Computational Intelligence in the Design of Optimum Industrial Control Systems

Copyright 10 IFAC Control Applications and Ergonomics

in Agriculture, Athens, Greece, 1998

COMPUTATIONAL INTELLIGENCE IN THE DESIGN OF OPTIMUM INDUSTRIAL CONTROL SYSTEMS

V. Goggos & R. E. King Department of Electrical & Computer Engineering University of Patras Patras 26500, Greece e-mail: [email protected]

Abstract: This paper proposes a new technique which fuses evolutionary computation and fuzzy inference in the design of industrial controllers. In the proposed technique, a genetic algorithm is used to perform a stochastic search for the optimum values of the controller parameters. Fuzzy linguistic rules relating overshoot, rise time and settling time of the step response of the controlled system to controller suitability are used in computing the fitness of the design. The technique is applied to the design of a two-term controller of the temperature of a green-house. Copyright© 1998 [FAC Keywords: Evolutionary computation, stochastic search, industrial controllers, tuning, fuzzy inference, genetic algorithms.

1. INTRODUCTION The tuning of two and three-term industrial controller on which so many industrial plants depend, is usually performed by tuners in the field or by heuristic techniques such as those by Ziegler and Nichols and Astrom and Persson (Astrom, et al. 1995). These heuristic techniques assume a simple first order approximant of the controlled plant whose basic attributes (e.g. rise time, dead time and final value) ate used to derive the "best" values (in some sense) of the controller parameters.

among acceptable closed loop response attributes such as rise time, overshoot, steady state error and settling time. Model-free knowledge-based methods are now available from a number of vendors (Astrom, et al. 1995, Anderson, et a1.1988 , Pagano 1991, Porter, et al. 1987). In these, small step changes are made to the set-points of the controlled plant, after which the response of the closed system is evaluated. When steady conditions return, the controller parameters are modified on the basis of tuning rules and the procedure is repeated until the overall system behavior is considered satisfactory.

Tuning in the field is critically dependent on the human tuner's knowledge and experience. Experienced tuners can rapidly assess the performance of the overall plant by making systematic changes to the controller parameters and observing its response to small step disturbances in the set-points. The criteria of suitability of the controller are a result of a compromise

In classical SISO systems, there exist a variety of design techniques for the design of controllers, typical examples of which are based on minimization of the integral squared error (ISE) and integral time absolute error (ITAE). Numerous numerical techniques have been proposed for computing the optimum parameters of two and three term controllers of specified to-

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pology. Most often however, the resultant design leaves much to be desired with responses exhibiting unacceptable overshoot. The reason is that in all these quantitative methods there is no direct control over the closed system attributes. In this paper a new technique is proposed for the design of industrial two and three-term controllers whose suitability is assessed qualitatively through linguistic design rules using overshoot, the rise time (i.e. the time required to reach 90% of the final value) and the settling time (i.e. the time required to reach within 2% of the final value) in response to a small step change in the set-point. In the proposed technique, a genetic algorithm is used to perform a stochastic search for the optimum values of the controller gains. Fuzzy linguistic rules relating the attributes of the step response of the closed system to controller suitability are used in computing the fitness of the design. The proposed method, uses Genetic Algorithm to obtain the optimum controller gains and differs from existing knowledgebased techniques in that it uses fuzzy logic to assess the suitability of a design. Computational Intelligence is the basis for the proposed method which does not require an explicit model of the controlled plant and assumes only that its step response sequence is available from experimental data and that convolution applies. 2. EVOLUTIONARY COMPUTATION

Evolutionary Algorithms are stochastic search techniques, based on natural evolution, which have been extensively used in the last years in many fields, principally for optimization. In these techniques, a population of possible solutions to a problem is evolved systematically with self-improvement as their primary objective. The most common types of Evolutionary Algorithms are Genetic Algorithms and Evolutionary Strategies (Davis, 1991 , Roger-Jang, et al. 1996, Foge, 1995, 1997, Goldberg, 1989, Michalewicz, 1992). Critical to the use of Genetic Algorithms is formulation of a measure of the ability for survival of an individual, i.e. its quantitative fitness value. Exploitation of the accumulated information is achieved by way of the selection operator which improves the probability of survival of the fittest individuals while forcing the search for the fittest to the most promising areas in the search space. The exploration of the search space is achieved by way of two other operators, recombination and mutation. Recombination combines genetic/ numerical material of two random individuals while mutation perturbs a portion of the genetic/numerical material of an in individual.

