Performance Assessment Measures of Batch Processes for Iterative Learning Control

Transcription

1 roeedings o the 7th World Congress The International Federation o Automati Control Seoul, Korea, July 6-, 8 erormane Assessment Measures o Bath roesses or Iterative Learning Control Junghui Chen, Cho-Kai Kong R&D Center or Membrane Tehnology Department o Chemial Engineering, Chung-Yuan Christian University Chung-Li, Taian ( jason@ avenet.yu.edu.t) Abstrat: A ne method is proposed or the assessment o the bath ontrol system hen the iterative learning ontrol is applied. Unlie the ontinuous proess, the perormane assessment o the bath proess requires partiular attention to both disturbane hanges and setpoint hanges. Beause o the intrinsially dynami operations and the nonlinear behavior o bath proesses, the onventional approah o the ontroller assessment annot be diretly applied. The bounds at eah time point are derived and omputed or the ontrolled output variane to reate simple monitoring harts. They an help traing the progress in eah bath run to monitor the ourrene o the observable upsets. Simulation ases are used to demonstrate the advantages o the proposed strategies.. INTRODUCTION Interest in researh and development o bath ontrol based on iterative learning ontrol (ILC) has inreased steadily sine the term, ILC, as irst presented (Arimoto et al., 98). The ontrol design in bath proesses is quite dierent rom that in ontinuous ones. When the proess is operated ontinuously, there is a variety o methodologies in the eedba ontrol loop system to ensure losed-loop stability and to ahieve aeptable steady-state perormane ith reet to setpoint and disturbane inputs. Beause o the intrinsially dynami operations o bath proesses, the onventional approah o the ontroller assessment annot be diretly applied. ILC o bath operation allos the extration o inormation rom the past bathes to reine the ne bath run and to improve the perormane o traing ontrol or produt quality. ILC utilizes a eedba ontroller or stabilizing the losed-loop system. It also uses a eedorard ontroller or designing the transient reonse o the operating proile. Numerous ILC shemes have been developed in the past deades. They enhaned the ontrol perormane over a ixed time interval iteratively (Chen et al., 997; Moore, 993; Luibello, 99). The eet o ILC on a ontinuous ontrolled system has been investigated to improve the perormane (Tan et al., 6; Ratlie et al., 5). Comprehensive revie o this topi is shon in the reerenes (Xu and Tan, 3; Moore, 993). The ebpage or iterative learning ontrol researh is lined ( Hoever, these ontrol researh papers oused mainly on design strategies. They did not sho ho good the urrent ontroller perormane o the bath operation as in omparison ith benhmar ontrol. I the deterioration o ontroller perormane annot be identiied in time, the maluntion ould ause inonsistent produt quality and monetary loss. The perormane assessment o the ontrol loop based on the minimum variane as irst presented by Harris (989). Several tehniques using the minimum variane have been proven useul in prioritizing the ativities o proess engineers, inluding monitoring and assessing the ontroller perormane (Huang et al., ; Desborough & Harris 993). Hoever, the ontroller perormane o the bath operation is inluened not only by the unmeasured disturbane but also by the deterministi regulation hih is deined by the setpoint hanges. Sine the deterministi regulation is very dierent rom the stohasti one, their ahievable perormane bounds should be separated (Isasson et al., 3; Sanda and Seborg, 999). Although there ere many researh papers on assessing ontinuous ontrol systems, to our best noledge, the assessment o the bath ontrol system has not been mentioned. In this paper, to issues are addressed to assess the ontroller perormane o the bath operation. First, the minimum variane perormane bound is developed or bath operation systems. The perormane bound an subsequently be used or the perormane assessment o the bath system ontrol loop. The remaining paper is strutured as ollos: The perormane assessment o the ontrol loop in the bath operation system is deined in Setion. In Setion 3, the perormane assessment bounds o the bath ontrol system are derived. The eetiveness o the proposed method and its potential appliations are demonstrated through to omputer simulation problems, inluding a simple linear system and a nonlinear bath reator in Setion. Finally, onluding remars are made.. ILC STRUCTURE OF BATCH Suppose there is an operation o a bath run ( i ).The eedba ontrol struture or the bath system is shon in Fig.. A disrete linear time-variant (LTV) proess is used to represent a bath operation system. Its orm hih is any /8/$. 8 IFAC 66.38/876-5-KR-.9

