FUZZY LOGIC TECHNIQUES TO EVALUATE GLOBAL DYNAMIC PERFORMANCE OF CONTROL SYSTEMS C.M. Polito” WMG
F. G. Joita UFiMG’
A. R Braga
R T. Pena UFMG
CEFET-MG
* CI’DEE - EEUFlMG AV.Antdnio CarIos, 6627 31270-901 Belo Horizonte, MG -BRAZIL e-mil:
[email protected] (l3mc: +55 31 448-5480) ABSTRACT The paper presents a method to calculate a GlohP Performance Assessment Index (GPI) for a multiloop control system. The method is based on fizzy logic techniques bemuse some of the behavioral plant variables, such as energy consumption, prcduct quality and plant trip costs are better ewes& by linguistics rather than plain numerical variables. The technique based on fizzy logic gives results that a e close to the human operator evaluation. The method has ha applied to a computer simulated model of a Continuous Stirred Tank Reactqr (CSTR). Typical simulation results are presented.The performance ofa multiloop control scheme applied to a real Interacting Tank System (ITS) has also been assessed by the GPI method. Both simulated and experimentalruns demonstrate the potentiality of the poposed method in assessing control systems performance.
1. INTRODUCTION The performance assessment of a control system is a very important subject in the day-to-day life of a real plant control engineer. In a previous work, the authors have proposed and tested a method for assessing controllers pefisrmance (Job et al, 1995). The computation of such an index is done based upon the error (deviation of the controlled variablle fiom the set point), control and output signals and upon classical error criteria (IAE, RAE, etc.). The objective of this paper is to extend such ideas to consider the overall plant performance (Polito, 1995). The optimal operation of a multiloop pirocess control system is heavily based upon good decisions on “where”, “when”, and “how much” tuning is needed. In answering these questions, the decision to be made is heavily dependent on well conditioned information. Therefore, a numerical oiladation of a global performance assessment index, allowing a consistent evaluation of the behavior of the whole plant unit, is highly desirable. The Global Performance Index (GPI) proposed here evaluates the global performance of the process, with respect to the final quality of a specified product. The numerical value of the GPI corresponds to the quantification of the assessment criterion, previously established, for a production unit which has tobe evaluated. Some variables involved in the plant operation like energy consumption, product quality, plant trip costs and other money losses are better expresses uy ungusucs ramer than p l m numerical values. The fuzzy Global Perfonnance Index
0-7803-3636-4197$10.00 0 1997 IEEE
presented in this paper has been designed to incorporate vague information associatedwith some of these variables. The paper shows results of the application of the method to a Continuous Stirred Tank Reactor (CSTR) model, shown in figure 1, and to a real, pilot-scale, Interacting Tank System (ITS), shown in figure 2. -
LC
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Figure 1 :Continuous Stirred Tank Reactor Diagram (Guy, J.L, 1982)
Figure2: Intmdng Tank System Diagram (Brags et al., 1995)
IL DMPLEMENTATION OF THE FUZZY INFERENCE
MACHINE The multivariable fuzzy inference machine m c h e l and Jota 1994), used in this work, is based on the one proposed by Viot (1994). Seven input variables have been considered: Energy Consumption, Mean Error (of a final quality product variable), Variance of the Error, Laboratory Analysis of the Product, Time Stoppage, Damage and Productivity. All fuzzy sets, and their respective membership functions, are delined based on the experience and insight of control engineering experts. The number of fuzzy sets and the shape of the membership functions depend on practical desired issues, like
aemracy, ispeed of
response and stability of the control system. It has been found
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that,for this application, the actual shape of the membership function does not matter very much and therefore very simple functions like triangles and trapezoids (defined by four points: a,b,c,d), have been used (table 1). These type of membership functions are very common and have proven to present a good compromise between effectiveness and efficiency of the machine (Viot, 1994). After fuzzyfjing all seven input variables, the inference rules are processed, following the previously established reasoning. This reasoning is based on a set of d e s that have the form of r f - men statements. The output (GPI - Global Performance Index) is generated using a min-max composition and Folger, 1988), as shown in the inference machine (I& example below: If Consumption is STANDARD and Mean Error is STANDARD then
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GPI is ST;" If Consumption is ACCEPTBLE and Mean Error is STMARLI then GPI is S T m A R D ; GPI STANDARD = max[min(ConsumptionSTANDARD, Mean Error STANDARD), min(Consumpti0n ACCEPTBLX, Mean Error STANDARLl)];
The output values are calculated using the center of gravity method for each output membership function. To validate the fuzzy assessor, the variables (produh4y, damage, laboratory analysis and energy consumption of the production unit,whose actual measurements are not available) have been inferred from other related variables. For example, the energy consumption has been taken as the arithmetic mean of the control signals. To quanm the "laboratory analysis", the changes in the variables that directly affect the product quality have been considered. The productivity has been considered proportional to the set-point for each variable. The damage is assumed constant. These are rough approximations but they give the necessary insight to perform comparisons among similar tests. The universe of discourse (domain) of the input variables were tailored to yield consistent assessment grades.
