Computation of PID stabilizing region with stabilized margins

On research of the stabilizing region of a PID controller, the control system is required a stabilized margin to compensate the uncertainty of plant modeling and the parameter deviation of PID controller. This paper defines four types of stability margins for the plant under PID controller to extend the conventional definition of stability margins (gain margin and phase margin). Based on the presences of Right Half Plane (RHP) poles or not, the closed-loop systems are classified into two categories and their necessary stabilized margins are stated. A method of constructing PID stabilizing regions by using the generalized Hermite-Biehler theorems is proposed for the PID controlled closed-loop system to meet the prescribed performance of stability margins. Then, two examples are employed to test the validity of the method proposed. Obtained results demonstrate that the PID stabilizing regions with stabilized margins can really be gotten by the proposed method for both cases.