This paper introduces genetic algorithms (GA) as a complete entity, in which knowledge of this emerging technology can be integrated together to form the framework of a design tool for industrial engineers. An attempt has also been made to explain "why'' and "when" GA should be used as an optimization tool.

odeling is a common but important technique for signal characterization. With the advent of computational power, many problems that were considered to be unsolvable in the past can now be tackled with ease. Successful applications in this area include the time-delay estimation modeled as a finite impulse response (FIR) filter [ 11 for sonar and radar systems; speech coding using linear predictive coding [2-41; wavelets for speech and image coding and recognition [5-81; fractals for image compression and recognition systems [9-111; and delayed-X filter [12-141 for active noise control [ 151, to name but a few.An efficient model for signal processing is not easy to come by and is often obtained with the aid of an optimization scheme. The accuracy of the model is generally governed by a set of variables or parameters that is optimized in the 22 IEEE SIGNAL PROCESSING MAGAZINE

This paper introduces an optimal fuzzy proportional-integral-derivative (PID) controller. The fuzzy PID controller is a discrete-time version of the conventional PID controller, which preserves the same linear structure of the proportional, integral, and derivative parts but has constant coefficient yet self-tuned control gains. Fuzzy logic is employed only for the design; the resulting controller does not need to execute any fuzzy rule base, and is actually a conventional PID controller with analytic formulas. The main improvement is in endowing the classical controller with a certain adaptive control capability. The constant PID control gains are optimized by using the multiobjective generic algorithm (MOGA), thereby yielding an optimal fuzzy PID controller. Computer simulations are shown to demonstrate its improvement over the fuzzy PID controller without MOGA optimization. Index Terms-Fuzzy control, genetic algorithm, optimization, proportional-integral-derivative controller.Manuscript received February 26, 2001. Abstract published on the Internet

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