Computation of stabilizing PI and PID controllers by using Kronecker summation method

In this paper, a new method for computation of all stabilizing PI controllers is given. The method is based on the plant model in time domain, and by using the extraordinary feature results from Kronecker sum operation, an explicit equation of control parameters defining the stability boundary in parametric space is obtained. Beyond stabilization, the method is used to shift all poles to a shifted half plane that guarantees a specified settling time of response. The stability regions of PID controllers are given in (kp, ki), (kp, kd) and (ki, kd) plane, respectively. The proposed method is also used to compute all the values of a PI controller stabilizing a control system with uncertain parameters. The proposed method is further extended to determine stability regions of uncertain coefficients of the system. Examples are given to show the benefits of the proposed method.