sys ems is shown and he use o fi s -o de sys ems is jus ified. A. n-o de sys ems The p oposed con olle ex ends he cos unc ion o he o iginal GPC ([11]) wi h an iden ifica ion e o e m added in he ollowing way: min xJ= N2  j=N1 δ(j)[ˆy( +j| )−w( +j)]2+(1) + Nu  j=1 λ(j)[∆u( +j−1)]2+ + N3  j=1 γ(j)[y( −j+1| )−φθ]2 s. ∆umax ≤∆u≤∆umin,u max ≤u≤umin ymax ≤y≤ymin,a imax ≤ai≤aimin bkmax ≤bk≤bkmin ,d max ≤d≤dmin 1356 ∀i=1...na and ∀k=1...nb, whe e N1and N2a e he minimum and maximum p edic ions ho izons ( aken as N1=d+1 and N2=d+N), Nuis he con ol ho izon and N3is he iden ifica ion ho izon, dis he delay o he inpu -ou pu p ocess model and δ(j),λ(j)and γ(j) a e weigh ing sequences. w( +j)is a u u e se -poin o e e ence sequence, u( )is he inc emen al con ol ac ion (u( )=u( )−u( −1)),ˆy( +j| )is he j-s ep ahead p edic ion o he sys em ou pu on da a up o ime and y( −j+1| )is he j-s ep backwa ds o he sys em eal ou pu on da a up o ime .φis he eg ession ma ix, θis he pa ame e ec o o be iden ified and finally ai,bi,d,a e he ans e unc ion pa ame e s o he disc e e polynomials o deg ee na and nb as shown below. I a CARIMA model is used o model he andom dis u - bances in he sys em and he noise polynomial is chosen o be 1, he ollowing equa ions a e ob ained1: A(z−1)y( )=z−dB(z−1)u( )+( ) ∆(2) Whe e Aand Ba e he ollowing polynomials in he backwa d shi ope a o z−1: A(z−1)=1+a1z−1+a2z−2+...+anaz−na (3) B(z−1)=b0+b1z−1+b2z−2+...+bnbz−nb hen he bes expec ed alue o he ou pu p edic ion ˆy( + d+j| )is gi en by, ˆy( +d+j| )=(1−a1)ˆy( +d+j−1| )+ (4) (a1−a2)ˆy( +d+j−2| )+...+ ana ˆy( +d+j−na −1| )+b0∆u( +j−1) + b1∆u( +j−2) + ...+bnb∆u( +j−1−nb) I equa ion (4) is applied ecu si ely o j=1,2,...,N, he p edic ion ec o is gi en by he ollowing equa ion exp essed in condensed o m as: ˆy=Gu++Sˆy−+Hu−(5) Whe e ˆy,u+,ˆy−and u−a e ec o s o sizes N×1,Nu×1, (na +1)×1and nb ×1 espec i ely. ˆy= ⎡ ⎢ ⎢ ⎣ ˆy( +d+1| ) ˆy( +d+2| ) ... ˆy( +d+N| ) ⎤ ⎥ ⎥ ⎦ u+= ⎡ ⎢ ⎢ ⎣ ∆u( ) ∆u( +1) ... ∆u( +Nu−1) ⎤ ⎥ ⎥ ⎦ ˆy−= ⎡ ⎢ ⎢ ⎣ ˆy( +d| ) ˆy( +d−1| ) ... ˆy( +d−na | ) ⎤ ⎥ ⎥ ⎦ u−= ⎡ ⎢ ⎢ ⎣ ∆u( −1) ∆u( −2) ... ∆u( −nb) ⎤ ⎥ ⎥ ⎦ And G,Sand Ha e ma ices o dimensions N×Nu,N× (na +1)and N×nb, espec i ely. The ollowing equa ions show how he ma ices G and S can be ob ained o n-o de sys ems in a s anda d o m. 1Pa ame e s ai,biand da e ime-dependan . Gis a lowe iangula ma ix which akes he o m: G= ⎡ ⎢ ⎢ ⎢ ⎣ g00... 0 g1g0... 0 . . .. . .. . .. . . gNgN−1... g 0 ⎤ ⎥ ⎥ ⎥ ⎦ and hei elemen s a e gi en by g0=b0 gj= j  i=1 aigj−i+ j−1  i=0 bij=1,...,N (6) I j< 0⇒gj=0 Sis gi en by s1,j =−˜aj+1,j=1,...,n˜a si,j = i−1  k=1 s1,ksi−k,j (7) i=2,...,N;j=1,...,n˜a Whe e ˜aand n˜aa e he elemen s and deg ee espec i ely o he polynomial ˜ A(z−1), ha is, ˜ A(z−1)=∆A(z−1)= (1 −z−1)A(z−1). His gi en by h1,j =bj,j=1,...,nb hi,j = i−1  k=1 (˜ak+1hi−k,j)+h1,i+j−1(8) i=2,...,N;j=1,...,nb And finally φis he eg ession ma ix o dimension N3× (na +nb +1)and θis he pa ame e ec o o be iden ified o dimension (na +nb +1)×1, which is calcula ed a e e y sampling ime using he eceding ho izon iden ifica ion. φ=[y( −j| )y( −j−1| )...y( −j−na | ) ∆u( −d−j| )... ∆u( −d−j−nb | )] (9) θ=[ 1−a1( )a1( )−a2( )... a na( )(10) b0( )... b nb( )]T The decision a iables o he p oblem p oposed a e he ollowing: x=[a1( )... a na( )b0( )... b