Delay Margin of Low-Order Systems Achievable by PID Controllers

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1958-1973
Journal / PublicationIEEE Transactions on Automatic Control
Issue number5
Online published5 Jul 2018
Publication statusPublished - May 2019


This paper concerns the delay margin achievable using PID controllers for linear time-invariant (LTI) systems subject to variable, unknown time delays. The basic issue under investigation addresses the question: What is the largest range of time delay so that there exists a single PID controller to stabilize the delay plants within the entire range? Delay margin is a fundamental measure of robust stabilization against uncertain time delays and poses a fundamental, longstanding problem that remains open except in simple, isolated cases. In this paper we develop explicit expressions of the exact delay margin and its upper bounds achievable by a PID controller for low-order delay systems, notably the first- and second-order unstable systems with unknown constant and possibly time-varying delays. The effect of nonminimum phase zeros is also examined. PID controllers have been extensively used to control and regulate industrial processes which are typically modeled by first- and second-order dynamics. While furnishing the fundamental limits of delay within which a PID controller may robustly stabilize a delay process, our results should also provide useful guidelines in tuning PID parameters and in the analytical design of PID controllers.

Research Area(s)

  • Delay margin, robust stabilization, uncertain time delay, time-varying delay, PID controller