O.OO,O.OO, 0.01,0.07
Analysis (input>
I
(output)
Gpl
0.00,0.00,0.07,3.00 Acceptable Not Acceptable 0.07,3.00, 100.00, 100.00
Standard Acceptable Not Acceptable
70.00, 90.00, 100.00, 100.00 60.00,70.00, 100.00, 100.00 0.00,0.00, 60.00,70.00
Table 1:Membership Functions The figure 3 shows a the system functional diagram.
I
I
Figure 3 :Functional B i d Diagram ofthe Assesanent (SP is the Set Point, U is the control signal and CV is the conh-olled variable).
111. SIMULATED AND E2CPERrmENTA.LRESULTS
The performance assessment of both, the CSTR and the ITS, have been made applymg a series of step changes in the relevant variables: for the CSTR, Level, Temperature, Reagent A flow and Reagent B flow and for the ITS,Level and Flow. The figures 4 and 5 show these test signals. Apart from that a final quality product variable far a process and i@ dwired value
must be w e d .The GPI will measure how close is the final quality product variable from its desired value. In the case of the C S m this variable is the final product concentrations. In the case of the ITS, these variables are the level and flow. Figures 4 to 7 and figures 8 to 13 show final GPI results performance assessment profiles for the CSTR and the ITS, respectively. At a first glance, it can be seen that all variables behaved well since the GPI classified the performance as "standarfl or "acceptable"
5.00 15.00 15.00 20.00
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for most of the time. The test in the temperam: loop (fig. 7) deteriorated sigmficantly the system performana:, showing its great sensitivity to variations in the temperature. In this case, the performance has been classified as not-acceptable, after the changes in set point. Note that the strength of the non-acceptable fuzzy set has increased fiom 0.02 to 0.5, while the one of the standard set decreased fiom about 1to 0.4 The significant influence of the vaniable "energy consumption" in the Global Index can be verified by noting the sudden change that occurs in the Global Index grade, particularly in the flowrate loops (figs. 8 to 9). The energy consumption strongly depends on the control signal which suffers great variations at the set-point changes instants, when the Global Index also presents sigmficant variation (figs. 6 to 9). This is due to the simplifying assumption Wit the average energy consumption is proportional to the average value of the control signal (for the four control loops of the CSTR). In the case of the ITS plant, figs. 10 to 15 show the GPI sensitivity to the overall control system behavior. Note that, after the changes in set point, the strength of the non-acceptable fuzzy set increases while the one of the standard and the acceptable fuzzy sets decrease. 0
Continuous Stirred Tank Reactor (CSTR)
Semplmq ,,me
Figure 7 Output strengths of the Fum/ Assessor membership hctim for the TemperatrUeLoq,M
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Figure 8 :Output sbgths of the Fuzzy A s s o r membership fundions for the Flow Laol,(FA)=
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Figure 9 :Output s!rm#hs of the Fum/ Assessor membership functionsfor the Flow
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Interacting Tank System (ITS)
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figure4 :Test Signal usedinthe CSTR (wa = set-poincwb =.wa - 5% de wa; wc = wa + 5% de wa). 100,
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samplmq lime
Figure 1O:OutputstrenghsoftheF~Assessor"bershipfunctionsforthe Level Loopfirsttest
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Figure5:TestSignaiusedintheITS. : '0'
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Figure 11 : Outputseengths ofthe Fuzzy Assessor membedu'p hctim for the Level Loop second test
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Figure 6 : Output strengths of the Funy Assessor membership functions for the Level Looptst
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Figure 12 : output strengths of the Fuay Assessor membership functions for the Level Loop thirdtest
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and formal definitions allows a great potential for practical applications.
