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, the proposed method is based on finding the explicit equation of control parameters defining the stability boundary in parametric space. 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 region of PID controllers is given in (k_p,k_i), (k_p,k_d) and (k_i, k_d) plane respectively. Examples are given to show the benefits of the proposed method.