2 7th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-, 8 linear time-invariant proess governed by the transer untion models is given by y( i, ) G, ) u( i, ) G, ) ( ) () p ontroller ( G, ) ) undertaes orretion based on nondeterministi disturbanes and modeling errors. The eedorard ontroller ( G, ) ) adjusts the reerene based on the modeling errors. Based on both ontrollers, the ne reerene signal ( x i, ) is designed. here the ontrolled output, y i at time point ( ) an be expressed as the sum o to terms, one or the deterministi manipulated input ( u i, ) and the other or the hite noise disturbane ( ). The proess ( G, ) ) and the disturbane ( G, ) ) transer untions vary ith time. In the blo diagram o Fig., hen the set point ( x i, ) and the disturbane ( ) hanges our, the output ( yi, ) under losed-loop ontrol an be obtained: x G ( i, ), ) Feedba roess G, G, G ei, i y, y Run i ( ) G q G q GC q C C (, ) (, ) (, ) y( i, ) ( i, ) x ( i, ) G, ) G, ) G, ) G, ) In Fig., the dashed blo represents lumping o all the elements in the eedba proess. The bath ontrol system aims not only at ahieving disturbane rejetion but also at traing the desired reerene. () x ( i, ) G, ) Feedba roess G, G, G, e i i y, y Run i ( ) x ( i, ) G C, ) G G, ), ) i Fig.. Blo diagram o eedba ontrol or the bath system. y, Fig.. The shematis o ILC ith the eedba ontroller ( G, ) ) and the eedorard ontroller ( G, ) ). The learning ontrol objetive is to determine the ontrollers, G, ) and G, ), and generate an appropriate ontrol input time history to produe a detailed output history through iterative trails. In minimum variane ontrol, the minimum variane bound o the ILC system or all bath runs is deined as To omplement this, the iterative improvement strategy in a struture ith to-degree o reedom is idely applied to traing errors by improving its ontrol ation estimates. In Fig., a blo diagram interpretation o the ILC sheme is shon. The dashed blo in Fig. denotes the eedba proess or the time-varying losed loop system at a partiular run in Fig.. The priniple o ILC maes use o the measurement ( y i, ) and the reerene signal ( x i, ) o the previous bath run or ontrol during the urrent bath ( i ) under the disturbane input ( ). The eedba T min J min E e( i, ) G, ) G, ) G, ) G, ) here e( i, ) y ( ) y( i, ), T is the duration o eah bath run, and E is the expetation operator. In the above deinition, the expeted perormane bound oe ( i, ) is omputed based on all bathes. It is apparent that the variane (3) 67

3 7th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-, 8 o e( i, ) depends on all the system ontroller untions, G, ) and G, ). The alulation desribed by Eq. (3) is also provided or examination. 3. ERFORMANCE ASSESSMENT MEASURES OF ILC When ILC is applied to the proess, the output error ( e( i, ) ) at the time point ( ) an be represented by e( i, ) y ( ) y ( i, ) det sto G, ) y ( ) G, ) ( i, ) deteriministi stohasti e( i, ), the measurement o the output error variable at time or a partiular bath i, is represented by a deterministi det dynamis ( G, ) ) plus a stohasti disturbane sto ( G, ) ). The stohasti disturbane is oten alled the unexplained measurement error. It is resulted rom the unertain variations and disturbanes among the luring variables. The deterministi dynamis, hih is explainable, is the untion o y ( ), that eeps the mean onstant trajetory. Thus, the perormane bound ( J ) in Eq. (3) an be expressed by to parts: the stohasti eet ( J Disturbane ) rom unmeasured disturbane in the eedba loop and the deterministi eet ( J ) rom the desired setpoint trajetory in the eedorard loop, JE e i J ( G, G ) J ( G, G ) () (, ) (5) C Disturbane C To ahieve the minimum bound, Eq. (5) ill be min Jmin E e( i, ) J J GC, G GC, G Disturbane (6) Thus, the eedorard learning ontroller ( G, ) ) an be obtained JDisturbane C C G, ) G, ) G, ) G, ) G, ) an be regrouped into ontroller-invariant and ontroller-dependent terms. Using the Diophantine identity, (7) d G, ) Q, ) q R, ) (8) here Q is LTV polynomials o degree d and R is a proper LTV transer untion. Ater substituting the eedorard ontroller (Eq. (7)) and the Diophantine identity (Eq. (8)) into Eq. (5), the output error ill ome rom the J Disturbane disturbane only. To ahieve, the ontroller dependent term must be zero. The eedba ontroller ( C ( G q, ) ) an be obtained R, ) GC, ) G, ) Q, ) here G, ) is the proess model ithout any time delay. Hene, the minimum variane (MV) o the perormane bound an be derived into T j ( ) Td j J d T d j ( ) j ( ) T d j d j (9) () here ( ) is the time-variant oeiients o the polynominal j disturbane ( ( ) Q, ). Here the same variane o the ) ith a normally distributed random variable at any time and at any bath run is assumed. is the variane o the unmeasured hite noise. For the duration o eah bath run, the varianes ( ( ) ) at time represented by the MV benhmar ontroller an be obtained by here J GC, G J Disturbane min J. min J GC, G J Disturbane and an be identially zero under peret ontrol. This means that the inal output error is zero over the hole bath duration i there is no disturbane. j ( ) Td e ( ) j ( ) d j ( ) Td j () 68

