Journal of Process Control

Transcription

1 Journl of Process Control 19 (9) Contents lists ville t ScienceDirect Journl of Process Control journl homepge: Model predictive control monitoring using multivrite sttistics Ashrf AlGhzzwi, Brry Lennox * Control Systems Centre, School of Electricl nd Electronic Engineering, University of Mnchester, Oxford Rod Simon Buliding, Mchester M13 9PL, UK rticle info strct Article history: Received 8 My 7 Received in revised form 17 Jnury 8 Accepted 9 Mrch 8 Keywords: Control condition monitoring Multivrite sttisticl process control Model predictive control Principl component nlysis (PCA) Prtil lest squres (PLS) Recursive PCA nd PLS Condenste frctiontion Control loop monitoring hs ecome n importnt reserch field over the pst decde. Reserch hs primrily trgeted single-input single-output (SISO) feedck control systems with limited progress eing mde on the monitoring of multi-input multi-output (MIMO) control systems nd lrge scle model predictive control (MPC) systems in prticulr. The size nd complexity of MPC systems mens tht identifying nd dignosing prolems with their opertion cn e chllenging. This pper presents n MPC condition monitoring tool sed on multivrite sttisticl process control (MSPC) techniques. The proposed tool uses intuitive chrts to enle csul users of MPC technology to detect norml controller opertion nd to identify possile cuses for this ehviour. Through its ppliction to dt collected from lrge scle MPC system, the proposed technique is shown to e le to identify nd dignose poor control performnce resulting from vrious issues including inpproprite interction y process opertors. Ó 8 Elsevier Ltd. All rights reserved. 1. Introduction Over the pst decde the oil, gs, nd chemicl mnufcturing industries hve invested hevily in the implementtion of dvnced process control (APC) pplictions, of which the most populr form is model predictive control (MPC). MPC ridges process modelling, control nd optimistion to enhnce the profitility nd stility of process opertions. Sustining the performnce of the instlled MPC system is usully dependent on vrious fctors tht ffect their performnce. As highlighted in AlGhzzwi et l. [3], the fctors found to e most contriuting to the poor performnce of MPC pplictions from prcticl point of view re: Lck of properly trined opertors nd support personnel. Lck of MPC condition monitoring pplictions. Significnt process modifictions nd enhncements. Poor controller tuning nd inccurte models. Unresolved sic (regultory nd PID) control prolems. To ddress the ove issues, cdemic reserchers, prctitioners, nd control technology providers hve developed keen interest in monitoring the performnce of control pplictions in generl, nd the condition monitoring of MPC pplictions in prticulr. This effort hs resulted in plethor of pulictions s well s severl commercil tools imed t monitoring the condition of control system pplictions. * Corresponding uthor. E-mil ddress: rry.lennox@mnchester.c.uk (B. Lennox). Interest in control loop monitoring cn e trced ck to the work of Hrris [] who explined how the performnce of single-loop control system could e compred with wht would e chieved if minimum vrince (minvr) controller were pplied. It is rrely sensile to implement minvr controller on n industril system, however, their nticipted performnce does provide lower ound for the vrince of the controlled vrile. Hrris [] proposed sttistic, now referred to s the Hrris index, which is defined s the rtio of the vrince chievle using minvr control to the vrince mesured under the current control lw. As the vlue of this sttistic reduces then so too does the mesured performnce of the control system. The key dvntge of the Hrris pproch to control loop monitoring is tht only routine operting dt is required to determine the performnce of the control system. This fct hs mde the pproch very ttrctive to industry nd it is now pplied s mtter of routine y mny compnies. The Hrris technique hs een investigted nd expnded in mny studies over the lst few yers. Desorough nd Hrris [6], for exmple, extended the technique to mke it suitle for MISO systems. Hrris et l. [11] lter dpted this work nd developed n pproch for MIMO systems. Further modifictions to the pproch hve een proposed y Tyler nd Morri [33], who ccommodted the presence of non-minimum phse zeros nd unstle poles in the performnce criteri, nd Kozu nd Grci [], who suggested tht the controller performnce should e compred with the desired first order response of the closed loop system. Arguing tht minvr performnce is not relistic gol for n industril control system, mny reserchers hve proposed lterntive performnce indices. Ko nd Edgr [16], for exmple, /$ - see front mtter Ó 8 Elsevier Ltd. All rights reserved. doi:.16/j.jprocont.8.3.7

