Application of simple cascade GPC with robust behaviour to a sugar refinery

APPLICATION OF SIMPLE CASCADE GPC WITH ROBUST BEHAVIOUR TO ASUGAR REFINERY C. Bo dons and E.F. Camacho Dp o. Ingenie a de Sis emas y Au oma ica, Uni . o Se il le, Spain. Camino de los Descub imien os sn, 41092 Se il la, Spain. Phone: +34-95-4487348 Fax: +34-95-4487340 E-mail:bo dons,edua do@ca uja.us.es Keywo ds : P edic i eCon ol, P o cess Con ol, Ro- bus Con ol. Abs ac This pap e p esen s he applica ion o a Gene alized P e- dic i e Con olle  gpc  o sludge densi y con ol in a suga ac o y. The lo op is con olled by a cascade s a egy, whe e b o h he mas e and he sla econ olle s a e p edic- i e ones. The con ol law is ex emely simple o compu e and he uning is s aigh o wa d since a me ho d o im- plemen gpc p e iously de eloped by he au ho s which is e y simple o implemen and une has b een used. The con olle s a e embedded in he exis ing con ol sys em, needing he same compu a ional equi emen s as pid ou- ines. The o iginal gpc algo i hm is imp o ed by he use o he so-called T p olynomial, which inc eases he s abil- i y obus ness by l e ing he p edic ions in o de o cop e wi h mo del unce ain ies and die en p ocess dynamics caused bychanges in he p o cess op e a ing p oin s. 1In o duc ion This pap e shows an applica ion o a gpc o a p o cess in a suga ac o y.The implemen a ion was ca ied ou by he au ho s in collab o a ion wi h he  m p ocisa .The suga ene y is lo ca ed in Pe~nael Valladolid, Spain and b elongs o Eb oAg icolas . The con ol s a egy uns in a o si In eg al Cub e Con ol Sys em, whe e he gpc has b een included as a lib a y ou ine which can b e inco - p o a ed in acon ol sys em as easily as he buil -in pid ou ine. Mo del Based P edic i eCon ol  mbpc o mpc is in- c easingly gaining accep ance and has b een used in qui e anumb e o applica ions ac oss he wo ld wi h sp ec acu- la esul s,  s in he ene y and p e o chemicals sec o and nowadays also in many o he elds in indus y. The e a e many applica ions o p edic i econ ol success ully in use a he p esen ime 10, no only in he p o cess in- dus y bu also applica ions o he con ol o a di e si y o p o cesses 8, 11, 12. Mpc is pa icula ly a ac- i e o s a wi h only a limi ed knowledge o con ol, b e- cause he concep s a e e y in ui i e, and i can b e used o con ol a g ea a ie yo p ocesses, om hose wi h ela i ely simple dynamics o o he mo e complex ones. The e m Mo del P edic i e Con ol do es no designa e a sp ecic con ol s a egy bu a e y ample ange o con- ol me ho ds whichmake an explici use o a mo del o he p o cess o ob ain he con ol signal by minimizing a cos unc ion. The gpc me ho d p op osed by Cla ke e al. 5 is a easonable ep esen a i e o his amily o me hods and has b ecome one o he mos p opula mpc me ho ds, b eing success ully implemen ed in many indus ial applica ions 3. As is well known, he basic idea o gpc is o cal- cula e a sequence o u u e con ol signals in suchaway ha i minimizes a mul is age cos unc ion dened o e a p edic ion ho izon. The index o b e op imized is he ex- p ec a ion o a quad a ic unc ion measu ing he dis ance be ween he p edic ed sys em ou pu and some p edic ed e e ence sequence o e he ho izon plus a quad a ic unc- ion measu ing he con ol eo . A Gene alized P edic i eCon olle esul s in a linea con ol law which is easy o implemen once he con olle pa ame e s a e known. The de i a ion o he gpc pa am- e e s equi es, howe e , some ma hema ical complexi