Genetic Auto-Tuning and Rule Reduction of Fuzzy PID Controllers

This paper presents a novel method for parameter auto-tuning of a fuzzy proportional-integral-derivative (PID) controller. Different from PID controllers with fixed gains, the fuzzy PID controller is expressed in terms of fuzzy rules, in which the input variables are the error signals and their derivatives, while the output variables are the PID gains. In this manner, the PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than the traditional ones. When tuning the fuzzy PID gains, a genetic-algorithm-based method is proposed, in which the centers and the widths of the Gaussian membership functions, the fuzzy control rules corresponding to every possible combination of input linguistic variables, and the PID gains are chosen as parameters to be determined. In encoding the parameters into corresponding chromosomes, a mixed-coding technique is adopted. To expedite the convergence speed of the evolutionary process, the concept of enlarged sampling space and ranking mechanism are used. To show the effectiveness and validity of the designed fuzzy PID controller, a multivariable seesaw system is used for illustration.