A real coded genetic algorithm for matrix inequality design approach of robust PID controller with two degrees of freedom

In this paper we present a new genetic algorithm (GA), that is a real coded genetic algorithm, and propose a new design method for robust PID controller with two degrees of freedom. This design method is based on the matrix inequality and the real coded genetic algorithm for optimization technique. The PID controller with two degrees of freedom designed by proposed method satisfies robust stability of closed-loop system against the parametric uncertainties of plant and multiple design specifications for robust performance. This method demonstrated by numerical simulations and shows good control performance.