2 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) dopted strtegy tht used PID controller s the enchmrk control performnce, whilst Horch nd Isksson [12] proposed performnce index tht recognised tht it my e desirle for t lest one closed loop pole to e locted wy from the origin. An overview of recent developments in control performnce monitoring for MIMO pplictions ws covered in Qin nd Yu [], where numer of control performnce enchmrks other thn the populr minimum vrince were presented. Due to the nture of some MIMO systems with respect to strong interctions etween vriles, this work recommended dignosing control performnce reltive to enchmrk, nd suggested using multivrite sttistics to help yield meningful dignosis. A cse study on n industril oiler ws presented in this pper. A comprehensive review of the current sttus of control performnce monitoring is presented in Jelli [15]. This pper provides thorough review of control performnce monitoring literture over the pst decde s well s review of the commercilly ville tools nd technologies for control performnce monitoring. A set of comprehensive recommendtions were lso mde, sed on the current tools nd n outline of the future needs in control loop monitoring ws presented. In ddition, proposed methodology tht comines severl ssessment enchmrks nd methods ws proposed. A further review of control monitoring techniques cn e found in Hung nd Shh [13]. More pertinent to MPC pplictions, Ko nd Edgr [17,18] developed monitoring scheme tht compred the performnce of n MPC system to tht chievle using constrined minimum vrince control. Ptwrdhn et l. [28] proposed performnce index which compred the cost function of the controller t ny given time with the cost function from period of time when the controller ws ssumed to e operting well. The fundmentl prolem with the vst mjority of techniques pplied to monitor the performnce of control loops is tht they rely on mesure of the errors etween the controlled vriles nd set-points. However, the mjority of industril MPC systems tend to operte to soft constrint limits for controlled vriles rther thn set-points nd hence there will not e n explicit error mesurement for ech controlled vrile. This mens tht the techniques tht hve een proposed for MPC systems re unlikely to e suitle for industril ppliction. Moreover, prcticl spects of performnce ssessment of MPC ws presented in the work of Agrwl et l. [1] where the reltionship mong process vriility, constrints, nd proilistic economic performnce of MPC ws investigted. This proposed pproch considered the uncertinties induced y the process vriility nd evluted the economic performnce through proilistic clcultions. Further development of this pproch ws presented in Agrwl et l. [2], where Byesin inference ws used for decision mking in order to tune the constrints to chieve optiml economic MPC performnce. In the work of Xu et l. [36], it ws shown tht vrince sed performnce ssessment could e trnsferred to ssessment of MPC performnce. The MPC economic performnce is evluted y solving enefit potentils through either vriility reduction of output vriles or tuning constrints. Algorithms for MPC performnce ssessment nd tuning guidelines for constrints nd vrince were developed in this pper using liner mtrix inequlities nd process dt nd stedy-stte gins. An innovtive technique for monitoring MPC performnce hs een proposed in the work of Loqusto III nd Seorg [23]. Principl component nlysis (PCA) nd distnce similrity fctors were used to monitor MPC performnce, where severl PCA pttern clssifiers were developed to monitor the control system, nd to identify norml ehviour. This technique ws used to monitor the performnce of n MPC controlled Wood Berry distilltion column model. Another pproch to monitor MPC performnce ws presented in Loqusto III nd Seorg [24]; s in Loqusto III nd Seorg [23], current MPC opertion is compred to simulted dtse of closed-loop MPC opertion. However, in this work, neurl network clssifiers were used to determine whether or not the controller ws exhiiting norml performnce. The performnce of the neurl-network sed clssifiers in monitoring n MPC-controlled Wood Berry distilltion column model were exmined for vrious scenrios including the detection of norml opertion, modelplnt mismtch, nd norml disturnces. As result of the industry requirements for MPC monitoring tools, severl leding process utomtion technology providers hve developed tools to help monitor the condition of MPC pplictions. These systems ddress the needs of users to ensure tht these controllers re functioning properly to ensure tngile enefits re relized from their opertion. Exmples of commercilly ville MPC monitoring tools re presented in Tle 1. The ove mentioned tools provide MPC support stff with comprehensive informtion on controllers performnce, effectiveness, model ccurcy, s well s rnge of performnce enchmrks for oth the MPC controller nd the regultory or PID control lyer. Such tools hve contriuted gretly over the pst few yers in ensuring tht instlled controllers re functioning properly for prolonged periods. Although these tools provide gret insight into the condition of control systems they re primrily imed t expert users of MPC technology. Such users re typiclly senior process or control engineers with considerle experience in MPC pplictions. The informtion generted from the ville monitoring tools focuses on control enchmrks, MPC specific prmeters or even frequency domin nlysis. Thus despite the enefits otined from recent monitoring tools, there remins need for monitoring tool tht would help the front-line users such s control room opertors nd junior engineers in understnding the MPC ppliction condition without eing required to hve thorough understnding of the theory, enchmrks or prmeters of MPC technology. Consequently, the specific focus of the work descried in this pper ws to develop n MPC condition monitoring tool tht serves the need for control room opertors nd csul users of MPC pplictions. The desired tool should provide users with informtion eyond the sic service fctor, lso referred to s up-time, or the primitive on/off indictor. Furthermore, it should drw the user s ttention to norml ehviour in the controller performnce, or possily ny process normlity. It is worth noting tht this tool does not replce the MPC monitoring tools mentioned erlier ut rther complements such tools, since MPC technicl support stff need the informtion provided y such tools for in-depth nlysis nd trouleshooting of controller performnce. In this pper, the ility of multivrite sttisticl process control (MSPC) techniques to monitor industril MPC systems is investigted. Intuitive MSPC chrts re used to ssist plnt opertors nd process engineers in monitoring the controller performnce nd help detect norml ehviour. The proposed technique compres current controller performnce with tht otined from n Tle 1 Commercil MPC monitoring tools Compny Tool Supported MPC technology Wesite Honeywell APC Scout Ò RMPCT Ò Aspen Tech Aspen DMCplus Ò Wtch Ò Mtrikon Process RMPCT Ò DMCplus Ò Doctor Ò Shell Yokogw MDpro Ò SMOC Ò