nb( )d( )(11) ∆u( )∆u( +1)... ∆u( +Nu−1) ]T The algo i hm complexi y g ows wi h ega d o o de sys em and con ol ho izon. B. Fi s -o de sys ems Mos p ocesses in indus y, when conside ing small chan- ges a ound an ope a ing poin can be desc ibed by a linea model o , no mally, e y high o de . This is because mos in- dus ial p ocesses a e composed o many dynamic elemen s, usually fi s o de , so he ull model is o an o de equal o he numbe o elemen s. In ac , each mass o ene gy s o age elemen in he p ocess p o ides a fi s -o de elemen 1357 in he model. Conside , o ins ance, a long pipe used o hea exchanging pu poses, as he case o sola collec o . The pipe can be modelled by b eaking i in o a se o small pieces, each o which can be conside ed a fi s -o de sys em. The esul ing model will ha e an o de equal o he numbe o pieces used o model he pipe, ha is, a e y high-o de model. These e y high-o de models would be di ficul o use o con ol pu poses bu , o una ely, as shown in [12], i is possible o app oxima e he beha iou o such high-o de p ocesses by a sys em wi h one ime cons an and a dead ime. The plan o be con olled can be desc ibed by his kind o model. I he sampling ime is an in ege mul iple o he delay, he disc e e ans e unc ion is gi en by: G(z−1)= bz−1 1−az−1z−d In his case na =1and nb =1and he me hodology shown abo e is educed conside ably. The e o e φand θa e educed o dimensions N3×3and 3×1 espec i ely: φ=[y( −j−1| )y( −j−2| )∆u( −d−j| )] (12) θ=1−a( )a( )b( )T(13) And he decision a iables numbe becomes 3+Nu: x=[a( )b( )d( )∆u( )∆u( +1)(14) ... ∆u( +Nu−1) ]T Consequen ly he op imiza ion p oblem is also educed and now he algo i hm complexi y g ows linea ly wi h he con ol ho izon. The algo i hm complexi y is independen on he sys em pa ame e s. C. Op imiza ion p oblem The op imiza ion p oblem is composed o a bilinea ob- jec i e unc ion (con ol and es ima ion canno be designed sepa a ely, he es ima ion is a ec ed by he con ol) subjec o inequali y cons ain s ( he ones ha can be handled by any MPC plus hose imposed on model pa ame e s) in he p esence o con inuous and in ege a iables (dead ime d). The e o e i is a non-con ex Mixed In ege Non-Linea P og amming (MINLP) p oblem. This kind o p oblem has a high compu a ional bu den, mainly i he global minimum wan o be ound. The e a e B anch&Bound algo i hms a ailable in he ma ke ha sol e his op imiza ion p oblem wi h he help o he use , who can influence he choice o b anching a iable by p o iding p io i ies o he in ege a iables. Anyway, his is no an easy p oblem o be sol ed on-line. In o de o simpli y he me hod so ha can be used in eal ime, wo app oxima ion ha e been used: a) A simple op imiza ion algo i hm has been used. The Ma lab Op imiza ion Toolbox unc ion ( mincon) has been used o sol e he p oblem. mincon uses de i a i e- based sea ch algo i hm and do no gua an ee a glo- bal minimum. All he pa ame e s o he op imiza ion unc ion can be modified in o de o each an accep a- ble comp omise be ween execu ion ime and he sub- op imal solu ion o he algo i hm. b) On he o he hand, he p oblem has been elaxed ea ing he in ege a iable as eal, ha is, i is con e ed in o Non-Linea P og amming wi h eal a aibles. The alue gi en by he algo i hm is unca ed in o de o sa is y he equi emen s o he sys em. The only uning pa ame e s o he con olle a e: 1) Con ol ho izon: Nu. 2) P edic ion ho izon: N1=d+1,N2=d+N. 3) Iden ifica ion ho izon: N3. 