Predictive fuzzy PID control theory is developed in this paper, which offers a new approach for robust control of time-delay systems. The paper describes the functional structure, design principle, and stability analysis of a new predictive fuzzy PID controller. Sufficient computer simulations are provided for illustration and verification. First, the structure of the controller is derived from both the fuzzy PID control and the generalized predictive control concepts. Then, on-line model identification, optimal cost index, fuzzification, rule base, and defuzzification of the representative predictive fuzzy PD+I controller are discussed in detail. Lyapunov asymptotic stability analysis is conducted. Then, many computer simulations are performed to compare with several closely related controllers such as the fuzzy PD+I controller and the Smith-type predictive fuzzy PD+I controller. In the simulations, second-order linear systems with/without time delays, nonlinear systems with/without time delays, uncertain linear systems with time delays, and uncertain nonlinear systems with time delays are used to confirm the advantages of the new predictive fuzzy PD+I controller. Finally, this method is applied to control some chaotic systems with success. This predictive fuzzy control method provides a new way for controlling uncertainty and complex linear and nonlinear systems, even with significant time delay.
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