3 316 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) MSPC model derived from dt set representing optimum controller performnce. This work compres the performnce of the two most frequently used MSPC techniques, Principl Component Anlysis (PCA) nd Prtil Lest Squres (PLS) in monitoring MPC performnce. Recursive techniques re lso pplied in designing the proposed monitoring tools so tht it is le to trck the timevrying nture of the process. The results presented in this pper provide n indiction of the enefits provided y the proposed tool nd the types of control system normlity tht the system is le to detect. Furthermore, mny of the prcticl considertions involved when developing multivrite sttisticl monitoring solution for ppliction to n industril MPC system re ddressed. For exmple, which vriles should e included in the nlysis nd how cn time-vrying nd non-sttionry dynmics e ctered for in the model? Although MSPC techniques hve een used routinely for the detection of fults nd norml conditions in industril studies [25,19], the use of PCA/PLS methods to monitor the condition of n industril MPC system sed on dt collected from n industril process is considered novel. 2. Multivrite sttisticl process control (MSPC) MSPC refers to collection of lgorithms tht cn e used to extrct informtion from lrge multivrile dt sets. Although the lgorithms differ considerly, they shre the similrity tht they typiclly identify severl rtificil vriles, s liner or nonliner comintions of the originl vriles. The enefit tht MSPC techniques offer is tht in situtions where there is lrge mount of correltion etween the originl vriles, such s with industril process dt, they cn descrie most of the informtion in the dt set using reduced numer of rtificil vriles, which cn mke nlysis of the dt set, nd process, simpler. There hve een mny studies completed over the lst few yers which hve highlighted how MSPC techniques cn successfully e used to detect process fults nd normlities (Kourti, 5) [19], clssify mterils nd products [26] nd more recently e used to regulte complex processes [5]. These studies hve tended to focus on two specific MSPC techniques, principl component nlysis (PCA) nd prtil lest squres (PLS). These two lgorithms re descried riefly in the following Sections 2.1 nd 2.2. For further detils regrding these lgorithms, the reder is referred to Jckson [14] for PCA nd Geldi nd Kowlski [7] for PLS Principl component nlysis PCA is n unsupervised dt nlysis technique. The pproch trnsforms mtrix contining m oservtions of n process vriles, Z, into mtrix of independent rtificil vriles, or scores, t k (where k = 1ton) of length m. The reltionship etween the scores nd the originl mtrix, Z is defined s follows: Z ¼ Xnp<n t k p T k þ E k¼1 where the p k vectors, of length n, re known s the lodings. The lodings re equl to the eigenvectors of the dt covrince mtrix, Z T Z. The t k nd p k pirs re ordered so tht the first pir cptures the lrgest mount of vrition in the dt nd the lst pir cptures the lest. In situtions where there exists significnt co-linerity it is generlly found tht smll numer of principl components (np) cn ccount for much of the power, nd hence informtion, in the covrince mtrix. The remining power constitutes the error term E. When Eq. (1) is pplied to single vector of new oservtions, z T, the resulting term e is clled the prediction error. There re severl methods for determining suitle vlue for np. In this work, the ð1þ pproch suggested y Wise nd Gllgher [34] ws dopted. This pproch pplies cross vlidtion, with due considertion of the vrince explined y the scores, to select n pproprite vlue for np. Hving identified the PCA model, two monitoring sttistics re used to identify norml conditions. These norml conditions my e identified in the dt tht is used to develop the model or new dt tht my e susequently collected nd nlysed in rel-time. These two sttistics, T 2 nd, re defined s follows: T 2 ¼ Xnp k¼1 t k r 2 k tt k where r 2 k is the vrince of the kth t score. ¼kEk 2 2 Provided ny dt presented to the PCA model is consistent with the dt used to identify the model, then the vlues of the T 2 nd sttistics should remin low, nd elow sttisticl threshold limit. Elevted vlues of these sttistics provide n indiction of norml conditions. Goulding et l. [8] provide further informtion regrding the use of these sttistics to detect nd isolte norml conditions Prtil lest squres PLS is regression tool tht cn e pplied whenever process vriles cn e prtitioned into cuse (X) nd effect (Y) vlues. The method is commonly used in preference to lterntive identifiction lgorithms, such s multiple liner regression (MLR) when developing dt driven models. Its dvntge over these lterntive identifiction lgorithms is tht it is le to produce ccurte nd roust models in situtions where high levels of correltions exist etween the cuse vriles [7]. The PLS lgorithm is similr to PCA nd selects fctors of cuse vriles in sequence which successively mximises the explined covrince etween the cuse nd effect vriles. Given mtrix of cuse dt, X, nd effect dt, Y, fctor of the cuse dt, t 1, nd effect dt, u 1, is evluted, such tht np<nx X ¼ X np<nx t k p T k þ E nd Y ¼ X u k q T k þ F ð2þ k¼1 k¼1 These equtions re referred to s the outer reltionships. The score vectors t k, which re different to those otined using PCA re mutully orthogonl. These vectors nd the u k vectors re selected so s to mximise the covrince etween ech pir, (t k,u k ). nx is the numer of cuse vriles tht re contined within mtrix X nd E nd F re error mtrices. Liner regression is performed etween the t k nd the u k,to produce the inner reltionship, such tht u k ¼ k t k þ e k where k is regression coefficient, nd e k refers to the prediction error. The PLS method provides the potentil for regulrised model through selecting n pproprite numer of scores, or ltent vriles, u k in the model (np). Furthermore, it is often found tht reltively smll numer of the low-index ltent vriles cn explin the greter prt of the vrition in oth the cuse nd effect vriles. Cross vlidtion cn e used to select the necessry numer of ltent vriles. As with PCA, severl univrite sttistics cn e used to identify when new dt is inconsistent with the dt tht ws used to identify the PLS model. In this pper three sttistics ssocited with the PLS lgorithm hve een used: T 2, x nd y which re defined s follows: ð3þ

