Design of robust PID controllers using decoupling at singular frequencies

Algorithms for computation of the total set of PID stabilizers based on decoupling of PID parameter space at singular frequencies are presented. Nonconvex stability regions are built up by convex polygonal slices. Two problems are thereby discriminated: (A) assertion of kPkP-intervals with stable polygons and (B) automatic detection of stable polygons for a fixed kPkP. This paper includes solutions to both problems. The methods apply also for robust PID stabilization of a multi-model uncertainty.