CONTROLLER PERFORMANCE MONITORING AND DIAGNOSIS. INDUSTRIAL PERSPECTIVE

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1 Copyrgh IFAC 5h Trennal World Congress, Barcelona, Span CONTROLLER PERFORMANCE MONITORING AND DIAGNOSIS. INDUSTRIAL PERSPECTIVE Derrck J. Kozub Shell Global Soluons USA Inc. Weshollow Technology Cener, Houson, TX Conroller performance monorng and dagnoss s benefcal o ensure profable mplemenaon of conrol n pracce. The goal of hs paper s share he experence of he auhor wh respec o useful echnology ha has been developed n hs feld. Parcular aenon s gven o he problem of monorng ndusral mulvarable conrollers. Indusral examples and opporunes for furher research are presened. Copyrgh IFAC Keywords: Monorng Feed Back Loops; Closed Loop Conrol; Conrol Analyss. INTRODUCTION Auomaed process conrol (APC) has long been recognzed as benefcal for mproved process operaon. Wh he ncreased peneraon of process conrol echnology n recen decades has become evden ha he realzaon of APC benefs requre ha roune monorng and manenance be carred ou boh effecvely and effcenly. The reasons nclude ncorrec a pror desgn assumpons, changng (me varan) process operang condons, process nonlneares, and changes/problems assocaed wh nsrumenaon and equpmen. The las decade has seen sgnfcan aenon devoed o hs opc by boh he academc and ndusral communes. Evdence of hs was shown a he Chemcal Process Conrol 6 Conference (CPC 6) (Tucson, ) where an enre sesson was devoed o he opc of conroller performance monorng. Readers neresed n an excellen source of revew maeral are asked o refer o hese papers (Harrs and Seppala, ; Desborough and Mller, ; Shah e al, ). The purpose of hs paper s o provde feedback on some of he relevan work ha we have found useful n our busness pracce. Some dscusson wll be provded on he sae of monorng wh respec o sngle npu / sngle oupu (SISO) conrol (e.g. base level). Parcular aenon wll be gven o he problem of monorng opmzng mulvarable conrollers. Examples wll be demonsraed wh daa from ndusral applcaons. I wll be shown ha, despe recen sgnfcan advances, here sll exss research opporunes for mproved echnology for conroller monorng and dagnoss n pracce. Ths s especally rue for he opmzng mulvarable conroller problem.. UPTIME Hsorcally, loop upme, or n servce facor, has been he mos frequenly ulzed sasc for monorng he performance of conrol sysems. Upme reporng makes mnmal use of avalable process daa. I can be vewed as he exreme form of daa compresson wh respec o conroller performance monorng. Only he sae of he conroller (On/Off) s used o calculae he sasc. Neverheless, hs frs, low level nformaon s essenal n any effecve conroller monorng sraegy. Loops wh low upmes are usually gven hgher prory wh respec o manenance work. The mos frequen causes of low loop upme are ofen assocaed wh nsrumenaon, acuaor, and process equpmen problems. Whle conroller upme nformaon can always be consdered essenal for monorng performance, experence has shown ha hs nformaon alone s no suffcen o ensure opmal performance. Loops operang a upmes greaer han 95 % are ofen encounered whch yeld sable, bu poor dynamc response characerscs. Mller and Desborough () carred ou a comprehensve aud of housands of ndusral base level conrol loops. Ther resuls led o he concluson ha, despe hgh upme, here was a sgnfcan opporuny for mproved performance wh a large percenage of loops nvesgaed. Anoher ssue ha poses problems wh upme reporng s he lack of conssency wh s calculaon. Ths s especally rue for he mulvarable case. In hs case, some weghed average of CV and MV upme s used. In exreme cases, upme s repored based on he conroller beng on, wh complee dsregard for he number of nacve CVs and MVs. The dscusson ha follows wll be concerned wh sascal nformaon ha wll serve o complmen he lmed nformaon provded by conroller upme. 3. Prelmnares 3. SINGLE CV/MV CONTROL The sngle npu / sngle oupu (SISO) conroller problem has been he mos horoughly nvesgaed case, and where mos of he applcaons experence