4 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) T 2 ¼ Xnp k¼1 t k r 2 k tt k where r 2 k is the vrince of the kth t-score. x ¼kEk 2 2 y ¼kFk 2 2 The key differences etween PLS nd PCA re tht PLS considers the explicit reltionship etween cuse nd effect vriles, which is prticulrly importnt when considering multivrile control system. The sttistics identified for PLS relte specificlly to either the cuse or effect vriles, which cn id in the isoltion of the cuse of ny normlity. 3. Methodology The generl pproch proposed in this pper for monitoring n industril MPC system is sed on designing PCA or PLS model tht will e used in rel-time to identify normlities with the controller. The models re sed on operting dt from periods where the controller ws operting in wht is elieved to e n optiml fshion. The methodology followed in developing the MPC condition monitor in this study involved the following steps: 1. Appliction design. 2. Dt collection nd nlysis. 3. MPC monitor prototyping nd testing. Although this pproch ppers reltively stright forwrd, severl issues need to e considered when developing MSPC models for prcticl industril pplictions. These include the following: The design ojectives nd criteri for the monitoring system. Type of dt used to develop the MSPC model. Process nd control vriles used in the model. MSPC technique est suited for the ppliction. How cn the informtion provided y the MSPC model e interpreted nd wht type of informtion does the model provide? The following sections descrie in detil how the ove steps were followed in this study. The pproch tken is elieved to e reltively generic for developing industril MPC monitoring systems, nd recommendtions re presented to del with the issues ssocited with designing such n ppliction for specific industril process exmple, which is condenste frctiontion process. 4. The condenste frctiontion process description The process investigted in this study ws condenste frctiontion process. Fig. 1 shows simplified process flow digrm of the process. This process seprtes hydrocron feed into mix of products for further processing or product lending. The plnt feedstock is condenste mixture from non-ssocited gs production tht contins vrious mixtures of petroleum frctions tht re seprted into vrious products using the difference in voltility etween the feed components y distilltion. Process cold feed is pumped through the preheting trin to het the feed up to the required deslting temperture. The plnt feed then enters deslter (not shown in Fig. 1) where slt is removed nd the first seprtion of light frctions occurs. The deslted feed is then fed to preflsh drum where light products nd ny remining free wter re removed. The preflsh drum product is then heted y set of het exchngers efore entering preflsh distilltion column. In this column, feed is distilled into light, medium nd hevy products, which re removed from the top, middle, nd ottom sections of the column, respectively. Hevy product from the ottom of the preflsh distilltion column is further heted y two furnces efore entering the min frctionting distilltion column. In the min column, feed is distilled into multiple products sed on the difference in their oiling tempertures. The distilled products re collected t the column s top, middle, nd lower sections nd re further processed to produce motor gsoline, kerosene, jet fuel nd diesel oils. A key ojective of the process is tight control of the min frctiontor column product specifictions (properties) such s oiling points nd flsh points while mintining mximum production rtes suject to equipment sfety nd physicl constrints. This refining process is chrcterised y its reltively slow dynmics (settling time is round 2 h), lrge numer of process Fig. 1. Simplified flow digrm of the process.

5 318 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) vriles, nd process interctions. Process interction not only exists etween composition (property) control loops ut lso etween process vriles s well. For exmple, mnipulting the process feed, furnce output temperture, or the min frctiontor column overhed temperture ffects ll products composition s well s the production rte of severl finished products. The complexity of operting het integrted distilltion processes ws investigted in [21] nd in [9] where modelling, simultion, nd controllility nlysis of such processes were investigted. An importnt control ojective in this process is controlling the composition (specifiction) of the six products of the process. A key chllenge in controlling this process is to ensure ll key product specifictions re met in the presence of chnging process conditions, interction etween vrious sections of the plnt due to het integrtion nd disturnces, while monitoring lrge numer of process vriles to ensure tht the plnt is well within its sfety limits; in ddition, opertors hve to lso operte nd monitor the condition of the instlled MPC. An instlled model predictive controller (MPC) system provides ccurte control of criticl product specifictions, minimises the impct of process disturnces, nd drives the process to operte closer to its economic optimum point. Six inferentil models (soft-sensors) re implemented in the process to provide timely prediction of criticl product specifictions (composition) nd to enle rel-time control of these product specifictions. The controller hs controlled vriles (CV), 17 mnipulted vriles (MV) nd 6 mesured disturnce vriles (DV), nd is considered resonly lrge with respect to industril stndrds. The key MPC CV re the process feed flow, furnce outlet temperture, nd the specifictions (composition) of the min frctiontor products: medium nphth 9% oiling point, hevy nphth 9% oiling point, kerosene flsh point, kerosene 9% oiling point, light diesel 9% oiling point, nd hevy diesel 9% oiling point. Since on-line nlysers re not ville to mesure these specifictions, soft-sensors re used to predict these product specifictions t the top of the pre-frctiontor distilltion column, s well s top nd side drw of the min condenste frctiontor, these soft-sensors re mong the controller CV. Other key CV re product flow rtes nd vlve position of key control vlves. Controller MV include feed flow setpoint, furnce outlet tempertures, min frctiontor overhed temperture, reflux flows in oth distilltion columns, recycle flows of side products. Key MV tht influence criticl CV re minly the reflux flows nd furnce outlet tempertures. An emedded optimiser in the MPC is set to mximise vlule products flows while mintining the product specifictions. As descried in Section 4 the mesured DV in the process include chnges in feed qulity, lending flows in etween Tle 2 Model predictive controller key vriles Controlled vriles (CV) Mnipulted vriles (MV) Disturnce vriles (DV) Process feed flow Feed flow setpoint, Feed qulity Furnce outlet temperture Furnce outlet tempertures, Blending flow etween products Medium nphth 9% Min frctiontor overhed Amient temperture oiling point temperture Hevy nphth 9% oiling point Reflux flows in oth distilltion columns Kerosene flsh point Recycle flows of side products Kerosene 9% oiling point Light diesel 9% oiling point Product flow rtes Vlve position of key control vlves the min frctiontor column products, nd mient temperture. A summry of key MPC vriles is presented in Tle MPC monitoring tool This section presents in detil the steps followed during the design of the MPC monitoring tool. The design methodology ws sed on tht presented y AlGhzzwi nd Lennox [4] nd Miletic et l. [27], however specific guidelines pertinent to the development of MPC monitors re given to ssist in the development of industril MSPC-sed MPC monitoring pplictions Appliction design The min ojective for this work ws to develop prcticl condition monitoring tool le to provide timely informtion on the performnce nd condition of n industril MPC system. The developed tool ws designed to e used y process opertors nd engineers to detect nd isolte ny normlity in the condition of n instlled MPC system so tht pproprite ction could then e tken. Users of this tool need not e expert users of MPC technology since condition informtion nd possile cuses of norml opertion is shown y intuitive chrts. The proposed MSPC monitor ims to ddress the following contriuting fctors to norml MPC ehviour; firstly the lck of properly trined opertors nd support personnel nd secondly the lck of MPC condition monitoring pplictions. Users of the proposed tool should e le to esily detect nd isolte norml controller condition through sic MSPC chrts, nmely the Hotelling (T 2 ), squre prediction error (), nd contriution chrts. The contriution chrts will enle the user to identify the root cuse of the norml MPC ehviour so tht pproprite ction cn e tken. Opertors nd support personnel would only need to e trined on using the proposed tool nd to hve sic understnding of MPC opertion. With respect to the second fctor, this serves s high level monitor of the MPC condition, nd together with ny of the tools shown in Tle 1 would form hierrchicl pproch for the condition monitoring of MPC systems, where opertors cn rely on the proposed MSPC tool to detect norml ehviour in controller performnce, nd ttempt to resolve the normlity. However if the prolem persists due to mjor prolem with the controller, then MPC support engineers cn rely on the tools in Tle 1 to identify the root cuse of the norml ehviour. Finlly, nd most importntly, the tool must e roust to cope with chnging process ehviour nd routine involvement nd intervention of MPC users in the form of temporrily turning off certin CVs or chnging setpoints or control limits of MV nd CVs. In summry, the im of the proposed condition monitoring tool ws to Identify norml MPC conditions nd indequte controller performnce. Detect ny violtion of key MPC vriles limits nd identify possile cuse. Assist csul users nd plnt opertors in monitoring the MPC performnce. Withstnd routine chnges in controller vriles nd limits. Detect occurrences of loss of controller degrees of freedom or inpproprite CV/MV limits setting Dt collection nd nlysis Process dt is of crucil importnce when developing empiricl models, nd hence dt collection nd nlysis is mjor contriutor

