A new optimisation method of PIDC controller under constraints on robustness and sensitivity to measurement noise using amplitude optimum principle

Abstract

This paper presents a new optimisation method for PID controller cascaded with a lead-lag compensator (PIDC). Parameters of the controller are obtained by solving the constrained optimisation problem. We propose two variants of the optimality criterion. The first one is defined through the max-min optimisation problem wherein objective function is the amplitude frequency response of the PIDC controller. The second one is based on an effective approximation of the minimum value of the amplitude frequency response of the PIDC controller. Consequently, we obtain a computationally less expensive problem. Both variants of optimality criterion result in efficient load disturbance and noise rejection, while robustness is ensured by constraining the value of the maximum sensitivity Ms. Good reference shaping is supported with proper constraints based on the Amplitude Optimum (AO) principle. Numerous batches of processes typically encountered in the industry are used to demonstrate the effectiveness of the proposed design method.