Opening the Black Box: Demystifying Performance Assessment Techniques

Transcription

1 contents Opening the Blck Box: Demystifying Performnce Assessment Techniques Roert C. Rice Rchelle R. Jyringi Dougls J. Cooper Control Sttion, Inc. Deprtment of Chemicl Engineering Deprtment of Chemicl Engineering One Technology Dr. University of Connecticut University of Connecticut Tollnd, CT 68 Storrs, CT Storrs, CT ABSTRACT Rel-time performnce monitoring to identify poorly or under-performing loops hs ecome n integrl prt of preventtive mintennce. While some control softwre pckges disply performnce metrics, it is importnt to understnd the theory, purpose, nd limittions since ech metric signifies very specific informtion out the nture of the process. This pper reviews performnce mesures from simple sttistics through complicted model-sed performnce criteri. By understnding the underlying concepts of the vrious techniques, reders will gin knowledge of how to use nd implement ech of the performnce criteri. Bsic lgorithms for computing performnce mesures re presented using exmple dt sets. A discussion with tips nd suggestions provides guidnce for interpreting the results. INTRODUCTION Over the pst two decdes, process control performnce monitoring softwre hs ecome stple of ny successful control engineer s toolox. The mount of performnce tests nd sttistics tht cn e clculted for ny given control loop cn e overwhelming. The prolem with controller performnce monitoring is not the lck of techniques nd methods; it is the lck of guidnce nd understnding s to how to turn sttistics into improved performnce. The performnce nlysis techniques discussed here re seprted into three sections. The first section detils methods for identifying process chrcteristics using tches of existing dt. The second section outlines methods used for rel-time nd dynmic nlysis of streming process dt. These re the techniques tht re vitl for the timely identifiction of chnging process ehvior or loop performnce deteriortion. The third section outlines techniques tht id in the identifiction of intercting control loops. The techniques presented here use Microsoft Excel to clculte the performnce mesures. Reders my otin complimentry copy of the Excel worksheet y contcting o.rice@controlsttion.com.

2 IDENTIFYING PROCESS CHARACTERISTICS Set Point Anlysis Explined here re techniques for nlyzing closed loop dt during set point response. These techniques permit n orderly comprison of process response shpes nd chrcteristics. When nlyzing set point response, criteri used to descrie how well the process responds to the chnge include the pek overshoot rtio, decy rte, set point crossing time, rise time nd settling time. The criteri cn e used oth s specifictions for commissioning of control loops nd for documenting chnges in performnce due to the djustment of the controller or process prmeters. Figure 1 shows closed loop response to set point chnge. To clculte the set point criteri listed ove, certin fetures re ssigned the following definitions: A = Size of the set point step B = Size of the first pek ove the new set point or stedy stte C = Size of the second pek ove the new stedy stte Process Vrile/Setpoint y ( ) 3.8 B C A (mins) Process Vrile/Setpoint y ( ± 5% of y(t) y(t) (mins) t t pek rise t settle Figure 1 - Process response to set point chnge with lels indicting response fetures As shown in Figure 1, the time when the mesured process vrile first crosses the new set point nd the time t which it reches its first pek re used to descrie controller performnce. Another populr mesurement is the settling time, which is the time required for the mesured process vrile to first enter nd then remin within nd whose width is computed s ± 5% (or 3 % or 1 %) of the totl chnge in y(t), leled s y(t) in Figure 1. Additionl criteri re summrized in Tle 1. Populr vlues include 1% pek overshoot rtio nd 5% decy rtio. Also, these criteri re not independent. A process with lrge decy rtio will likely hve long settling time. A process with long rise time will likely hve long pek time.

