Discrete-Time Robust PID and Three-Term Control

Abstract

It has been shown, that stability regions for PID-controllers in a (KD, KI)-plane for fixed Kp are convex polygons. This result allows a simple calculation of the set of all stabilizing PID controllers for a given plant. In the present paper this result is transfered to the case of discrete-time PID controllers or three-term controllers, where stability with respect to the unit circle or other circles in the z-plane must be checked. Since the orientation of the cross section planes for polygonial stability regions does not depend on the plant, it is easy to find the set of all simultaneous stabilizers for several representative plant parameters and to select a robust discrete-time controller from this set. A benchmark problem for digital robust control is used to illustrate the method