4 7th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-, 8 here the signal-to-noise ratio ( ( ) ) is used or simple expression. To detet i the urrent operations have deviations rom the minimum bounds, a statistial hypothesis testing approah an be applied to the ontrol output error at eah time point. Based on the traditional statistial proess ontrol methods, the upper ontrol limits (UCL), the enter line (CL) and the loer ontrol limits (LCL) at eah time point are given UCL( ) 3 ( ) () CL( ) (3) LCL( ) 3 ( ) () (a) hat harateristis o the underlying distribution might be during eah time point. The shaded regions overed by the upper and loer ontrol limits at eah operation time are also plotted. Thus, there is no la o the benhmar perormane hen the output error alls beteen the ontrol limits. Whether the urrent operating data rom a bath run is in ontrol ith good perormane an be determined.. ILLUSTRATIVE EXAMLES. Example : Linear Time Invariant System The proess and the disturbane are modelled as 5.q. q.9q.8q (5) G q q 6 UCL G q.5q (6) e/ - - here both models are linear time invariant. The unmeasured noise ( ) ith zero mean and unit variane enters the disturbane model. The reerene proile used in this example is shon in Fig. A eedba ontroller and a eedorard one are used to ontrol this system, -6 LCL (b) G G q q.38.3 q q (7) Relative Frequeny.5 e() y() Fig. 3. (a) The bath ontrol hart ith UCL and LCL; (b) the distribution untion at eah time point hose shaded region represents the region in ontrol. here,,, T. Fig. 3(a) shos the ontrol hart ith LCL and UCL is used to ompare the perormane o a urrent ontrol loop ith that o the ontrol loop ith benhmar ontrollers hen the benhmar s expeted output errors all on CL. Fig. 3(b) shos a pitorial dilay o 5 5 Bath Fig.. The ontrolled outputs or the initial designed ontrollers in Example. The bold lines are the reerene proiles and the dotted lines represent the ontrolled outputs or Bath, 5, 9 and. 9 69

5 7th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-, 8 Under the initial designed ontrollers, the reonses o the output traing to some bath runs are shon in Fig.. The ontrolled output is onverged ater bath runs. The system under the unmeasured disturbane hange seems to have some deviation rom the reerene setpoint; hoever, it is hard to evaluate the urrent perormane rom the bath output reonse. On the basis o the given proess and the disturbane models, the minimum variane bounds or eah bath an be omputed using Eqs. ()-(). The ontrol hart or the minimum variane perormane bounds is used to test the perormane o the ontrolled output or the bathes using the ontroller design (Eq. (7)). Fig. 5 shos the results o the ontrolled error hen the ontroller parameters are used. It is ound that 55 out o the total data points all out o the perormane bounds. This indiates the ontrollers should be tuned. e/ rom one bath to another. The duration o eah bath is 5 minutes. The sampling time o eah bath is minute. Fig. 6 also shos the plot o the reonse to the ontrolled temperature or to operating bath runs. From the operating proess data, hih ontrol system does the job better? To assess the perormane o the ontrolled system, the benhmar o the ontrol system should be set up irst. The benhmar perormane bounds are determined based on the proess and disturbane models. A total o 5 bath runs o the data are olleted. From the data, the dead time ( d ) o the proesses alulated by ross-orrelation analysis is three. Aording to the identiiation proedure, the proess ( Gp, ) ) and the disturbane models an be alulated. Due to the ae limitation, the detailed identiiation proedure is reerred to Yea and Chen (7). Thus, the estimated minimum variane bounds o the ontrolled output errors or a bath run an be alulated rom Eqs. ()-() To illustrate the ontrol perormane in Fig. 6, the ontrol harts or these to operation bath runs are shon in Fig. 7. The harts indiate that the ontroller perormane o the seond bath run outperorms that o the irst one, but the to ontroller designs annot all into the ontrol bounds beause the MV bounds, hih are the minimum perormane bounds, an be ahieved or MV ontrol only Fig. 5. The ontrol hart ith the minimum variane bounds (mared in solid line) or evaluating the ontrol outputs (mared in asteris). T 3 9 Controller Design I Controller Design II 8. Example : Nonlinear Bath Reator This example is intended to sho ho to evaluate iterative learning bath ontrollers or a typial exothermi hemial bath reator. The dierential equations and the parameter values desribing the reation proess are reerred to Luyben (99). The reation system involves to onseutive irstorder reations: A B C To stages are run in the system. In the irst (start-up) stage, the steam in the jaet initially heats up the reator ontent until the exothermi heat o reation is generated signiiantly enough. In the seond (maintenane) stage, the ooling ater in the jaet is used to remove the exothermi heats o reation. The reator temperature is ontrolled by to lit-ranged ontrol valves, a steam valve and a ater valve. Thus, eedba ontrol is used to eliminate the disturbane eet on the manipulated variables and eep the heat requirement ithin the bath run. The eedorard ontroller is used to modiy the eiied temperature proile Fig. 6. The ontrolled outputs or to designed ontrollers in Example. 6. CONCLUSIONS In pratial operation plant, the proess data an be aessible rom any time period at the touh o a button beause most modern hemial proesses utilize omputer systems in hih large amounts o data is stored heaply and eiiently. Many proesses have been around or years and engineers have aquired lots o experiene, but many operational problems still go undiagnosed or a prolong period o time. Thus, developing a irm gra o the data mining tehnique to identiy and perormane assessment o 7