2 les. The unconsraned, SISO case can be descrbed by y = P( z ) u + D ( z ) d + ν () u = C( z ) e + C ( z ) d () e = s y (3) where, a samplng nerval, y s he conrol oupu (CV), u s he manpulaed conrol npu (MV), d, s an h measurable dsurbance, υ represens he ne addve effec of nose and unmeasured dsurbances on he CV, s s he CV se pon, and e s he conroller error from se pon. P ( z ), C ( z ), D ( z ), and C f, ( z ) are he dscree me ransfer funcons represenng he effec of u, e, and d, on eher he CV or MV response. Usng hese equaons, The closed loop CV error from se pon and MV response wll be s ( P( z ) C f, ( z ) + D ( z )) d, v e = s y = (4) + P( z ) C( z ) u = C( z ) e (5) For he purpose of SISO conroller performance monorng and dagnoss, he dynamc response characerscs assocaed wh (4) and (5) are of concern. f, 3. ARMA Tme Seres Modellng The ne dynamc response assocaed wh e can be descrbed by an Auo-Regressve, Movng Average (ARMA) me seres model of he form θ ( z ) e = a ( ) (6) = + ψ z + ψ z + a φ( z ) where a s a whe nose me seres model arsng from any zero mean dsrbuon. These models can be easly denfed from process response daa usng mnmum varance, predcon error crera (Box and Jenkns, 976). A smlar me seres model can be denfed for u, or measured loop dsurbances. The mpulse response for (6) provdes some average e response for he daa wndow of observaon. The dynamc characerscs of he esmaed models are deermned by he rend feaures ha conrbue mos o he varance of he rend. As can be observed from (4) and (5), he esmaed ARMA model properes wll be deermned by boh he relave magnudes and dynamc feaures of υ, s and d, s n he wndow of observaon, and ransfer funcons P ( z ), C ( z ), D ( z ), and ( z )., C f,. ARMA model average response esmaon has been found useful n pracce. I s now reachng he pon of wdespread use, parcularly wh respec o SISO base level applcaons. Our experences have led us o conclude he followng: Average response modellng grealy faclaes he ask of loop monorng and audng. Performance can be easly accessed n a very shor me span wh sofware ha auomaes model esmaon and provdes he resuls n a user-frendly fashon. We have seen a remendous reducon n manpower effor relave o he sole use of vsual rend analyss and nrusve procedures. Relave o auo-correlaon and specral analyses, ARMA average response modellng has been consdered far more sraghforward o use. The former procedures, whle provdng smlar nformaon, have been consdered far more challengng o nerpre by conrol engneers n he chemcal engneerng feld. Performance nformaon ha was no readly apparen has been exposed wh heses analyses. Hence, sgnfcan opporunes for performance mprovemen were denfed. I has also been helpful n arrvng a opmal loop unng. The success of usng hs mehod n pracce requres a crcal hreshold of ranng. I does no replace process know how or use of rend daa. I complmens hs nformaon. The resuls of he analyses are a funcon of daa chosen. Hence, he daa mus be nformave, requrng good judgemen on he par of conrol engneers carryng ou he analyss. The resuls can also be a challenge o nerpre when sgnfcan mulple dsurbance sources are presen, and when me varan condons preval. Neverheless, our experence has been ha he nformaon provded s benefcal relave o s lmaons and nal ranng hurdles. 3.3 Mnmum Varance Esmaon Hsorcally, sandard devaon monorng of CV error from se pon has ofen been carred ou, and found useful. From he perspecve of conroller performance monorng, experence has shown hs nformaon can be boh lmed and msleadng. Se pon error sandard devaon s a funcon of he magnude of loop upses. Changes n hs sascal nformaon can be a funcon of changng process condons, and may no necessarly reflec performance of a conroller. Durng perods of large plan upses, hgher sandard devaons are o be expeced despe he fac ha conrollers are respondng as desgned. Durng calm perods of operaon, low sandard devaons can be observed wh poorly desgn conrollers. Harrs (989) showed ha he lowes achevable varance under feedback conrol, referred o as he condon of Mnmum Varance Feedback Conrol (MVC), can be easly esmaed by fng an ARMA me seres model o e daa. Relave o (6), he esmaed MVC response s gven by k + emvc, = ( + ψ z + ψ z + + ψ k z ) a (7) σ MVC = ( + ψ + ψ + + ψ k ) σ a (8) where k s he whole number of sample perods of connuous me delay, e s he esmaed MVC MVC, response, and σ s he esmaed MVC closed loop mvc varance for he daa wndow of observaon. By