6 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) to the success of prcticl MSPC pplictions. During this step, process dt tht represents optiml MPC opertion must e collected. The issues tht re ddressed during this stge re s follows: 1. Wht is considered optimum controller ehviour? 2. How much dt is ville? 3. Wht is the condition of the collected dt, nd is it suitle for modelling purposes? In this work, optimum controller performnce ws defined s periods where:. The MPC controller is ON.. Criticl CV nd MV re ctive nd within their specified trgets (rnges or set points). By definition, criticl CV/MVs re required to e ctive t ll times s per MPC design. c. All key control vlves re within the controllle rnge. In this work this mens vlve opening more thn % nd less thn 9%. d. Generl process condition is norml, nd process operting point is not different from tht which the MPC models were developed for The dt set chosen to represent optimum MPC performnce will provide the enchmrk which controller condition t ny given point in time is compred with. This dt set will e used to develop the MSPC models to e used for the MPC condition monitor. Since control vlves constitute the finl control element in the mjority of process control loops, it is importnt to mintin them within their controllle rge. When controller is unle to meet required CV trget due to control vlve eing fully closed or fully open, the control vlves is sid to e sturted. Vlve sturtion ffects tht ville degrees of freedom within n MPC system nd it is often recommended tht opertors relx some of the control trgets on certin less criticl CVs to provide the controller with more degrees of freedom. Vlve sturtion periods re often overlooked when collecting process dt for modelling 1 45 Hotelling T Fig. 2. Sttic PCA monitoring chrts. /T2 chrt for output vriles /T2 chrt for input vriles 15 5 y TsqY x TsqX Fig. 3. Sttic PLS monitoring chrts.

7 3 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) or nlysis purposes. In this work, periods where control vlves were sturted ws not included in the modelling dt set. Eliminting this dt will help the condition monitoring tool to identify periods of vlve sturtion or loss of degrees of freedom. Another considertion mde when identifying optimum MPC performnce ws to remove sections of collected dt when one or more of the controller CVs nd MVs were inctive or outside of their upper nd lower trgets. MPC is model-sed control lgorithm, where models of the process re derived from process testing where key MVs re pertured to generte step response trends for the CVs. For n MPC system to function properly, it is impertive tht controller models re representtive of the process, nd plnt-model mismtch is miniml. To develop n effective MPC condition monitor, the process operting point should not e significntly different from tht t the time when the MPC models were developed. The process dt used to develop the MSPC models in this study were collected from n instlled dt historin. MSPC models were developed from dt collected from one yer of opertion, of which pproximtely eight months of dt represented optimum opertion. An issue tht often ffects dt nlysis nd dt-driven modelling techniques is the compression of dt in plnt historins. Although it is dvisle to use uncompressed dt when developing empiricl models, it is not lwys possile to collect uncompressed dt for extended periods of time. For more detils on the effect of dt compression nd its effect on dt driven methods, the reder is referred to Thornhill et l. [32]. The dt used in this work ws found to e cceptle for modelling purposes s per the guidelines set y Thornhill et l. [32]. As for dt clening nd filtering, the Hmpel filter proposed y Person [29] ws used for outlier detection nd dt clening. AlGhzzwi nd Lennox [4] nd Miletic et l. [27] provide further informtion on dt processing for MSPC pplictions nd the generl pproches suggested in these ppers were followed in this study MPC monitor prototype nd testing Once the design ojectives were set, nd modelling dt hd een collected nd nlysed, prototype for the proposed MPC monitor ws developed using sttic PCA nd PLS models to evlute their ility in trcking process conditions nd identifying significnt normlities nd excursions. Control limits for oth the nd T 2 chrts re typiclly exmined in this step so tht pproprite levels cn e specified to ensure tht only significnt normlities exceed these limits. To gin etter understnding of the dt, sttic PCA nd PLS models were initilly developed using the y c 1 Mnipulted Vrile Fig. 4. Anorml condition from vlve sturtion () PCA chrt, () PLS Output vriles chrt, (c) vlve output rw dt.