4) Ou pu weigh ing ac o : δi. 5) Inpu weigh ing ac o : λi. 6) Iden ifica ion weigh ing ac o : γi. IV. SIMULATIONS RESULTS In o de o es he p oposed me hod be o e he final implemen a ion and o compa e i wi h o he s con olle s, a simula ion s udy was made. This sec ion shows simula ion o he p oposed con olle compa ed o a s anda d app oach using an sel - unig GPC wi h RLS iden ifica ion and o he MPCI p oposed by Shouche e al. [7]. The nominal model used o he design is he ollowing fi s o de linea sys em wi h a dead ime o h ee sampling pe iods: Gm(z−1)= −0.009546z−1 1−0.89654z−1z−4(15) The ollowing figu es show he beha iou o he p ocess ou pu , which is he sola field ou le empe a u e (T o) and he manipula ed a iable, which is al e opening (VM1)as well as model pa ame e s a,band d. The uning alues o he p edic i e con olle s a e: Nu=10,N=60,N3=60, λ=1,δ=1,γ= 1000, being he sampling ime Ts=40s. All he decision a iables ha e an ini ial alue equal o ze o, ha is, he con olle does no know he p ocess model. And he maximum and minimum alues o he a iables a e 100 and −100. Fig 2 shows a compa ison o he e olu ion o he p o- cess ou pu esponses unde a sel - uning GPC wi h a RLS iden ifica ion p ocedu e ( hin solid line) and he p oposed me hod GPC wi h simul aneous iden ifica ion (bold line). This simula ion was pe o med in o de o illus a e he beha iou o bo h con olle s unde changes in he ope a ing poin and se -poin . Ini ially, he model pa ame e s a e a= −0.89654,b=−0.009546 and d=3. They a e changed om hei nominal alues a = 159, aking he new alues a=−0.627,b=−1. The dead ime was no changed so ha bo h con olle s could wo k in he same condi ions, since he sel - uning con olle does no es ima e his alue. As can be seen, bo h con olle s beha e well in he nominal case, bu he p oposed con olle is able con go on con olling wi h he new alues o he pa ame e s while he sel - uning GPC beha es wo s . The RLS finds new alues o he pa ame e s ha make he sel - uning con olle beha e well, al hough hey a e no he ue ones. A = 340, he 1358 050 100 150 200 250 300 350 400 450 −2 0 2 4 T o(ºC) Simula ion I 50 100 150 200 250 300 350 400 450 −5 0 5 10 15 VM1(%) 50 100 150 200 250 300 350 400 450 −1 −0.5 0 pa ame e ,a 50 100 150 200 250 300 350 400 450 −1.5 −1 −0.5 0 pa ame e ,b 50 100 150 200 250 300 350 400 450 0 5 Samples ime pa ame e ,delay p oposed MPC MPC wi h adap a ion se poin Fig. 2. Simula ion I MPC wi h adap a ion modifies he alues pa ame e s. This e ec is based on he absence o Pe sis en Exci a ion in closed loop iden ifica ion [13]. A = 351, whe e a s ep change in he e e ence is pe o med, he p oposed s a egy gi es a good closed loop esponse while he MPC wi h adap a ion is fluc ua ing du ing 100 samples. The ollowing simula ion (figu e 3) p esen s he esul s o a es pe o med o show how he p oposed s a egy is able o iden i y he plan dead ime, apa om he o he model pa ame e s. 050 100 150 200 250 300 350 400 450 0 0.5 1 1.5 T o(ºC) Simula ion II 50 100 150 200 250 300 350 400 450 −1 −0.5 0 0.5 VM1(%) 50 100 150 200 250 300 350 400 450 −1 −0.5 0 pa ame e ,a 50 100 150 200 250 300 350 400 450 −1 −0.5 0 pa ame e ,b 50 100 150 200 250 300 350 400 