3 makng use of σ, he esmaed error from se mvc pon sandard devaon can be compared o hs heorecally lower bound ha wll change accordng dfferen process/dsurbance condons. Ths relave comparson of sascs can be vewed as normalzaon n some sense wh respec o conroller performance. Ths has lead o he nroducon of varous varance rao sascs ha have been advocaed for performance monorng (see references). There has been consderable hoopla, parcularly by academcs, concernng he usefulness of MVC wh respec o monorng conrollers. Relave MVC sandard devaon/varance monorng s hardly as nformave as he nformaon provded by more dealed ARMA average response curves. Our experences wh hs ype of analyss are lsed below. The MVC lower bound can be useful for separang conrol relaed problems from process ones. Suaons arse when problems exernal o a parcular conrol loop are yeldng hgher varaon han can be acceped (e.g. upsream dsurbances). Hgher varaon whou accompanyng poor relave MVC performance srongly ndcaes ha roo cause correcons should nvesgaed exernal o he conrol loop. Auomaon of he MVC assessmen, along wh oher sascal nformaon, can serve as a frs pass-monorng layer o brng obvous problems o mmedae aenon. By self, does no provde suffcen useful nformaon. The MVC lower bound can asss n seng reasonable performance arges. Specfcaon of overly opmsc and conservave performance arges can be avoded wh hs nformaon. MVC nformaon can also be benefcal n ncenve sudes. 3.4 SISO Example To llusrae he applcaon of hese conceps consder some daa colleced from an ndusral SISO base level conroller as shown n Fgure. The op plo shows he CV rend (black) and s se pon ha s fxed a a consan value. The second plo shows he MV rend. Snce he se pon s consan, he goal wll be o evaluae conroller dsurbance regulaon n he daa me range. The sgnfcan drfng MV rend ndcaes ha dsurbances are presen. The hrd plo shows sldng wndow calculaons of CV error from se pon (black) and he MVC esmaed sandard devaons (grey). The wdh of he bars ndcaes he me span of he sldng wndows used o carry ou he sandard devaon calculaons. The dashed lne n hs plo shows he requred upper bound lm for he CV error from se pon ha mus be me. The localsed, wndowed sandard devaon sascs ndcaes ha performance hroughou he enre daa range appears o been conssen. The relave raos of he MVC o CV error from se pon sandard devaon bars ndcae performance no far from mnmum varance feedback. However, he sandard devaon performance specfcaon s no beng me. The resuls shown n he hrd plo clearly ndcae ha he performance specfcaon would no have been me even f he ghes possble, mnmum varance feedback conrol were appled. CV MV CV ERROR & MVC STD Fg.. SISO Loop Response a) CV/Se Pon Trend; b) MV rend; c) CV error & MVC sandard Devaons More nsgh can be ganed by lookng a he average response curves for boh he CV error response (op) and MV rend (boom), as shown n Fgure. CV ERROR MV Tme Fg.. Average Responses a) CV Error From Se Pon; b) MV rend The esmaed average response curves were generaed by fng ARMA models o he enre daa se. In Fgure, he black curves ndcae he esmaed average response rends whle he grey lnes provde a 95% confdence nerval. The rapd decay of he CV error relave o he me scale of concern clearly ndcaes gh conrol. For hs process, here s no MV/CV deadme. Hence, he absence of MVC conrol from he nformaon n Fgure s confrmed by he average response analyss snce CV error does no decay o zero a he frs samplng nerval. However, he response s no far from hs condon. The MV average response can be observed o be very good. The MV rses rapdly close o s fnal seady value wh only a slgh amoun of overshoo. These analyses lead o he concluson ha he performance of he conroller s good. The problem wh he performance specfcaon no beng me canno be addressed by a beer feedback conroller. Dsurbance varance reducon a he source n hs case needs o be nvesgaed. Ths concluson would no be easly arrved a whou he analyses carred ou.