ies, which a e dicul o sol e in some indus ial con olle s. The indus ial applica ion o gpc in small con ol sys ems in indus y has some dicul ies ha mus be o e come. Apa om needing low compu a ional equi emen s, i mus b e accep ed by he plan op e a o s. Fi s , he un- ing p o cedu e mus b e simple enough, so ha a gpc can b e uned as easily as a pid , and second, he con olle mus b e obus , ha is, i mus b eha ewell in he p esence o he ine i able mo delling e o s. The applica ion shown he e combines he p owe o p e- dic i e con ol wi h he simplici y and ease o use o he adi ional con olle s commonly ound in indus y. The simplici yisachie ed by using a me ho d de elop ed by he au ho s which can b e used wi h mos p o cesses in indus y 1. Due o his simplici yin he compu a ional equi e- men s, wo gpc algo i hms can be used as cascade con- olle s. In o de o imp o e he obus ness o he closed &VSPQFBO$POUSPM$POGFSFODF&$$ "VHVTUo4FQUFNCFS,BSMTSVIF(FSNBOZ *4#/  lo op sys em, he T p olynomial has b een added o he o - mula ion. The pap e is o ganised as ollows: Sec ion 2 desc ib es he applica ion: he sludge densi ycon ol in a suga ac- o y. The adap a ion o he s anda d gpc algo i hm o a wide class o indus ial p o cesses in o de o educe calcu- la ions and imp o e obus ness is p esen ed in sec ion 3 sec ion 4 is dedica ed o he ob en ion o he plan mo del, sec ion 5 shows some op e a ing esul s and nally he con- clusions o he wo k a e p esen ed in sec ion 6. 2 P o cess Desc ip ion The ac o y p o duces suga om suga -b ee by means o a se ies o p o cesses such as p ecipi a ion, c is aliza ion, e c. The ac o y handles a la ge quan i yo wa e  wa e is mainly necessa y o p o ducing s eam in he b oile s, o he diusion p o cess and o washing he suga -b ee . The wa e is no ac ually consumed so al hough used in a ious p o cesses i is eco e able. The ob jec i eis ha he ac o y should b e comple ely sel -sucien wi h ega d o wa e consump ion. One o he p o cesses which consumes mos wa e is washing he b ee . Because i is a o o plan g owing b e- low g ound i always a i es a he ac o y co e ed in soil. Thus he  s p o cess necessa y o he bee is o wash i . The aw ma e ial is washed using clean wa e o elim- ina e any emaining soil which logically mus no en e in o he suga p o ducing p o cess. This op e a ion esul s in la ge amoun s o di y wa e sludge b eing p o duced whichmus b e ecycled. The eco e y o clean wa e om his sludge is achie ed by using he p o cess shown in gu e 1. A sepa a ing ank is used whe e sedimen a ion by g a i y akes place, he wa e s ays on he su ace and he sludge sinks o he b o om. This sepa a ing ank is an op en con aine wi h a diame e o 40 me e s and an a e age dep h o 5 me e s. I is  ed wi h a blade which e ol es a 0.05 pm and which ejec s he hicke emains in o a 35 m 3 homogenize cylinde om which i is pump ed in o he cen i uge which e ol ing a g ea sp eed sepa a es he wa e om he soil by cen i uga ion. The wa e hus ob ained e u ns o he sepa a ing ank om whe e he usable wa e is again d awn ou . The cen i uge wo ks co ec ly o sludge ows o be- ween 14 and 22 m 3 h and a densi y which should be be ween 1100 and 1200 gl. This densi y is he basic a i- able o b e con olled as i mus emain wi hin his ange o ensu e he co ec wo king o all he ins alla ion. This densi y dep ends up on he wa e ecycled om he cen- i uge o he sepa a ing ank and he e o e on he sludge ow ha ci cula es om he cylinde o he cen i uge. I is dicul o mo del he ela