Abstract
It has been shown, that stability regions for PID-controllers in a (κD, κI)-plane for fixed κP 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 transferred 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 2-plane must be checked. Since the orientation of the cross section planes for polygonal 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 mass-spring-mass system proposed in (Bernstein and Wie, 1990) as a benchmark control problem for digital robust control is used to illustrate the method.
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