3 Criteri Interprettion Clcultion Pek Overshoot Rtio (POR) The POR is the mount y which the process (POR) = B/A vrile exceeds the set point. An ggressive controller cn increse the mount of overshoot ssocited with set point chnge. Decy Rte A lrge decy rte is ssocited with n ggressive Decy Rtio = C/B controller, nd visile oscilltions re present in the set point ump. The smller the decy rte, the fster the oscilltions will dmpen. Pek & Rise These mesurements guge the time response to chnge in the set point. A lrge pek nd rise time could e the result of sluggish controller. Rise = t rise Pek = t pek Settling The settling time is the time for the process Settling = t settle vrile to enter nd then remin within nd. spent outside the desired level generlly reltes to undesirle product. Therefore, short settling time is sought. Tle 1 - Interprettion of Set Point Response Criteri The integrl of error indexes focus on devition from set point. The Integrl Squred Error (ISE) is very ggressive ecuse squring the error term provides greter punishment for lrge error. The Integrl Asolute Error (ITAE) is the most conservtive of the error indexes; the multipliction y time gives greter weighting to error tht occurs fter longer pssge of time. The Integrl Asolute Error (IAE) is moderte in comprison to these two. Additionl indexes cn e derived depending on the system requirements. Integrl Squred Error (ITSE) comines the time weighting with the exggerted punishment for lrger error. The formul for clculting the Integrted Error indexes re listed elow. T IAE = e() t dt T ISE = e () t dt (1) () T ITAE = t e() t dt (3) T ITSE te () t dt = () Often the ove indexes re used s criteri in controller tuning. Users will choose one of the ove nd define optiml control s tuning tht will give the minimum vlue of the index. Figure shows the process vrile s response to set point chnge under vrious controller tunings rnging from poor/unstle to conservtive. The results re summrized in Tle.

4 Process Vrile / Set Point Poor Tuning PV / SP Aggressive Tuning Process Vrile / Set Point Convsertive Tuning Conservtive Tuning c Figure - Set Point Response of ) poorly, ) ggressively, c) conservtively tuned PI controller Set Point Bump Criteri Integrl of Error Poorly Tuned Aggressively Tuned Conservtively Tuned POR 33% 1% Decy Rte % % Rise. min.9 min 13.7 min Pek. min.1 min 13.7 min Settling 1.8 min 6.5 min 1.7 min IAE ISE ITAE ITSE Tle - Results of Set Point Response Criteri, nd Integrl of Error clcultions for Figure Disturnce Anlysis A disturnce is defined s nything other thn the controller output signl tht ffects the mesured process vrile. In n intercting plnt environment, ech control loop cn hve mny different disturnces tht impct its performnce. By understnding the type of disturnce nd its impct on the control loop, engineers, opertors nd technicins cn more esily identify the cuse nd work towrds solution. Autocorreltion is method tht is used to determine how dt in time series re relted [1]. By compring ptterns in current process mesurements with those exhiited in the pst, the nture of disturnces nd how they ffect the system cn e ssessed. The eqution for clculting the utocorreltion reltionship is: rk ( ) = i [( yi ( ) y)( yi ( k) y)] i ( yi ( ) y) Where: y is mesured process dt y is the set point or the series verge if there is n offset k is time dely in smples (5)

5 i is smple numer (or smple time) Autocorreltion vlues re lwys etween negtive one nd one. If dt is rndom, the vlues will e pproximtely zero for ll time. Any vlue tht is significntly non-zero indictes the dt is nonrndom. A strong utocorreltion will hve n initil vlue ner one or negtive one nd the trend will e liner; this shows tht the ech mesurement dicttes the next. A moderte utocorreltion is one in which the plot egins elow one (or ove negtive one) nd decreses mgnitude towrds zero ut displys noise. An utocorreltion of closed loop dt cn lso give n estimte of the response time for n isolted disturnce. Another performnce sttistic tht is useful for identifying trends in dt is the power spectrum. It is clculted y computing the discrete Fourier trnsform of the process dt. A Fourier trnsform is mthemticl expression of the dt s series of two-dimensionl sine wves, nd the power spectrum is computed y squring the complex coefficients determined y those sine wves. The power spectrum shows the frequency t which chnge is occurring nd the mgnitude of the chnge [9]. The shpes nd heights of peks on power spectrum plots give informtion out the system. The shpe of the power spectrum curve yields informtion out the nture of the disturnces y displying its frequency. An increse in pek heights compred to historicl dt indictes tht the process hs greter devition from set point or historicl men. Low powers nd low frequencies re most desirle, s they re ssocited with smll devitions from set point or lower verge vlues. Figures 3-6 show four different scenrios in which the utocorreltion nd power spectrum cn e useful in understnding the nture of the disturnce impcting the system. Only the single pulsed disturnce shown in Figure 3 is noticele from csul evlution of the process dt, ut using the utocorreltion nd power spectrum tools one cn identify chrcteristics for ll four disturnces. In Figure 3, the process is upset with single pulsed disturnce. The utocorreltion shown in Figure 3c shows n initil pek where the process is responding to the step up then the negtive pek occurs pproximtely 1 minutes lter when the disturnce steps ck down. This is chrcteristic of n isolted disturnce. If second pulse occurred, nother similr pttern would pper on the utocorreltion plot. The power spectrum of the process dt is shown in Figure 3d. Since the frequency of chnge corresponds to the frequency of the disturnce, n isolted disturnce is locted t pproximtely zero frequency on the power spectrum plot. There is no other disturnce occurring t ny other frequency, so the power quickly drops off nd the remining vlues re close to zero. Figure shows the process with no disturnce impcting the system. Neither the utocorreltion nor the power spectrum contins ny ovious peks. In fct, oth trends show rndom vlues close to zero. This indictes the control loop is undistured nd performing well. The oscillting disturnce depicted in Figure 5 yields n oscillting utocorreltion. The power spectrum shows the oscillting disturnce is single cycle sine wve since there is one strong dominnt pek t the wve s frequency. If second disturnce ws cting on the system second pek would pper.