8 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) full processed dtset. Figs. 2 nd 3 show the T 2 nd of the PCA nd PLS models, respectively. Both PCA nd PLS models were developed with six principl components (ltent vriles) tht helped explin 85% of the vriility for PCA models, nd for PLS models explined 9% nd 78% of the vriility of the input nd output vriles, respectively. The models used ll MPC vriles including the inferentil estimtes (soft-sensors) tht were included in the controller. Tests were conducted to nlyse the effects of removing ny of these vriles. By removing the mesured disturnces, the developed monitor ws found to e slightly more sensitive to issues relting to the control system itself, however, overll using ll the vriles ws found to produce the most roust nd useful monitoring system. The smple time ws tken to e min. 6. Results This Section presents the results of the MPC condition monitor using oth PCA nd PLS models. In this study, eight months of operting dt were used to develop the MSPC models nd nlyse the controller performnce. During this period, the MPC controller ws modified. In this modifiction severl soft-sensors were updted nd numer of the controller models were improved. Dt ws collected fter its revmp nd these dt were used to test the ility of the condition monitoring tool to cope with such chnges Sttic PCA/PLS models The optiml operting dt ws used to develop sttic PCA nd PLS models using the lgorithms nd equtions presented in Section 2. Figs. 2 nd 3 show the T 2 nd chrts produced when this dt were pssed through the identified PCA nd PLS models, respectively. Both models were tested for their ility to effectively monitor the condition of the MPC system. Key res of interest were the ility of the developed MSPC models to detect normlities such s poor control performnce nd unmesured disturnces. The chrts shown in Figs. 2 nd 3 disply numer of violtions of the T 2 nd control limits, which were set t 9% nd 95% confidence levels. For exmple, the violtion round smple point 69 is shown in detil in Fig. 4. This upset ws clerly reflected in oth the PCA nd PLS chrts. The contriution chrts for this time instnt highlighted tht sturted control vlve ws responsile for this normlity. The rw mesurement for the control vlve is shown in Fig. 4c which clerly shows tht the vlve ws sturted t the smple point nlysed. The MSPC monitor ws y c 32 d Process Vriles Mnipulted Vrile Fig. 5. Anorml condition from process disturnce () PCA chrt, () PLS Output vriles chrt, (c) rw dt for vriles cusing normlity, (d) rw dt for MV controlling the vriles in (c).

9 322 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) le to successfully identify the normlity s well s isolte the cuse, nd thus could hve helped opertors ddress the prolem upon its occurrence. Another normlity highlighted y the condition monitoring ppliction ws t smple numer. As shown in Fig. 5, cler excursion of oth the PCA nd PLS output (effect) vrile x Mnipulted Vrile Fig. 6. Anorml condition from controller MV () PLS input vriles chrt, () rw dt of MV with upper nd lower limits y c 1 d 7 6 Process Vrile Mnipulted Vrile Fig. 7. Anorml condition from poor control performnce () PCA chrt, () PLS output vriles chrt, (c) rw dt for vrile cusing normlity, (d) rw dt for MV controlling the vriles in (c).

10 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) occurs t this smple point. Contriution chrts highlighted two CVs responsile for this norml condition. Fig. 5c shows the rw mesurement of oth these vriles long with their lower nd upper trgets. The MV tht ws used to control the flow of oth CVs, displyed in Fig. 5d, shows no norml movement t smple numer, nd hence this upset ws likely the result of n externl disturnce upstrem of the frctiontion process tht ffected the flow of oth vriles. A likely cuse of this ws drop in the supply line of these two flows. Erly detection of this normlity cn help opertors to provide pproprite mesures through mnul control or pproprite djustments to MPC trgets to compenste for this disturnce. Another non-relted normlity t pproximtely smple numer ws shown in the input (cuse) vriles chrt, Fig. 6. Anlysis of the rw dt of the contriuting vrile, which is shown in Fig. 6, identifies n unusul ehviour with this MV, where it ruptly chnges etween its higher nd lower limits. Although this is not n norml condition per sy, it is not typicl in this prticulr process to hve n MV switch suddenly from one production trget to nother. Fig. 7 shows n interesting oservtion recorded y oth PCA nd PLS chrts etween smple numers 3 nd. Exmining the rw dt for the CV contriuting to this nomly showed poor control ehviour for this vlve output s shown in Fig. 7c. When the rw dt nd limits of the MV controlling this vlve were nlysed, it ws evident tht the reson for this poor control ehviour could e ttriuted to the pinched limits tht the opertors hve set for the MV. Fig. 7d shows tht the MV limits during the upset period were reduced to ±1 C s opposed to the required ±3 4 C rnge tht is recommended nd typiclly pplied for this vrile. The results ove hve shown tht PCA nd PLS offer gret potentil for developing tools to monitor the ehviour of industril MPC controllers. The developed prototype using sttic MSPC models ws le to identify MPC normlities cused y disturnces, vlve sturtion nd poor control performnce due to the opertors specifying inpproprite limits. In the following section the enefits offered in using recursive condition monitor re detiled Recursive PCA/PLS modelling This section descries the development nd testing of recursive PCA/PLS models to the control monitoring system. It ws nticipted tht the recursive models would enle the monitoring tool to trck processes tht re time-vrying nd non-sttionry, such T2 15 Recursive PLS Model - Input Vriles c Recursive PLS Model - Output Vriles 5 T2 T2 Fig. 8. Recursive models monitoring chrts () recursive PCA T 2 nd chrts, () recursive PLS input vriles T 2 nd chrts, (c) recursive PLS output vriles T 2 nd chrts.

11 324 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) Recursive PCA Model 18 Recursive PLS Model- OutputVriles y Fig. 9. Recursive models monitoring chrts for poor control performnce () recursive PCA chrt, () recursive PLS Output vriles chrts. Recursive PCA Model T Recursive PLS Model c Recursive PLS Model x 5 y T2 x T2 y Fig.. Recursive models monitoring chrts () recursive PCA T 2 nd chrts, () recursive PLS input vriles T 2 nd chrts, (c) recursive PLS output vriles T 2 nd chrts.

