Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller

This paper presents approaches to the design of a hybrid fuzzy logic proportional plus conventional integralderivative (fuzzy P+ID) controller in an incremental form. This controller is constructed by using an incremental fuzzy logic controller in place of the proportional term in a conventional PID controller. By using the bounded-input/bounded-output “small gain theorem,” the sufficient condition for stability of this controller is derived. Based on the condition, we modify the Ziegler and Nichols’ approach to design the fuzzy P+ID controller. In this case, the stability of a system remains unchanged after the PID controller is replaced by the fuzzy P+ID controller without modifying the original controller parameters. When a plant can be described by any modeling method, the fuzzy P+ID controller can be determined by an optimization technique. Finally, this controller is used to control a nonlinear system. Numerical simulation results demonstrate the effectiveness of the fuzzy P+ID controller in comparison with the conventional PID controller, especially when the controlled object operates under uncertainty or in the presence of a disturbance.