6 The continuously pulsed rndom disturnce depicted in Figure 6 is difficult to identify since the mgnitude of the disturnce is within the rnge of noise. The disturnce is not impcting the system t regulr frequency ecuse the length of time of the disturnce pulses re not constnt. Therefore the power spectrum does not show ny significnt peks outside the rnge of the noise. The utocorreltion gives n indiction of disturnce other thn noise ecuse there is strong pek t 5 minutes. Also, there re slight clusters ove nd elow the x-xis, especilly close to zero, ut they re not s regulr s the oscillting disturnce. In this sitution comprison to historicl dt nd fmilirity with the process is vitl. Single Pulsed D isturnce D isturnce Profile.5 P ro cess V ri le / Distur (min) Autocorreltion - Single Pulsed (min) Power Spectrum - Single Pulsed.5..3 c.1.1 d..8 Correltion Power Lg (Min) Frequency Figure 3 - For process sujected to pulsed disturnce here re the ) process vrile response ) disturnce profile c) utocorreltion nd d) power spectrum plots D isturnce N ot C hnging Disturnce Profile Process V rile / Distur (min) (min) Autocorreltion - Disturnce Not Chnging Power Spectrum - Disturnce Not Chnging.5.1 Correltion c Power d Lg (min) Frequency Figure - For n unchnging process here re the ) process vrile response ) disturnce profile c) utocorreltion nd d) power spectrum plots

7 O scillting D isturnce D istu r n c e P ro file Process V rile D is tu r (min) T im e ( m in ) Autocorreltion - Oscillting Disturnce Power Spectrum - Oscillting Disturnce.5..3 c.1.1 d..8 Correltion Power Lg (min) Frequency Figure 5 - For process sujected to n oscillting disturnce here re the ) process vrile response ) disturnce profile c) utocorreltion nd d) power spectrum plots C ontinuously Pulsed R ndom D isturnce D isturnce Profile Process V rile / (min) Autocorreltion - Continuously Pulsed Rndom Disturnce Distur (min) Power Spectrum - Continuously Pulsed Rndom Disturnce.5..3 c.1.1 d Correltion Power Lg (min) Frequency Figure 6 - For process sujected to continuously pulsed rndom disturnce here re the ) process vrile response ) disturnce profile c) utocorreltion nd d) power spectrum plots REAL-TIME PERFORMANCE MONITORING Control loop monitoring is incresingly populr. Mny employ the Hrris index, sed on minimum vrince control principles, s the preferred strtegy. Presented here is comprison of the Hrris index to simpler strtegies for monitoring controller performnce. At the hert of every performnce monitoring system is the ility to identify prolem within the control loop s soon s possile.

