On computation of the total set of robust discrete-time PID controllers

TL;DR

This paper presents a method to compute the complete set of robust discrete-time PID controllers ensuring stability across multiple models, using convex polygonal slices in parameter space.

Contribution

It introduces a novel approach leveraging invariant decoupling at singular frequencies to characterize stable regions as convex polygons, completing the solution to stability interval detection.

Findings

Stable regions are convex polygonal slices in parameter space.

The method effectively identifies intervals with stable polygons.

Complete set of multi-model robust PID controllers can be computed.

Abstract

The problem of finding the set of all multi-model robust PID and three-term stabilizers for discrete-time systems is solved in this paper. The method uses the fact that decoupling of parameter space at singular frequencies is invariant under a linear transformation. The resulting stable regions are composed by convex polygonal slices. The design problem includes the assertion of intervals with stable polygons and the detection of stable polygons. This paper completes the solutions to both problems.