4 3.5 Closed Loop Sysem Idenfcaon Whle ARMA me seres modellng has been proven useful n pracce, he nformaon provdes can be lmed because he conrbung effecs of all loop dsurbances and se pons become confounded. Kozub (996) advocaed he use of closed loop denfcaon o ake advanage of measured loop dsurbances o denfy models of he form: θ ( z ) e = S( z ) s + ( z ) d, + a (9) φ( z ) The nerpreaon of each of hese ransfer funcons can be easly arrved a by comparng (9) wh (4). Equaon (9) can be used o provde predced average responses o ndvdual, measured conrbuons, as well as he resdual unmeasurable dsurbance/nose conrbuon. Ths nformaon can provde far more nsgh abou he performance properes of a conroller. Refer o Kozub(996) for an example applcaon o ndusral daa. Closed loop denfcaon has been proven useful o us, and he concep exends easly o mulvarable problems. The lack of more repored use of closed loop denfcaon remans a mysery o hs auhor. 4. MULTIVARIABLE CONTROL The sae of research and applcaons experence n he area of mulvarable conroller performance monorng s much less evolved compared o he SISO case. In hs secon, some opnons/feedback wll be offered on hs subjec based on our experences. 4. MIMO Exenson of MVC Whle he concep of MVC s sraghforward n he SISO problem, he mulvarable exenson s far more challengng from boh a heorecal and applcaons vewpon. Huang and Shah (999) have advocaed he use of a weghed oupu error varance merc for MVC esmaon snce s closely relaed o he cos funcon employed n mulvarae, unconsraned lnear quadrac conroller desgns. The soluon for hs case s non-rval, and requres he esmaon of a unary neracor polynomal marx from he marx ransfer funcon, and he soluon of a polynomal, mulvarae dophanne equaon. Readers neresed n he deals are asked o refer o he ced reference. For he mulvarable case, he use of a weghed LQ MVC measure s somewha conroversal, and has no been wdely appled for varous reasons. Some of he ssues are lsed below: Sgnfcan process ransfer funcon nformaon, oher han deadme alone, s needed relave o he unvarae case. The negry of he MVC calculaon n he presence of modelng error s unknown. The oupu weghed, lnear quadrac cos funcon s ofen vewed as a convenen mahemacal formulaon o arrve a some analycal soluon for a feedback conroller. Hence, he oupu LQ weghs are ofen unng weghs ha don ruly reflec relave performance n pracce. One mporan praccal concern wh respec o onlne mplemenaon s ha hese weghs can change sgnfcanly, dependng on where CVs and MVs are posoned relave o consran lms. Ths makes he compuaon of MVC more of challenge o carry ou because of me varan weghng changes. Mos ndusral mulvarable conrollers are non-square, fne horzon, consraned model predcve conrollers wh smulaneous opmzaon carred ou wh he seady sae gans. The opmzaon problem s ypcally solved usng a lnear program(lp). Alhough hese conrollers have some feaures n common wh L.Q. conrol, mporan sgnfcan dfferences mus be aken no accoun when monorng hese applcaons. Ths wll be llusraed n an example ha wll follow bellow. A hs me, here s an absence of readly avalable, qualy/frendly code for ou carryng ou he advanced MIMO MVC calculaons. Adequae sofware s needed for praconers o ge a beer feel for he value of he analyss on commercal applcaons. 4. MIMO Tmes Seres Average Response The SISO dea of fng CV error rend daa o me seres models for he purpose generang average response nformaon has been exended o he mulvarable/mul-loop problem. Harrs & Seppala () dscuss he use of vecor auo-regressve (VAR) me seres models of he form Φ( z ) e = a () where e s he error from se pon vecor, a s a zero mean whe nose vecor, and Φ( z ) s an auoregressve, full marx polynomal. For mulvarae and mul-loop sysems, mpulse response analyss can poenally provde valuable nformaon relaed o mulvarae neracons and propagaon of he dsurbances relave o her effec on he oupus. An applcaon of VAR o ndusral daa s shown by Harrs & Seppala () where he usefulness of hs analyss s demonsraed. Whle lmed work and experence has been carred ou wh VAR, and closely relaed approaches (e.g. subspace), s he opnon of hs auhor ha hs approach s useful for connued research and evaluaon. 4.3 Example MPC Conrol To exemplfy some of he ssues relaed o mulvarable conroller monorng, consder some daa acqured from a commercally avalable MPC conroller. The characerscs of hs conroller are:

5 number of CVs s 8; number of MVs s ; and he number of feedforward dsurbances s 4. As far as ndusral mulvarable conrollers are concerned n he perochemcal ndusres, hs conroller can be consdered small. Neverheless, for he purpose of hs paper, s suffcen for llusrang some mporan pons. The CV versus MV sep response model used by he conroller s shown n Fgure 3. Blacked ou boxes ndcae a zero CV/MV response. The me span s 9 mnues for he responses. As can be seen n he Fgure, he mulvarae model s sparse, whch ends o be common wh mos of hese applcaons. Smlar sep response models for he CV/feedforward responses were employed by he conroller Fg. 3. CV versus MV Sep Response Models The MPC conroller has boh a seady sae LP opmzaon layer and a mulvarable feedback conrol layer ha operaes a he same execuon rae. The LP ulzes he gans from he sep response model wh LP cos facors specfed. Hgh and low lm consrans for all CVs and MVs are specfed, and can be adjused durng operaon. The feedback conroller s an unconsraned MPC formulaon. Hence, consrans are deal wh a he projeced seady sae by he LP ha passes arges o he feedback conroller. Approxmaely, wo weeks of daa were colleced for hs applcaon. The daa was consdered represenave of roune operaon. Fgure 4 provdes nformaon on he % me ha each CV (op) s beng drven o a consran. The boom plo show he % me ha each MV s no se o a consran, and herefore, avalable for feedback. From he CV nformaon, s apparen ha only 5 o 6 CVs are drven o LP lms by he conroller. The remanng CVs floa beween hgh and low LP lms. From a feedback conroller sandpon, a CV drven o an LP lm can be consdered o have a se pon durng hese perods as specfed by he consran bound. The CVs a LP lms are nuvely more mporan from a monorng perspecve relave o CVs whch are floang whn consran bounds. Durng floang perods, we have found from experence, ha he assocaed LP arges end o follow/rack he CVs whn bounds. These CVs are ofen assgned (or near ) weghng n he feedback conroller whch essenally pus hem no an open loop sae. Furhermore, he L.P. arges end o be noser relave o her CVs due o he nheren poor seady sae projecons. Hence, from a monorng vewpon, error from LP arge durng hese perods s essenally meanngless, or relavely unmporan. Neverheless, CVs rends ha erracally change beween floang and LP lm saes are a characersc ha s mporan o deeced and monor. From he MV bar plo (boom) n Fgure 4 can be observed ha 4 o 5 MVs appear o be sgnfcanly free from consrans for feedback conrol. The remanng MVs appear o be fxed a LP consran lms, and herefore, reman a an open loop sae. CV % TIME AT L.P. LIMIT MV % TIME NOT LIMITED CV NUMBER MV NUMBER Fg. 4. % Consran Acvy: a) % CV Tme a L.P. Lm b) % MV Tme no a L.P. Lm # MVs NOT AT LIMIT 4 3 # L.P. LIMIT CVs MVs me x 4 Fg. 5. Dynamc Consran Acvy Trends a) Number CVs Tme a L.P. Lm Trend b) Number MVs no a L.P. Lm Trend Fgure 5 provdes addonal nsgh no he performance of he conroller LP layer. The op plo shows he number of CVs beng drven o an LP bound as a funcon of me. The boom plo shows he number of MVs free for feedback conrol (no a lm) as a funcon of me. Ths nformaon shows how he LP s drvng he dmenson of feedback conrol as a funcon of me. The dmensonaly can be observed o be swappng from manly, 3, and 5, wh 3 beng he mos frequen case (3 by 3 conrol). The fgure also reveals ha consderable chaerng s occurrng wh respec o he conroller dmenson. Based on experence, hs can be a cause for concern because ofen he economcs/plan condons are no expeced o change a such a rapd me scale. Overall, hese wo smple-mnded plos have ndcaed ha here may be LP sably problems. Furhermore, he dmenson of he conroller seems o vary manly beween o 4, nvolvng mosly 6