ionship b e ween he eci - cula ion o w and he densi y, b ecause a ious ac o s come in o play and he e is no clea ela ionship b e ween said a iables. Howe e , i do es seem clea ha an inc ease Soil Flow con ol Bu e FT Decan e DT cleaning p ocess Wa e om he Cen i uge Sludge Densi y Figu e 1: Wa e Reco e y P o cess in a Suga Rene y in he ow causes mo e wa e o b e eci cula ed and hus he densi y o he sludge o be dec eased a dec ease o densi y has he opp osi e eec . An exhaus i e mo delling is a he complica ed so a s o de sys em wi h delay will b e used o y o app oxima e he esp onse. An added p oblem is ha he ow measu emen s a e no e y eliable due o he pa icles in susp ension. Fu - he mo e he e a e con inuous blo ckages in he con ol al e which cause b usque al e a ions in he ow. On he o he hand, b ecause o he mo emen o he blades in he sepa a ing ank which s i he mud ha will b e pump ed owa ds he cen i uge, he densi y measu emen s a e no uni o m b ecause hey keep alling like lumps o soil e e y- ime he blade passes o e he d ain. 3 P ecompu ed GPC This pap e uses a o mula ion o Gene alized P edic i e Con ol  gpc  de elop ed by he au ho s, easy o imple- men and une, ha is alid o he ma jo i y o indus ial p o cesses 1, 2. The me ho d makes use o he ac ha a gene alized p edic i e con olle esul s in a con ol law ha can be desc ib ed wi h ew pa ame e s. The con olle is alid o a wide class o p o cesses in indus y and a se o simple unc ions ela ing he con olle pa ame e s o he p o cess pa ame e s has b een ob ained. Wi h his se o unc ions ei he a xed o a sel uning gpc can b e im- plemen ed in a s aigh o wa d manne . Mos p o cesses in indus y a e high o de sys ems ha a e no sui able o con ol pu p oses, bu in gene al i is p ossible o app oxima e he b eha iou o such high o de p o cesses wi h a simplied mo del consis ing o a  s o - de p o cess combined wi h a dead ime elemen 7. This yp e o sys em is hen desc ib ed by he ollowing ans e unc ion: G  s = K 1+ s e , s  d 1 whe e K is he p o cess s a ic gain,  is he ime cons an o p ocess lag, and  d is he dead ime o delay. This  mo del is widely used in indus y o desc ib e he dynamics o many p o cesses, as shown by he p opula i y o he eac- ion cu e me ho d and he op en lo op Ziegle -Nichols pid uning ules. Ob iously b e e app oxima ions could be ob ained by using highe o de mo dels, bu his would e- qui e iden ica ion packages which a e no no mally a ail- able in indus y. When he dead ime  d is an in ege mul iple o he sampling ime T   d = dT , he co esp onding disc e e ans e unc ion o equa ion 1 has he o m: G  z , 1 = bz , 1 1 , az , 1 z , d 2 whe e disc e e pa ame e s a , b and d can easily be de- i ed om he con inuous pa ame e s by disc e iza ion o he con inuous ans e unc ion, esul ing in he ollowing exp essions: a = e , T  b = K 1 , a  d =  d T The e o e he ca ima mo del used o he p edic ion is: A  z , 1  y  = B  z , 1  u  , 1 + C  z , 1  4    whe e C is he noise p olynomial. I i is chosen equal o one, he mo del esul s: 1 + az , 1  y  = bz , 1 u  , d + 1 4    The p edic ions along he ho izon om + d +1 o + d + N can be calcula ed by means o he ollowing equa ion: ^ y  + d + j j  = 1 + a ^ y  + d + j , 1 j  , a ^ y  + d + j , 2 j + b 4 u  + j , 1 3 In 1 he gpc algo i hm is de i ed o his kind o p o- cesses, leading o he con ol s a egy shown in gu e 2. The plan pa ame e s a e used o compu e he con olle co ecien s  l y 1 , l y 2 , l 1  as desc ib ed in 1. These co- ecien s a e