8 Descriptive sttistics re roken into three ctegories: mesures of centrl tendency, mesures of spred, nd mesures of shpe. The men is the most common mesure of centrl tendency. The mesures of spred provide informtion out the degree to which individul vlues re clustered or devite from the men vlue in distriution. The minimum nd mximum re the simplest mesures of spred nd give only the rnge of vlues. The vrince nd stndrd devition re other populr mesures of spred tht provide more useful numericl vlue sed upon the devition from the men. Mesures of shpe re used to descrie the dt vlue distriution; the skewness refers to the degree of symmetry present in the dt set. Ech of these descriptive sttistics cn provide insight into how the control loop is functioning. These sttistics re most commonly clculted for the process vrile, controller output, nd controller error. Shown in Eq. 6, the Hrris Index is vlue sed on compring performnce under current control to performnce if minimum vrince control, MVC, were used. In clculting the minimum vrince, n utoregressive moving verge model is fit to the process dt. This is predictive model tht represents ction minimum vrince controller would hve tken. If the disturnces tht ffected the process could hve een predicted y MVC then the current controller is performing poorly in comprison, ut if the disturnces were rndom then the controller is performing s well s MVC. Since the Hrris index is difficult to clculte, it is importnt to note tht under MVC the utocorreltion of the dt is zero fter the initil process dely; therefore utocorreltion could e used to ssess if the system is displying minimum vrince. The Hrris index is computed s []: σ y I H = (6) σ mv Where: I H is the Hrris index σ is the vrince of the process dt σ y mv is the minimum vrince When the process displys minimum vrince, the Hrris index is one. To estlish seline, the Hrris index should e clculted while the system is in pek performnce nd then used s comprison ginst future vlues. The Hrris index is useful for ssessing the output vrince due to stochstic disturnces. It cnnot give ny specific informtion out set point chnges, known disturnce vriles, settling time, decy rtio or stility [1]. The reliility of the Hrris index depends on the strength of the model nd the estimtion of the process ded time. The prmeters for the model need to e determined y Box nd Jenkins method [1], prior knowledge, or tril nd error. Wrong choice of model or error in estimting the ded time will give misleding vlues of the Hrris index. An dditionl performnce metric introduced in this pper is stndrd vrition. The stndrd vrition is normlized mesure of devition of the mesured process vrile from the set point of process, nd is detiled y Eq. 7.

9 PV SP n 1 Stndrd Vrition = 1% Averge( PV ) Where: PV : Mesured Process Vrile SP : Set Point n : Numer of Dt Points (7) A smller stndrd vrition represents less devition from set point. Some fctors tht cn impct the stndrd vrition include the numer of set point chnges nd the numer of disturnces tht impct the process. The stndrd vrition cn e used to guge the improvement fter loop is re-tuned, if the stndrd vrition is smller fter retuning, then performnce hs een improved. It should e noted tht when compring efore nd fter performnce index, the dt needs to e collected for long enough time so tht the numer of disturnces impcting the system re pproximtely equl. Two distinct techniques for computing performnce mesures include moving nd sttic clcultions. Moving clcultions re computed on moving suset of the complete dt set. Sttic clcultions would compute the performnce mesurements on the entire dt set. The results of the moving suset clcultion re grphed with the performnce mesure plotted long the verticl xis nd time long the horizontl xis. By using moving suset in lieu of complete tch clcultion, it is possile to identify the point in time when loop performnce egins to chnge. This in turn signls when to egin n investigtion into the cuse of the chnge. Becuse of the ility to identify in rel time chnging performnce, the moving suset method is preferred for control loop monitoring. Figure 7 shows the process vrile nd controller output trces for time-vrint process. A timevrint process is system whose dynmic ehvior chnges with time. This chnge in ehvior could e the result of degrding vlve performnce, het exchnger surfce fouling, ctlysts dectivting, or even fluctuting wether conditions. In this exmple, the system is under PI control nd the tuning vlues re constnt during the process trnsition. By using the moving window technique, the time t which the process egn to shift will e clerly identifile. Process Vrile / Set Point Controller Output Vrint Process Under PI Control Figure 7 - Process Dt nd Controller Output