6 and 5 CVs and MVs respecvely. If he daa s ruly represenave, he mplcaon of hs observaon s ha here mgh be an opporuny o prune he conroller sze, whch would yeld a smaller, smpler conroller o manan. The nformaon s also helpful for prorzng CVs and MVs for monorng analyss. CV: 9 AVG. CV 9 ERROR TREND x x TIME Fg. 6. CV number 9: a) Trend Plo; b) Average CV Error Response (LP bound only) Fgure 6 (op) shows rend nformaon assocaed wh CV 9 n he conroller. The CV rend s ndcaed n black. The LP hgh and low lms are ndcaed n gray. The LP arge s shown by he (--) rend. Ths CV s he second mos frequen CV (see Fgure 4) ha rdes LP lms. Usng only daa when he LP arge (se pon) s a a bound he average error response, as dscussed n secon 3., can be esmaed. Ths s shown n he boom plo n Fgure 6. The performance of he conroller n holdng he CV a he upper arge can be observed o be poor. The selng me s abou 4 mnues, whch s very sluggsh relave o he 9-mnue open loop sep response models. As dscussed earler, ncluson of he daa durng CV floang arge perods yelds msleadng nformaon. A smlar dynamc response analyss can be carred ou on he remanng 5 CVs ha spend sgnfcan me beng drven o LP bounds. Based on our experences, hs analyss has proven o be very useful, provded he sae of he CV wh respec o he LP s accouned for. The resuls from hs relavely smple example serve o show ha he scope of MIMO conroller monorng s far more nvolved relave o he SISO case. Some mporan ssues for he reader o apprecae are: The amoun of he daa ha needs o analyzed and nerpreed accuraely s nonrval. The LP layer, beng negraed wh he feedback conroller, canno be gnored when carryng ou monorng analyss. Boh s dynamc properes and effec on he feedback layer mus be examned. Models are always avalable for analyss. Alhough hs ssue was no dscussed here, would be hghly benefcal o make effecve use of hs nformaon. Some of he unvarae conceps have been shown o exend o hese problems, However, ssues, such as MIMO MVC need o be reconsdered relave o he framework of commercal MPC n order o be proven useful. I s he opnon of he auhor ha far more research s needed o fnd effecve soluons o MIMO conroller monorng. The role of MIMO performance s fel o be mporan o he fuure of MPC conrol. The opmzaon formulaon and sze of hese conrollers n pracce has been somewha conroversal n he MPC communy. Quanave monorng has he poenal of provdng some mporan nsgh n addressng hese ssues. 5. CLOSING REMARKS Conroller performance monorng s mporan o ensure he success of process conrol echnology. The nformaon presened n hs paper has shown ha useful echnology has been proposed ha s now becomng adoped n pracce. Whle he sgnfcan progress has been made wh unvarae (base level) conrol, far more challengng research opporunes sll reman o address he praccal ssues concerned wh ndusral mulvarable conrol. REFERENCES Box, G.E.P, and G.M. Jenkns (976), Tme Seres Analyss Forecasng & Conrol, Holden-Day Desbourough, L. and Randy Mller (), Increasng Cusomer Value of Indusral Conrol Performance Monorng Honeywell s Experence, Proc of he CPC V Meeng, Tucson Harrs, T.J. (989), Assessmen of Conrol Loop Performance, The Canadan Journal Of Chemcal Engneerng, Vol. 67 Harrs, T.J. and C.T. Seppala (), Recen Developmens n Conroller Performance Monorng And Assessmen Technques, Proc. of he CPC V Meeng, Tucson Huang, Bao and S. L. Shah (999), Performance Assessmen of Conrol Loops. Theory & Applcaons, Spnger. Kozub, D. J. (996), Conroller Performance And Dagnoss: Experences and Challenges, Proc. of he CPC V Meeng, Lake Tahoe, p. 83 Shah, S.L., R. Pawardhan, and B. Huang, Mulvarae Conroller Performance Analyss: Mehods, Applcaons and Challenges, Proc. of he CPC V Meeng, Tucson.