p ecalcula ed as a unc ion o he sys em pole  a and he con ol weigh ing ac o   wi h ho i- zons N 1 = d +1, N 2 = d + N , N u = N , N = 15. No ice ha he dep endence o hese co ecien s on pa ame e b can b e a oided i he con olle is designed conside ing he plan oha e a uni a y s a ic gain. The alues ^ y  + d j , ^ y  + d , 1 j  a e ob ained by he use o he p edic ion which basically consis s o a mo del o he plan whichis p o jec ed owa ds he u u e wi h he alues o pas inpu s and ou pu s and only equi es s aigh o wa d compu a- ion. The con ol signal is di ided by he p ocess s a ic gain in o de o ge a sys em wi h a uni a y s a ic gain since he con olle co ecien s ha e b een calcula ed con- side ing he sys em o ha e uni a y gain. The con ol law is gi en by: 4 u  = l y 1 ^ y  + d j + l y 2 ^ y  + d , 1 j + l 1   The con ol algo i hm educes o: 1 - a z -1 b z -1 -d z l l + + + + y y P edic o z -1 Δu z -1 Δu k-1 k+d k+d-1 k y1 y2 k u k y k l 1 Figu e 2: Con ol Scheme 1. Compu e k ji as unc ions o he con ol weigh ing ac o  . 2. Make l yi = k 1 i + k 2 i ^ a k 3 i , ^ a o i =1  2and l 1 = , l y 1 , l y 2 3. Compu e ^ y  + d j and ^ y  + d , 1 j  using equa ion 3 ecu si ely. 4. Compu e con ol signal u   wi h: 4 u  = l y 1 ^ y  + d j + l y 2 ^ y  + d , 1 j + l 1   5. Di ide he con ol signal by he s a ic gain. 6. Go o s ep 2. I can be seen ha he algo i hm is eally simple and can b e easily included in any comme cial con ol sys em wi h- ou complex calcula ion equi emen s. This algo i hm has b een success ully es ed in some exp e imen al plan s. Howe e , i has also been shown 2 ha al hough i is a he obus o gain and ime cons an unce ain ies, i has small obus ness o dead ime unce ain ies, ha a e commonly ound in eal plan s. Tha is why he algo i hm mus b e mo died o conside his ci cums ances, since he p o cess o b e con olled p esen ha kind o unce ain y as will b e seen la e . The s abili y obus ness o gpc can b e imp o ed wi h he use o an obse e polynomial, he so-called T  z , 1  p olynomial. In 4 a e o mula ion o he s anda d gpc algo i hm including his p olynomial can b e ound. In o - de o do his, he ca ima mo del is exp essed in he o m: A  z , 1  y  = B  z , 1  u  , 1 + T  z , 1  4    Up o now he T  z , 1  has b een conside ed equal o 1, de- sc ibing he mos common dis u bances o as he colou - ing p olynomial C  z , 1 . This p olynomial is e y dicul o ob ain and in many cases i is conside ed as a design pa ame e . In consequence he p edic ions will no b e op- imal bu highe obus ness in he ace o unce ain ies can b e achie ed, in a simila in e p e a ion as ha used  GPC2GPC1 P ocessPipes - - Se poin Densi y Flow Se poin Flow Densi y Figu e 3: Cascade con olle s byLjung 9. This p olynomial can b e conside ed as a p e- l e as well as an obse e . The eec i e use o obse e s is known o play an essen ial ole in he obus ealiza ion o p edic i econ olle s see 4 o he eec o p el e - ing on obus ness and 14 o guidelines o he selec ion o T . The T p olynomial can b e easily added o he p op osed o mula ion, compu ing he p edic ion wi h he alues o inpu s and ou pu s l e ed by T  z , 1 . Then, he p edic o wo ks wi h y  = y   T  z , 1  and u  = u   T  z , 1  . The ac ual p edic ion o he con ol law is compu ed as ^ y  + d = T  z , 1 ^ y  + d . The co ec choice o he T p olynomial is a p oblem ha has no comple ely b een sol ed, al hough i s eec on he obus ness o he closed loop sys em has b een analysed in se e al pap e s 6, 4, 13, 15. In his applica ion, T is made equal o A  z , 1 1 , z , 1 , b eing  a alue close o he sys em p ole, as sugges ed in 15. 