Stability of PID-Controlled Linear Time-Delay Feedback Systems

TL;DR

This paper extends the analysis of PID-controlled linear time-delay feedback systems to arbitrary-order plants, providing explicit stability boundaries and computation methods based on Pontryagin's studies.

Contribution

It generalizes existing stability boundary results from first-order to arbitrary-order plants using Pontryagin's framework.

Findings

Explicit stability boundaries for arbitrary-order plants.

Finite-step computation procedures for stability regions.

Extension of classical methods to higher-order systems.

Abstract

The stability of feedback systems consisting of linear time-delay plants and PID controllers has been investigated for many years by means of several methods, of which the Nyquist criterion, a generalization of the Hermite-Biehler Theorem, and the root location method are well known. The main purpose of these researches is to determine the range of controller parameters that allow stability. Explicit and complete expressions of the boundaries of these regions and computation procedures with a finite number of steps are now available only for first-order plants, provided with one time delay. In this note, the same results, based on Pontryagin's studies, are presented for arbitrary-order plants.