450 0 5 Samples ime pa ame e ,delay GPC p oposed MPC se poin Fig. 3. Simula ion II In his case he compa ison has been ca ied ou wi h a fixed GPC.TheGPC logically beha es wo s , since i is no able o adap o his change. The model used in he simula ion has been changed om he one in equa ion (15) o Gm(z−1)= −0.9z−1 1−0.6723z−1z−1 No e how, in spi e o he g ea a ia ion o he pa ame e s (e en dead ime), he s a egy desc ibed in his pape is able o mee he new model pa ame e s wi hou he need o a Pe sis en Exci a ion. I is able o ack he se -poin in s eady s a e and when i is changed. The s anda d GPC is no able o mee hese changes. The las simula ion compa es he p oposed me hod wi h he MPCI p oposed by Shouche e al.. The model is aken om case s udy (B) o [7] and is gi en by: y( )=ay( −1) + bu( −1) + e( ) Whe e he ini ial model pa ame e s a e a=0.4,b=0.4and e=−0.05. The ue pa ame e s a e a=0.6,b=0.2and e=0, which pe ec ly iden ified by bo h con olle s. Table I shows he acking capabili ies o bo h con olle s quan ified as IAE (In eg al o Absolu e E o ) and ISE (In e- g al o Squa e E o ). Bo h con olle s find good es ima es o he ue alues, bu MPCI imposes cons ain s on he inpu in o de o ha e Pe sis en Exci a ion, de e io a ing he acking capabili ies o he con olle . The di e ence in con olle s pe o mance is clea ly shown. TABLE I MPCI VS PROPOSED MPC Con olle IAE ISE MPCI 0.0817 2.5017 ×10−5 P oposed MPC 1.3279 ×10−46.6304×10−11 V. EXPERIMENTAL RESULTS Se e al expe imen s ha e been pe o med on he sola plan o show he beha iou o he p oposed con olle . The uning alues used a e: Nu=10,N=60,N3= 150, λ=1,δ=10,γ= 100. All he decision a iables s a wi h a ini ial alue equal o ze o, ha is, he e is no p e ious knowledge o he plan dynamics. The bounds o all he a iables a e 100 and −100 excep ∆umax =20and ∆umin =−20. The ollowing g aphics show he ac ual sola field ou le empe a u e (T o) oge he wi h i s e e ence, al e opening, sola adia ion, field inle empe a u e, which is he accumula o s ou pu empe a u e (Tac)aswellas model pa ame e s a,band d. Figu e 4 p esen s he esul o he expe imen ca ied ou o show e e ence acking capabili ies. The expe imen akes o e h ee hou s, and co esponds o a clea day (see sola adia ion). The e exis s a slow a ia ion in he sola adia ion and inle empe a u e Tac du ing all day which gi es ise o changes in p ocess dynamics. In his case he delay emains unchanged (d=5), bu he o he pa ame e s (aand b), a e modified by he con olle in o de o ob ain a good closed loop beha iou . One o he mos appealing ea u es o his me hod, as is i capabili y o s a ing o con ol wi hou p io knowledge o he plan , is shown in he nex expe imen . Figu e 5 shows he e olu ion o he plan a he beginning o he day. Du ing he s a -up phase, he con ol s a egy is 1359 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 80 85 90 95 T o(ºC) Expe imen al esul s I 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 35 40 45 50 VM1(%) 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 800 950 1100 Radia ion (W/m 2 ) 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 60 70 80 Tac (ºC) 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 −0.8 −0.7 −0.6 pa ame e a 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 −0.1 −0.08 −0.06 −0.04 pa ame e b 