Methods for robust PID control

TL;DR

This paper reviews a comprehensive theory for designing robust PID controllers, providing algorithms to efficiently compute stabilizing regions in parameter space for various plants, emphasizing the geometric structure of stability regions.

Contribution

It introduces algorithms for fast computation of robust stability regions in PID parameter space and highlights the convex polygonal structure of these regions.

Findings

Stable regions can be constructed from convex polygonal slices.

The theory has matured into a simple and elegant framework.

Algorithms enable rapid stability analysis for multiple plants.

Abstract

A comprehensive theory for robust PID control in continuous-time and discrete-time domain is reviewed in this paper. For a given finite set of linear time invariant plants, algorithms for fast computation of robustly stabilizing regions in the ($k_P, k_I, k_D$)-parameter space are introduced. The main impetus is given by the fact that non-convex stable regions in the PID parameter space can be built up by convex polygonal slices. A simple and an elegant theory evolved in the last few years up to a quite mature level.