4Mo del A ainmen As has b een explained, i is p ossible o con ol he densi y wi h he eci cula ion ow. As his ow sue s equen dis u bances due o he p esence o discon inui ies in he uid comp osi ion, i is necessa y o keep i con olled wi h ano he egula o . The con ol s a egy is, he e o e, go- ing o b e a cascade con ol, he densi ycon ol ac ing on he emo e se p oin o he local con olle o he o w o he cen i uge sla econ olle , see gu e 3. This lo cal con- ol can b e ca ied ou using ei he a pi con olle o a gpc indis inc i ely. The dynamics o his lo op a simple ow lo op do es no jus i y i sel he use o a gpc ins ead o a pi , bu as he gpc ou ine is al eady ins alled in he con ol sys em and he compu a ion ime is simila in b o h cases, hisloopwas also used as a es b ed o he con olle . Be- sides, he uning o he gpc is done au oma ically e e y ime he sys em pole is up da ed. A ea men o he densi y me e signal is needed o a ain he mo del. P io l e ing is necessa y o elimina e he noises and he eec o he blade s okes in he sepa- a ing ank, in o de o b e able o wo k wi h an eec i e alue indica i e o he e olu ion o he ac ual densi y. Following an ini ial analysis i is obse ed ha he cha - ac e is ic ime o he sys em esp onse is in he o de o hou s. In o de o ob ain a mo del, a s ep is p o oked a he inpu , whichis heow se poin , om 18 o 16 m 3 h. I is p ossible o ob ain om he da a a dead ime o 2.6 hou s, a ime cons an o 1 hou and a gain o -25 g=l m 3 =h . 5 Op e a ing Resul s The con ol was s a ed up using l e ing wi h he T- p olynomial. This p olynomial is made equal o A  z , 1 1 , z , 1 , wi h  = 0 : 9. The con ol eo  was chosen equal o 0.1. The lo cal owcon olle had p e iously b een adjus ed by he s ep esp onse p o cedu e ob aining K = 2 : 5,  =4s and  d =10 s no ice he clea die ence in he dynamics b e ween he ou e and inne lo ops. Fo op e a i e easons i was necessa y o limi he ow se p oin be ween 14 and 22 m 3 h, al hough i was no p os- sible o use a p edic i e s a egy wi h cons ain s b ecause o compu a ional limi a ions. Wi h he nominal mo del chosen o he densi yloopand wi h a sampling ime o 12 minu es, he disc e e pa ame- e s o he p o cess mo del a e gi en b y: a =0 : 8187 b = , 0 : 4531 d =13 The con olle co ecien s can b e compu ed see 1 cal- cula ing k ji    and hen l y 1 , l y 2 and l 1 as unc ions o he sys em p ole in he o m: l yi = k 1 i + k 2 i a k 3 i , a i =1  2 l = , l y 1 , l y 2 k 11 = , exp0 : 3598 , 0 : 9127  +0 : 3165  2  k 21 = , exp0 : 0875 , 1 : 2309  +0 : 5086  2  k 31 = 1 : 05 k 12 = exp , 1 : 7383 , 0 : 40403   k 22 =exp , 0 : 32157 , 0 : 81926  +0 : 3109  2  k 32 = 1 : 045 As he sys em p ole is in 0 : 8187, i a alue o  equal o 0.1 is chosen, he con olle co ecien s a e l y 1 = , 4 : 7454 l y 2 =2 : 5930 l 1 =2 : 1524 A simila p o cedu e is used o he ob en ion o he as owcon olle , wi h alues: l y 1 = , 3 : 2448 l y 2 =2 : 1294 l 1 =1 : 1154 The con ol sys em op e a ion is shown in he ollowing diag ams. No e he ime scale, whe e he slowness in he densi ye olu ion can b e seen, wo hou s b eing necessa y in o de o ca y ou a change in he se p oin see gu e 4. No ice ha he ou pu shows an oscilla o y signal added o he mean alue. These oscilla ions a e densi ychanges due o he eec o he blades which s i he mud in he decan e , so he densi y measu emen s show his esp onse b ecause hey keep alling