10 Visul inspection of the process trends shown in Figure 7 does not indicte ny significnt chnge in controller performnce. The plots tht follow sed on the methods just discussed revel tht something in the process indeed hs chnged. By detecting this chnge efore it hs significnt impct on controller performnce, solutions including updting controller tuning cn e considered efore lrms re triggered. Figure 8 shows the Hrris index, stndrd devition, vrince nd stndrd vrition of moving suset of dt for the time-vrint process. The dotted line in ech trce represents the pre-defined seline vlue. Since no two processes re like, ech process should hve its own seline or cceptle performnce limit determined y mesurements collected under norml operting conditions when the system is thought to e running under good control. If the vlue for ny performnce criteri moves outside its performnce limit for specified mount of time, then tht system hs drifted to wrning sitution. All four methods show tht the process egins to drift from its seline vlue t out 55 minutes. Hrris Index of Percent Error Stndrd Devition of Percent Error Averge StDev 3.35E-3 E E-3 E-3.95E-3.85E Moving Vrince of Percent Error Stndrd Vrition Vrince 1.11E-5 1.6E-5 c 1.1E-5 9.6E-6 9.1E-6 8.6E-6 8.1E Stndrd Vrition.7.69 d Figure 8 - ) Hrris index, ) stndrd devition, c) vrince, nd d) stndrd vrition re clculted y the moving suset method. The time when the process model egins to chnge is pprent in ll plots. IDENTIFYING INTERACTING PROCESSES Intercting processes cn e troulesome in ny mnufcturing process. By identifying which systems interct, the disturnces cn e countercted rther thn perpetuted throughout the system. Even if n upstrem disturnce cnnot e eliminted, y identifying the source, feed-forwrd controller could e used to improve downstrem loop performnce.

11 Cross-correltion nlyzes the reltionship etween two dt series. By clculting set of correltion vlues t incresing time delys, picture develops tht shows how the dt series re relted through time. The cross-correltion is clculted s: rk ( ) = i i [( y ( i) y )( y ( i k) y )] ( y ( i) y ) ( y ( i k) y ) i (8) Where: y nd y re process dt y nd y re the set point vlues (or the series verges) k is time dely in smples i is smple numer (or smple time) Cross-correltion vlues re lwys etween negtive one nd one. Positive vlues indicte tht process A directly ffects process B, so tht n incresed devition from verge in process A cuses n incresed devition in B. Negtive vlues indicte n inverse reltionship such tht n incresed devition in process A cuses decresed devition in process B. If there is no reltionship etween the dt sets, then the cross-correltion vlues will e close to zero. Cross-correltion cn lso e used to determine exctly how much time elpses efore the downstrem process is reched. At the point when there is gretest impct on the downstrem loop, there will e pek in the cross-correltion trend. Additionlly, cross-correltion is used to identify when disturnces re eing cused y recycle strem. If recycle strem occurs within single control loop, n utocorreltion cn e used to identify how the recycle influences the system. Power spectrum is lso employed to identify nd nlyze intercting loops. Intercting loops re ffected y the sme events nd therefore hve power spectrum peks t the sme frequencies. Power spectrum cnnot identify how long it tkes for chnge in one system to rech nother like crosscorreltion cn, ut it cn e more useful when there re mny processes seprting the suspected intercting loops. Cross-correltion cn e muddled when there re mny processes in etween with vrying reltionships, ut the power spectrum is more sensitive nd if processes re ffected y events occurring t the sme frequencies it will identify the interction. Controller Output 1 Tnk Level 1 Disturnce 1 Tnk Level Figure 9 - The intercting tnks process used to demonstrte power spectrum nd cross-correltion

12 To explore the ility of cross-correltion nd power spectrum to identify intercting loops, consider the rry of tnks shown in Figure 9. The two upper tnks ech drin into the two lower tnks. Two controllers connect lower tnks to the upper tnks. If the level controllers on the ottom tnks re put into utomtic, disturnce in one of the lower tnks will ffect ll four tnks. If the level controllers re left in mnul, the tnk connectivity is roken nd disturnce impct remins locl to the prticulr tnk ffected. Consider the system of tnks in mnul mode. Figures 1, 1, nd 1c show the process dt when there is step in the controller output 1 incresing the flow to upper tnk 1. Figures 11 nd 11 show the cross-correltion of controller output 1 nd the levels in lower tnks 1 nd, respectively. The lrge peks on the grphs signify strong correltion for oth nd tht the mximum effect tkes pproximtely 15 minutes to impct tnk level 1 nd 3 minutes to impct tnk level. Figures 1, 1, nd 1c show process dt collected during step disturnce in lower tnk 1. From the utocorreltion plots shown in Figures 13 nd 13, it is cler the disturnce hs n lmost instntneous negtive effect on the level in tnk 1 nd no effect on tnk. Figure 1 shows the power spectrum of controller output 1, tnk level 1, nd tnk level scled so they cn e displyed on the sme grph. All three systems shre peks t the sme frequencies nd this indictes they re intercting. Figure 1 shows the reltionship etween disturnce in tnk 1 nd the levels in tnks 1 nd. Disturnce 1 shres similr peks with tnk level 1, indicting they re intercting. Tnk level hs unique power spectrum, indicting it is responding to different stimuli. 66 Controller Output 1 Tnk Level 1 Tnk Level c Figure 1 Process dt during step chnge of controller output 1 ) controller output 1 ) tnk level 1 c) tnk level Cross-correltion of Controller Output 1 nd Tnk Level 1 Cross-correltion of Controller Output 1 nd Tnk Level Figure 11 - Cross-correltion digrms of the reltionship etween controller output 1 nd