6 7th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-, 8 the ILC system is strongly required to maintain good perormane o the operating bath unit hen produing produts. On the basis o the operating data rom the repeated traing tas hih is run at a inite time interval in the time domain and an ininite repetition along the iteration domain, the perormane bounds o ILC benhmar or the LTV bath operation system is developed in this paper. From the routine operation data, the advantages o the proposed method are demonstrated through simulated examples. The examples also explain ho to build the perormane bounds and aurately identiy the ontrol perormane o the urrent bath operation at eah time point. Hoever, beause o the aggressive ontrol input o MV ontrol, the loer perormane bound is impratial or the general ontrol appliation. Thus, the ahievable minimum variane o eiied ontrol ill be developed in our uture researh.. (b) e/ e/ (a) ACKNOWLEDGEMENT This or is partly onsored by National Siene Counil, R.O.C. and by the Ministry o Eonomi, R.O.C. REFERENCES Chen, Y.; Xu, J.-X.; Lee, T. H.; Yamamoto, S. Comparative Studies o Iterative Learning Control Shemes or A Bath Chemial roess', IEEE Int. Symposium on Control Theory and Appliations, Singapore, 997. Desborough, L.; Harris, T. J. (993). erormane assessment measures or univariate eedorard/eedba ontrol, Canadian Journal o Chemial Engineering, 7, 65. Harris, T. J. (989). Assessment o ontrol loop perormane, Can. J. Chem. Eng., 67, 856. Huang, B.; Shah, S. L.; Miller, R. (). Feedorard plus eedba ontroller perormane assessment o MIMO systems, IEEE Transations on Control Systems Tehnology, 8, 58. Isasson, A. J. and Horh, A., Dumount, G. A. Eventtriggered deadtime estimation rom losed-loop data. ro. ACC, Arlington, Virginia,, Luibello,., Learning ontrol o linear systems. ro. ACC, Chiago, 99. Luyben, W. L. (99). roess Modeling, Simulation and Control or Chemial Engineers, MGra-Hill, Ne Yor. Moore, K. L. (993). Iterative learning ontrol or determine systems, Advaned in industrial ontrol. Spring-Verlag, Berlin. Ratlie, J. D.; Hatonen, J. J.; Lein,. L.; Rogers, E.; Harte, T. J.; Oens, D. H. (5) -type iterative learning ontrol or systems that ontain resonane, Int. J. Adapt. Control Signal roess., 9, 769. Sanda, A..; Seborg, D. E. Controller perormane assessment based on setpoint reonse data, ro. ACC, San Diego, Caliornia, 999. Tan, K. K.; Zhao, S.; Chua, K. Y.; Ho, W. K.; Tan, W. W. (6) Iterative learning approah toard losed-loop automati tuning o ID ontrollers, Ind. Eng. Chem. Res. 5, 93. Xu, J.-X; Tan, Y. (3). Linear and nonlinear iterative learning ontrol, Springer-Verlag, Germany. Yea, Y.; Chen, J. (5). Diagnosis o losed ontrol loop status using perormane analysis based approah, Ind. Eng. Chem. Res.,, Fig. 7. The ontrol hart ith the minimum variane bounds (mared in solid line) or evaluating the ontrol outputs (mared in asteris) o (a) the ontroller design I and (b) the ontroller design II in Example. 7