A genetic algorithm based minimax optimal design of robust I-PD controller

We present a new robust minimax design method of the I-PD controller improved PID controller (that has proportional, integral and derivative actions), based on the generalized ISE (integral of squared error) criterion with a penalty on the derivative of the manipulated variable. It is shown that the generalized ISE is a weighted sum of the two ISEs for the I-PD and PID controllers. A GA (genetic algorithm) based method is developed for solving the minimax problem. For the first and second order systems with a time-delay, we show that the robustness of the closed-loop responses to parameter variations is greatly improved over the earlier designs based on the ISE criterion.