13 ) tnk level 1 ) tnk level Disturnce 1 Tnk Level 1 Tnk Level c Figure 1 Process dt during pulse disturnce in tnk 1 ) disturnce 1 ) tnk level 1 c) tnk level Cross-correltion of Disturnce 1 nd Tnk Level 1 Cross-correltion of Disturnce 1 nd Tnk Level Figure 13 - Cross-correltion digrms of the reltionship etween disturnce 1 nd ) tnk level 1 ) tnk level Impct of Controller Ouput, CO1, on Tnk 1 nd Tnk Level Impct of Disturnce, D1, On Tnk 1 nd Tnk Level 3E- E- Tnk 1 Level, PV1 Controller Output, CO1 [1^-5] Tnk Level, PV [1^1].E- E- 3.E- Tnk 1 Level, PV1 Disturnce, D1 [1^-] Tnk Level, PV [1^] Power E- 1E- Power.5E-.E- 1.5E- 5E-5 1.E- 5.E-5 E Frequency.E Frequency Figure 1 - Power spectrums of ) controller output 1 nd tnk levels 1 nd nd ) disturnce 1 nd tnk levels 1 nd. The spectrums hve een scled so tht they cn e view on the sme grph.

14 CONCLUSIONS Performnce mesures re n integrl prt of optimizing nd mintining system performnce. Industry nd cdemi re constntly deriving new methods for performnce ssessment, ut the methods re only useful when they cn e fully understood nd used properly. It is importnt to understnd the theory, purpose nd limittions of the mesures efore relying on their informtion. In mny cses, the performnce ssessment methods only identify the strt of prolem, not the source. By understnding the sic principles nd disturnces tht impct your system, engineers will know wht to expect during norml opertion nd will e le to identify more quickly wht is norml opertion. This pper ddressed wide vriety of commonly used performnce ssessment techniques in n ttempt to demystify them for etter ppliction in monitoring. The techniques detiled in this pper for tckling rel-time process monitoring re twofold. First one cn identify when process strts to drift wy from seline opertion nd towrds triggering n lrm. Once prolem is identified, the use of utocorreltion, cross-correltion, nd power spectrum cn e used for detect the root-cuse. REFERENCES 1. Box G.E.P., Jenkins, G.M., (197), Series Anlysis forecsting nd control, Holden-Dy, Inc. Sn Frncisco, CA. Burch, R. (). Monitoring nd Optimizing PID Loop Performnce. ISA Annul Meeting, Houston, TX. 3. Desorough, L. nd R. Miller (1). Incresing Customer Vlue of Industril Control Performnce Monitoring--Honeywell's Experience. 6th Annul Interntionl Chemicl Process Control Meeting, Tucson, AZ.. Hrris, T. J. (1989). "Assessment of Control Loop Performnce." Cndin Journl of Chemicl Engineering 67: Hoo, K. A., M. J. Piovoso, et l. (3). "Process nd controller performnce monitoring: overview with industril pplictions." Int. J. Adpt. Control Signl Processing 17: Horch, A. nd A. J. Isksson (1999). "A modified index for control performnce ssessment." Journl of Process Control 9: Hung, H.-P. nd J.-C. Jeng (). "Monitoring nd Assessment of Control Performnce for Single Loop Systems." Ind. Eng. Chem. Res. 1: Ptwrdhn, R. S., S. L. Shh, et l. (). "Assessing the Performnce of Model Predictive Controllers." The Cndin Journl of Chemicl Engineering 8: Press W.H., et l(1986), Numericl Recipes: The Art of Scientific Computing, Cmridge University Press, New York, NY 1. Qin, S. J.(1998), Control Performnce Monitoring review nd ssessment, Computers nd Chemicl Engineering, 3,

15 11. Thornhill, N. F.(1998), Performnce Assessment nd Dignosis of Refinery Control Loops, AIChe Symposioum Series N o 3, 9,