3. QUALITATIVE CONTROLLER SUITABILITY Human knowledge about controlling a plant or system can often be expressed in linguistic rather than analytical terms. This knowledge exists in the form of if-then-else rules whose antecedents (i.e. controller attributes) and consequents (controller suitability) uniquely specify the measure of fitnesS/suitability of a particular design. A set of qualitative rules on how the three attributes affect the performance of the closed system is elicited from expert controller tuners. Fuzzy reasoning is used to infer the suitability of a particular design. De-fuzzification of the membership function of the suitability yields a numeric value for the fitness that is subsequently used in the optimization procedure. Finally, a Genetic Algorithm using an elitist strategy is used to determining the global optima of the controller parameters. The controller attributes are described by fuzzy sets each of which can have three to five linguistic variables to describe the attributes of any desired design. The linguistic variables which are used to describe the Rise_Time, Overshoot and SettlinjLTime are Small, Medium and Large while the linguistic variables for describing the resultant Suitability are Very_Small, Small, Negative_ Medium, Medium, Positive_Medium, Large and Very_Large, A sample of suitability rules is given below: RI: if (Rise_Time is Small) and (Overshoot is Small) and (SettlinjLTime is Small) then (Fitness is Very_Large) R2: if (Rise_Time is Medium) and (Overshoot is Small) and (SettlinjLTime is Small) then (Fitness is Large) R3: if (Rise_ Time is Medium) and (Overshoot is Medium) and (SettlinjLTime is Large) then (Fitness is Negative_Medium) R4: if (Rise_Time is Large) and (Overshoot is Medium) and (SettlinjLTime is Large) then (Fitness is Small)) R5: if (Rise_Time is Large) and (Overshoot is Large) and (SettlinjLTime is Large) then (Fitness is Very_Small) The membership functions used in the proposed design technique are shown in Figure 1. The complete set of linguistic rules constitutes the rule-base of the proposed design procedure. The rule-base contained 33=27 rules. MATLAB© and its Fuzzy Toolbox were used to implement the design technique, all rules being given unit weighting.

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Figure 2. Schematic of the controlled plant The proposed technique is not model-based thus no attempt is made to generate a low order approxi-mant with which to tune the closed system. It is sufficient to know only the continuous or discrete step response, as in the case considered .

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The design objective here is to find the optimum parameters (Kp' Ki)· of a two-term controller for the system with a closed system having nominal rise time Trise=26 units, a nominal overshoot of p=lOO/O and a nominal settling of Ts=20 units.

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fhe evolutionary-fuzzy design technique is applied to he design of a two-term controller (PI) for the control )f the temperature in a greenhouse. The temperature of he air in the greenhouse of Figure 2 in response to a ;tep demand typically possesses a step response whose :haracteristic shape is shown in Figure 3, i.e. a deadime followed by an exponential rise.

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Figure 3. Normalized step response of the plant The fuzzy sets of the three attributes that form the inputs to the inference engine are assumed to be triangular while the fuzzy sets of the suitability function are Gaussian. Following some experimentation, it was found that use of these membership functions led to a smooth fitness surface and improved system responses. Assuming the settling time to be constant, the manner in which the fitness

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surface varies with rise time and overshoot is shown in Figure 4. In deriving this surface Mamdani min-max inference and center of gravity (COG) de-fuzzification were used (Ross, 1995). A simple Genetic Algorithm, which follows an elitist strategy, is used to obtain the global optima of the controller parameters. It is observed that fitness decreases with increasing overshoot and increasing rise time, a logical interpretation.

5. CONCLUSIONS The determination of the optimum parameters of an industrial controller for a greenhouse whose step response sequence is known is a relatively simple matter using the proposed evolutionary design method based. In the method, fuzzy variables are used to express the principal design attributes that are then related to controller suitability while a Genetic Algorithm is used to search for the global optima of the controller parameters. The proposed hybrid technique has obvious advantages to the non-specialist.

REFERENCES Astrom K. 1. and T. Hagglund (1995). PlD Controllers - theory, design and tuning, ISA, N.C. Anderson K. L., G. L. Blankenship and L. G. Lebow (1988). A rule-based PID controller, Proc. IEEE CDC, Austin. Pagano D. (1991). Intelligent tuning of PID controllers based on production rules system, Proc. IFAC Int!. Symposium on Intelligent Tuning and Adaptive Control, Singapore. Porter B. A., A. H. 10nes and C. B. McKeown (1987). Real-time expert tuners for PI controllers, Proc. lEE, Part D, 134,4, 260-263. Davis L. (1991). Handbook of Genetic Algorithms Algorithms, VanNostrand. Roger-lang 1.-S., C.-T. Sun and E. Mizutani (1996). Neuro-Fuzzy and Soft Computing, Prentice Hall. Fogel D. B. (1995). Evolutionary Computation: Towards a new philosophy of machine intelligence, IEEE Press. Fogel D. B. (Editor) (1997). Handbook of Evolutionary Computation, Oxford. Goldberg D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley. Michalewicz Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs, SpringerVerlag. Ross T. 1. (1995). Fuzzy logic with Engineering Applications, McGraw Hill.

Figure 4. The fitness surface The step response of the optimum greenhouse temperature control system designed with the hybrid Evolutionary - Fuzzy (E-F) technique is shown in Figure 5. Though it is unfair to compare the results of this design procedure with that of a controller designed for minimum ITAE, it is simply noted that the E-F design has improved damping and is faster in reaching the steady state than the ITAE design. .

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