NEW DESIGN AND STABILITY ANALYSIS OF FUZZY PROPORTIONAL-DERIVATIVE CONTROL-SYSTEMS

This paper describes the design principle, tracking performance, and s tability analysis of a fuzzy proportional-derivative (PD) controller. First, the fuzzy PD controller is derived from the conventional contin uous-time linear PD controller. Then, the fuzzification, control-rule base, and defuzzification in the design of the fuzzy PD controller are discussed in detail. The resulting controller is a discrete-time fuzz y version of the conventional PD controller, which has the same linear structure in the proportional and the derivative parts but has noncon stant gains: both the proportional and derivative gains are nonlinear functions of the input signals. The new fuzzy PD controller thus prese rves the simple linear structure of the conventional PD controller yet enhances its self-tuning control capability. Computer simulation resu lts have demonstrated this advantage of the fuzzy PD controller, parti cularly when the process to be controlled is nonlinear. After a detail ed stability analysis, where a simple and realistic sufficient conditi on for the bounded-input/bounded-output stability of the overall feedb ack control system was derived, several computer simulation results ar e shown to compare with the conventional PD controller. Although the c onventional and fuzzy PD controllers are not exactly comparable, we sh ow their comparison in order to have a sense of how well the fuzzy PD controller performs. For this reason, in the simulations several first -order and second-order linear systems, with or without time-delays, a re first used to test the performance of the fuzzy PD controller for s tep reference inputs: The fuzzy PD control systems show remarkable per formance, as well as (if not better than) the conventional PD control systems. Moreover, the fuzzy PD controller is compared to the conventi onal PD controller for a particular second-order linear system, showin g the advantage of the fuzzy PD controller over the conventional one i n the sense that in order to obtain the same control performance the c onventional PD controller has to employ an extremely large gain while the fuzzy controller uses a reasonably small gain. Finally, in the cas e of nonlinear systems, we provide some examples to show that the fuzz y PD controller can track the set-points satisfactorily but the conven tional PD controller cannot.