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 4 4.5 5 5.5 6 Samples ime (Ts=40s) pa ame e d Fig. 4. Expe imen al esul s I able o d i e he plan owa ds he desi ed ope a ing egime and ack he se poin , e en wi h changes in adia ion. In his case he pa ame e s cons ain s a e: amax =−0.6, amin =−1,bmax =1,bmin =−0.9,dmax =10,dmin =1. No ice ha some o hese cons ain s a e ac i e du ing he expe imen , showing ha a cons ained MPC is sol ed on line. The esul s ob ained in bo h expe imen s a e good in spi e o he a ying condi ions, showing ha he p oposed me hod is a good candida e o con ol his kind o plan s. VI. CONCLUSIONS The pape has shown he applica ion o a p edic i e con olle wi h simul aneous iden ifica ion o a sola plan . The con ol s a egy allows he s a -up o he plan wi hou a edious iden ifica ion p ocedu e and has shown good pe - o mance in changing ope a ing condi ions. The use o a sub-op imal solu ion o he MINLP p oblem allows i s use in eal ime wi h low compu a ional equi emen s. While he applicabili y o he me hod has been illus a ed, u u e in es iga ion is needed ela ing he op imiza ion p ocedu e and s abili y issues. 2000 2500 3000 3500 4000 4500 5000 5500 6000 60 80 100 T o(ºC) Expe imen al esul s II 2000 2500 3000 3500 4000 4500 5000 5500 6000 0 20 40 VM1(%) 2000 2500 3000 3500 4000 4500 5000 5500 6000 400 700 1000 Radia ion(W/m 2 ) 2000 2500 3000 3500 4000 4500 5000 5500 6000 48 49 50 51 Tac(ºC) 2000 2500 3000 3500 4000 4500 5000 5500 6000 −0.9 −0.8 −0.7 −0.6 −0.5 pa ame e a 2000 2500 3000 3500 4000 4500 5000 5500 6000 −1 −0.75 −0.5 −0.25 0 pa ame e b 2000 2500 3000 3500 4000 4500 5000 5500 6000 2 3 4 5 6 Samples ime (Ts=40s) pa ame e d Fig. 5. Expe imen al esul s II REFERENCES [1] E. Camacho and C. Bo dons, 2nd Edi ion. Model P edic i e Con ol. London: Sp inge Ve lag, 2004. [2] C. Cu le and B. Ramake , “Dynamic Ma ix Con ol- A Compu e Con ol Algo i hm,” in Au oma ic Con ol Con e ence, San F ancisco, 1980. [3] D. Ram´ ı ez and E. Camacho, “Cha ac e iza ion o Min-Max MPC wi h Global Unce ain ies,” in P oc. Ame ican Con ol Con e ence, ACC, 2002. [4] E. Mosca, Op imal, P edic i e and Adap i e Con ol. P en ice Hall, 1995. [5] E. Camacho, M. Be enguel, and F. Rubio, Ad anced Con ol o Sola Powe Plan s. Sp inge -Ve lag, London, 1997. [6] K. As ¨ om and B. Wi enma k, Adap i e Con ol. Addison-Wesley, 1989. [7] M. Shouche, H. Genceli, and M. Nikolaou, “E ec o On-line Op i- miza ion Techniques on Model P edic i e Con ol and Iden ifica ion (MPCI),” Au oma ica, ol. 23/2, pp. 137–160, 2002. [8] G. Goodwin and K. Sin, Adap i e fil e ing: p edic ion and Con ol. P en ice Hall, 1984. [9] A. N´ u˜ nez-Reyes, J. No mey-Rico, C. Bo dons, and E. Camacho, “A Smi h P edic i e based MPC in a Sola Ai Condi ioning Plan ,” Jou nal o P ocess Con ol, ol. 15/1, pp. 1–10, 2005. [10] N. Fila o and H. Unbehauen, Adap i e Dual Con ol. Be lin: Sp inge -Ve lag, 2004. [11] D. Cla ke, C. Moh adi, and P.S.Tu s, “Gene alized P edic i e Con ol. Pa I. The Basic Algo i hm,” Au oma ica, ol. 23, no. 2, pp. 137–148, 1987. [12] P. Deshpande and R. Ash, Elemen s o Compu e P ocess Con ol. ISA, 1981. [13] B. Ande son, “Adap a i e Sys ems, Lack o Pe sis en Exci a ion and Bu s ing Phenomenon,” Au oma ica, ol. 21, pp. 247–258, 1985. 1360 View publica ion s a sView publica ion s a s