Design of stabilizing PI and PID controllers

In this paper, a new method for the calculation of all stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the (k(p), k(i))-plane and then computing the stabilizing values of the parameters of a PI controller for a given control system. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus, it offers several important advantages over existing results obtained in this direction. The proposed method is also applied for computation of all stabilizing PI controllers for multi-input multi-output ( MIMO) control systems with consideration given to two-input two-output (TITO) systems using decoupling technique. Beyond stabilization, the method is used to compute all stabilizing PI controllers which achieve user-specified gain and phase margins. Furthermore, the method is extended to tackle 3-parameters PID controllers. The limiting values of PID controller parameters which stabilize a given system are obtained in the (k(p), k(i))-plane for fixed values of k(d) and (k(p), k(d))-plane for fixed values of k(i). However, for the case of PID controller, a grid on the derivative gain or integral gain is needed for computation of all stabilizing PID controllers. Examples are given to show the benefits of the method presented.