like lumps o soil e e y ime he blade passes o e he d ain.  0 20 40 60 80 100 120 140 160 180 200 Time (minu es) 1090 1095 1100 1105 1110 1115 1120 1125 1130 Densi y (g/l) Figu e 4: Se p oin change 0 50 100 150 200 250 300 350 400 450 500 Time (minu es) 1050 1060 1070 1080 1090 1100 1110 Densi y (g/l) Figu e 5: Dis u bance ejec ion in he densi yloop No e he imp o ance o in o ducing he T-p olynomial, gi en ha he dead ime ob ained exp e imen ally is no e y p ecise and ha also o he es s showed ha i s alue a ied subs an ially om one si ua ion o ano he . As is known, gpc is no e y obus when aced wi h dead ime mo delling e o s and he T-p olynomial should b e used in o de o inc ease he obus ness. The con ol ob jec i e is o main ain he app op ia e condi ions o he cen i uge o wo k co ec ly. This e- qui es o main ain he densi y a a cons an alue. The main densi y lo op ob jec i e is o ejec dis u bances. Fig- u e 5 show he beha iou o he con olle du ing eigh hou s keeping he densi y a he igh alue o 1090 gl. The b eha iou o he inne lo op  he owcon ol lo op is d as ically die en om he densi yloop. The dynam- ics a e as e , wi h apid changes in he o w alue. Figu e 6shows he b eha iou o his loop when aced o se poin changes p o oked by he mas e con olle . I can b e seen ha he signal is e y noisy due o he dicul y o measu - ing a he e ogeneous ow in a zone wi h la ge ib a ions due o he p oximi y o he cen i uge, bu i s means alue ollows he e e ence. No ice ha he ou e lo op is op en du ing his es in o de o show he beha iou o he inne lo op. The con olle in e ace allows he p o cess pa ame e s o b e changed on line. The mo dels a e uned by he op e - 0 20406080100 Time (minu es) 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25.0 Flow (m3/h) Figu e 6: Se p oin ollowing in he owloop a o as so on as a disc epancy b e ween he ac ual and he p edic ed ou pu s  ha app ea on he sc een is de ec ed. I should b e emphasised ha his con olle wo ked sa - is ac o ily and wi hou in e up ion un il he end o he yea 's campaign, b eing handled wi hou dicul yby he plan op e a o s. The esul s ob ained using his con olle in e ms o e o a iance imp o ed he ones ob ained in he las yea 's campaign, when he p ocess was con olled by an op e a o , since hey did no da e o une a pid b ecause o he long dead ime. 6Conclusions An applica ion o a Cascade Gene alized P edic i e Con- olle  gpc  o he sludge densi y con ol in a suga ac- o y has b een p esen ed. The con ol lawwas ex emely simple o compu e and he uning was s aigh o wa d b e- cause a me ho d o compu e gpc p e iously de elop ed by he au ho s whichis e y simple o implemen and une was used. The o iginal gpc algo i hm was imp o ed by he use o he T p olynomial o inc eases he s abili y o- bus ness, since mo del unce ain ies app ea ed when wo k- ing a die en op e a ing p oin s. The con olle has b een success ully wo king in he ac o y, showing ago o d be- ha iou . The applica ion shown he e combines he p owe o p e- dic i e con ol wi h he simplici y and ease o use o he adi ional con olle s commonly ound in indus y, show- ing howa gpc can b e easily used in clasical con ol s uc- u es like cascade con ol in he same wayas pid s. 7 Acknowledgmen s The au ho s would like o acknowledge Juan He mida om p ocisa by his in e es and supp o in he de elop- men o he con olle and he people om Eb o Ag icolas by he acili ies o es ing he con olle in he plan . 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