12 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) s the condenste process under test. Furthermore, the recursive models performnce ws tested for its ility to hndle chnges in controller configurtion. In the dt set used in this study, period where severl chnges to the controller tuning prmeters were mde s well s mjor chnges in three soft-sensors, which were defined s CVs in the MPC system. All three soft-sensors re criticl controller vriles representing key product specifictions. Severl recursive MSPC lgorithms hve een proposed in the literture in recent yers to cter for the time vrying nture of mny process systems [35,22]. In this pper reltively simple pproch to recursive MSPC ws pplied, which identified new PCA model t ech smpling instnt using moving window of process dt. For the recursive PLS modelling, the pproch proposed y Qin [31] ws employed. Similr to the recursive PCA lgorithm, this method involved updting the PLS coefficients using moving window of dt t ech smpling instnt. The window size selected in this study ws, which represented round four months of operting dt. The selection ws mde sed on considertions of process modes of opertion nd is thought to e consistent with the rte t which the feed stock nd other disturnces to the process occur. Fig. 8 shows the T 2 nd chrts for the recursive PCA nd PLS (RPCA/RPLS) models. Similr to the results from the sttic PCA/PLS models, oth RPCA nd RPLS were le to identify the poor control ehviour etween smples 3 nd in Fig. 9. The normlity ws clerly shown in oth RPCA nd RPLS output vriles chrts, nd the sme contriuting vrile were highlighted y oth models. All mjor excursions identified in the sttic models developed in the previous section were identified lso y the recursive technique. Two mjor normlities however in the recursive models were highlighted tht were not clerly visile in the sttic models t pproximtely smples numers 39 nd 47; Fig. shows the RPCA/RPLS T 2 nd chrts round these two segments of the MPC operting dt. The process normlity shown in Fig. t pproximtely smple numer 39 is ttriuted to the portion of dt representing the period where the MPC controller ws revmped y chnging numer of tuning prmeters s well s djustment the coefficients nd models of three of the soft-sensors. The chnges in the soft-sensors re shown in Fig. 11, where it is shown tht for the first sensor, the mgnitude of chnge is considerle since the sensor ws reconfigured to predict different product property from the one previously computed. The tuning prmeter chnges primrily ffects the controller dynmic performnce nd is unlikely to contriute to the stedy stte nlysis shown here. The chrts shown in Fig. shows tht despite the chnged mde in the controller configurtion the recursive models hve dpted quickly to this new dt. An interesting oservtion from the recursive results ws noted t smple numer 469, where cler normlity ws detected 3 Soft Sensor Soft Sensor Soft Sensor Fig. 11. Soft-sensors rw dt.

13 326 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) Process Vrile Mnipulted Vrile Fig. 12. Contriuting process vriles to the normlity in RPLS input vriles chrts t 469 () rw dt for process vrile most contriuting to the normlity, () rw dt for process dt for nother contriuting vrile Process Vrile Process Vrile Fig. 13. Contriuting process vriles to the normlity in RPCA chrts t smple Process Vrile Process Vrile Fig. 14. Contriuting process vriles to the normlity in RPLS chrts t smple 47.