ACKNOWLEDGMENTS 200
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Figure 13 :Output strength ofthe Fuzzy Assessor m&p LoopfKStteSt
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functionsfor the Flow
The authors achowledge the financial suport provided by the following Brazilian Research Agencies: CNPq, CAPES and FAPEMIG. REFERENCES Braga, A. R., Job, F. G., Polito, C. M. e Pena, R. T.(1995), “Development of an Interacting Tank System for the Study of
Advanced Process Control Strategies”, EEE 38th Midwest Symposium on Circuits and Systems, Rio de Janeiro, pp .441445 Guy, J. L. (1982): ‘Dynamc M o d e h of Tank-Type Reactor Systems”, procesS Dynamics, in Mathey, J. (1986): ‘1practical Proms I”entation and Control’’, McGraw-Hill, New York.
I200
ramplinD Itme
Figure 14 : Output strengthofthe Fuzzy Assessor membership functionsfor the Flow Loopsecondtest
Job, F. G., Braga, A. R. e Pena, R. T. (1995), “Performance Assessment of Advanced Process Control Algorithms Using an Interacting Tank System”, IEEE Industry Applications Society - 30th Annual Meeting, Orlando, Florida, pp. 1565-1571. ‘0
200
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800
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s e m p t ~ o ol i m e
Figure 15 :Output strengths of the Fuzzy Assessor membership functionsfor the How Loop third test
IV. CONCLUSIONS The results presented in the paper demonstrate the capability of assessing the overall control system p e r f o m c e using a fuzzy logic assessment. It has been verified that few rules are necessary to get a reasonably good assessor. The performance of the control system is expressed in terms of linguistic variables and can be immediatelyevaluated in terms of the previous knowledge, incorporated in the definition of the membership function of the GPI and in the d e s . Furthermore, the method takes into account variables, such as damage, laboratory analysis and time lost, that, for their nature, cannot be easily incorporated in an overall (numeric) assessment. Other variables, such as mean error and variance of the error, have also been considered (Polilo, 1995). The chosen indexes indicate the subjective nature of the global index. It is evident fi-om the results that the assessment depends on the variables used as inputs and on the membership functions for both inputs and outputs. Normally, the choice of these parameters is made considering the final goals of the specific production unit. Nevertheless, after the definition of the Global Index, it certainly will present consistent outputs that can be vefied by the Control system experts visual inspecton. This characteristic gives the GPI the potencial to application in real plants. It can be seen that the fuzzy rules used to quanhfj the performance give results close to a human evaluation. The simplicity of the method, without too much precision, strictness
Klir, G.J. and Folga, TA. (1988): “Fuzzy Sets Uncertainty and Mormation”, Prentice Hall. Michel, K. F. and Jota, F. G. (1994): “An Adaptive Learning Fuzzy System”, CPDEE - UFMG (in Portuguese). Polito, C.M. (1995): “Using Global Behavior Assesment Criteria for Multilcop procesS Control SystemsTuning“,M.E.E. Dissertation, PPGEEYWMG, Brazil (in Portuguese). Sutton, R. and Towill, D. R. (1985): “An Introduction to the Use of Fuzzy Sets in the Implementationof Control Algorithms”, Joumal of the Institution of Electronic and Radio Engineers, vol. 55, N“ 10, p ~357-367, . October. Trewhella, D.W. (1989): “AMethod of Evaluatq the Performance of Environmental Control Systems Within Buildmgs”, OUEL
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1794/89, Oxford. Viot, G. (1993): ‘Fwq Logic in C”,Dr. Dobb’s Joumal, February, pp 40-49 and 94. Zadeh, L. A. (1973): “Outline of a New Approach to the Analysis of Complex Systems and Decision Precess", IEEE Trans. on Systems, Man, and Cybernetics,vol SMC-3, No. 1, January.
