Design of optimal disturbance rejection PID controllers usinggenetic algorithms

This paper presents a method to design an optimal disturbance rejection PID controller. First, a condition for disturbance rejection of a control system-H_∞-norm-is described. Second, the design is formulated as a constrained optimization problem. It consists of minimizing a performance index, i.e., the integral of the time weighted squared error subject to the disturbance rejection constraint. A new method employing two genetic algorithms (GA) is developed for solving the constraint optimization problem. The method is tested by a design example of a PID controller for a servomotor system. Simulation results are presented to demonstrate the performance and validity of the method