14 A. AlGhzzwi, B. Lennox / Journl of Process Control 19 (9) y the RPLS input vriles chrts, s seen in Fig.. The contriution chrts during this period reveled tht the vriles shown in Fig. 12 re the primry contriutors to the limit violtions. Although there is nothing peculir out the rw dt of the process vrile shown in Fig. 12, other thn it ppering to e t the lowest operting point of the eight months periods, the min contriutor of the normlity ws in fct the vrile displyed in Fig. 12 which is shown with its upper nd lower control limits. The identified vrile ws controller MV tht hd een restricted from moving y closing the upper nd lower limits, thus clmping the vrile from moving freely to control its relevnt CV. It is shown in the figure tht opertors eventully took notice nd relxed the limits on this vrile. This result showed tht in this prticulr cse, RPLS gve etter informtion to isolte the cuse of the normlity. Finlly, the normlity t smple 47, identified y oth RPCA nd RPLS chrts ws investigted. The RPCA chrts contriution plots identified the vrile displyed in Fig. 13, which shows one vrile moving to lower thn norml operting point, while the other vrile is moving to higher operting point. One of the contriuting vriles ws lso identified y the RPLS contriution chrts s shown in Fig. 14. The use of recursive MSPC models ws studied in this section, nd showed potentil for prcticl pplictions involving timevrying processes, nd presence of MPC design chnges. Furthermore, results in this section showed n exmple where RPLS gve more informtion on the cuse of process normlity, while in ll other cses, oth techniques gve comprle results. 7. Conclusion This pper presented results from comprehensive study on the use of MSPC methods, nmely PCA nd PLS in developing MPC condition monitoring pplictions for prcticl pplictions involving industril MPC systems. Results from oth sttic nd recursive PCA/PLS techniques showed tht MSPC methods offer gret potentil for developing effective MPC condition monitoring tools tht would help csul users monitor the performnce of MPC systems nd tke pproprite ctions to resolve normlities when necessry. The developed sttic nd recursive techniques use intuitive user friendly chrts to help users quickly identify ny process nomly nd isolte prole cuses. The developed tool complements current commercilly ville MPC condition tools tht ssist expert MPC users nd support engineers in dignosing more complex MPC normlities. Results from this study showed tht the developed prototypes were le to identify normlities ttriuted to poor control performnce, process upsets nd disturnces, s well s inpproprite interference from process opertors. Both PCA nd PLS models gve comprle results, however in t lest one cse, PLS helped identify the root cuse of n norml condition more clerly. The use of recursive PCA/PLS models highlighted the enefits tht these techniques offer with their ility to withstnd time-vrying processes nd MPC chnges; which will significntly enhnce the roustness of the condition monitoring tool in prcticl ppliction. On finl note, lthough the developed tool helped identify normlities nd possile cuses, it ws evident tht process knowledge nd experience is necessry to nlyse MPC or process normlity. References [1] N. Agrwl, B. Hung, E. Tmyo, Assessing model predictive control (MPC) performnce. 1. Proilistic pproch for constrint nlysis, Industril & Engineering Chemistry Reserch 46 (24) (7) [2] N. Agrwl, B. Hung, E. Tmyo, Assessing model predictive control (MPC) performnce. 1. Byesin pproch for constrint tuning, Industril & Engineering Chemistry Reserch 46 (24) (7) [3] A. AlGhzzwi, J. Anderson, T. Soudni, Avoiding the filure: chieving sustined enefits fromdvnced process control pplictions, in: Proceedings of PETROTECH Middle Est Oil & Gs Technology Conference Mnm, Kingdom of Bhrin, 3. [4] A. AlGhzzwi, B. Lennox, Monitoring complex refining process using multivrite sttistics, Control Engineering Prctice 16 (8) [5] G. Chen, T.J. McAvoy, M.J. Piovoso, Multivrite sttisticl controller for on-line qulity improvement, Journl of Process Control 8 (2) (1998) [6] L. Desorough, T. Hrris, Performnce ssessment mesures for univrite feedforwrd/feedck control, Cndin Journl of Chemicl Engineering 71 (1993) [7] P. Geldi, B.R. Kowlski, Prtil lest squres regression: tutoril, Anlytic Chimic Act 185 (1986) [8] P. Goulding, B. Lennox, Q. chen, D. Sndoz, Roust inferentil control using kernel density methods, Computers & Chemicl Engineering 24 () [9] F. Gross, E. Bumnn, A. Geser, D. Rippin, L. Lng, Modelling, simultion, nd controllility nlysis of n industril het-integrted distilltion process, Computers & Chemicl Engineering 22 (1996) [] T. Hrris, Assessment of closed loop performnce, Cndin Journl of Chemicl Engineering 67 (1989) [11] T. Hrris, F. Boudreu, J.F. McGregor, Performnce ssessment using of multivrile feedck controllers, Automtic 32 (1996) [12] A. Horch, A.J. Isksson, A modified index for control performnce ssessment, Journl of Process Control 9 (1999) [13] B. Hung, S.L. Shh, Performnce Assessment of Control Loops, Springer, Berlin, [14] J. Jckson, A user s Guide to Principl Components, Wiley, New York, [15] M. Jelli, An overview of control performnce ssessment technology nd industril pplictions, Control Engineering Prctice 14 (6) [16] B.-S. Ko, T.F. Edgr, Assessment of chievle PI control performnce for liner processes with ded time, in: Proceedings of the AmericnControl Conference, Phildelphi, USA, [17] B.-S. Ko, T.F. Edgr, Performnce ssessment of constrined model predictive control systems, AIChE Journl 47 (1) [18] B.-S. Ko, T.F. Edgr, Performnce ssessment of multivrile feedck control systems, Automtic 37 (1) [19] D. Kourti, Appliction of ltent vrile methods to process control nd multivrite sttisticl process control in industry, Journl of Adptive Control nd Signl Processing 19 (4) (5) [] D.J. Kozu, C. Grci, Monitoring nd dignosis of utomted controllers in the chemicl process industries, in: Proceedings of the AIChE, St. Louis, USA, [21] A. Lenhoff, M. Morri, Design of resilient processing plnts I: process design under considertion of dynmic spects, Chemicl Engineering Science 37 (1982) [22] W. Li, H. Yue, S. Vlle-Cervntes, S. Qin, Recursive PCA for dptive process monitoring, Journl of Process Control () [23] F. Loqusto III, Seorg, Model predictive controller monitoring sed on pttern clssifiction nd PCA, Proceedings of the Americn Control Conference, IEEE, 3. [24] F. Loqusto III, Seorg, Monitoring model predictive control systems using pttern clssifiction nd neurl networks, Industril nd Engineering Chemistry Reserch 42 (3) [25] E.B. Mrtin, A.J. Morris, An overview of multivrite sttisticl process control in continuous nd tch process performnce monitoring, Trnsctions of the Institution of Mesurement nd Control 18 (1) (1996) 51. [26] E.B. Mrtin, A.J. Morris, Impurity detection in tch phrmceuticl production, Computer Applictions in Biotechnology (1). [27] S. Miletic, S. Quinn, M. Dudzic, M. Vculik, M. Chmpgne, An industril perspective on the implementing on-line pplictions of multivrite sttistics, Journl of Process Control 14 (4) [28] R.S. Ptwrdhn, S. Shh, G. Emoto, H. Fujii, Performnce nlysis of modelsed predictive controllers: An industril study, in: Proceedings of the AIChE, Mimi, USA, [29] R. Person, Outliers in process modeling nd identifiction, IEEE Trnsctions on Control Systems Technology (1) (2) [] S.J. Qin, J. Yu, Recent developments in multivrile controller performnce monitoing, Journl of Process Control 17 (7) [31] S.J. Qin, Recursive PLS lgorithms for dptive dt modelling, Computers nd Chemicl Engineering 22 (1998) [32] N. Thornhill, M. Choudhury, S. Shh, The impct of compression on dt-driven process nlyses, Journl of Process Control 14 (4) [33] M. Tyler, M. Morri, Performnce monitoring of control systems using likelihood methods, Automtic 32 (1996) [34] B. Wise, N. Gllgher, The process chemometrics pproch to process monitoring nd fult detection, Journl of Process Control 6 (1996) [35] S. Wold, Exponentilly weighted moving principl components nlysis nd projection to ltent structures, Chemometrics nd Intelligent Lortory Systems 23 (1994) [36] F. Xu, B. Hung, S. Aknde, Performnce ssessment of Model Predictive Control for vriility nd constrint tuning, Industril & Engineering Chemistry Reserch 46 (4) (7)