Optimization of PID Controller Based on Maximization of the Proportional Gain Under Constraints on Robustness and Sensitivity to Measurement Noise

This technical note presents a new, simple and effective, four-parameters proportional-integral-derivative (PID) optimization method. The set of adjustable parameters is defined by the proportional gain k, integral gain k_i, damping ratio of the controller zeros (DRCZ), and desired value of the sensitivity to measurement noise M_n. Given M_n and desired value of the maximum sensitivity M_s, for both maximization of k and maximization of k_i, only three nonlinear algebraic equations need to be solved for a few values of DRCZ. Contrary to the method based on maximization of k_i, in the method based on maximization of k the improvement of performance is obtained by decreasing DRCZ from 1 to the value corresponding to the minimum of the integrated absolute error (IAE). Moreover, this is achieved without deteriorating robustness to the model uncertainties, for a large class of stable processes. Compared to the recently proposed PID optimization methods, for the same M_s and M_n, lower values of IAE and M _p are obtained by using the method presented here.