Delay Margin of Low-Order Systems Achievable by PID Controllers
Dan Ma
College of Information Science and Engineering
Northeastern University
Shenyang, China
Abstract—This talk concerns the delay margin achievable using PID controllers for linear time-invariant (LTI) systems subject to variable, unknown time delays. The basic issue to be investigated addresses the question: What is the largest range of time delay within which there exists a single PID controller to stabilize the delay plants in question? 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 talk, we discuss a frequency-domain approach, focusing on low-order time-delay systems stabilizable by PID controllers. We develop explicit expressions of the exact delay margin and its upper bounds achievable by a PID controller for 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 are widely used to regulate industrial processes which are typically modeled by first- and second-order dynamics. Our results herein should thus provide useful guidelines in tuning PID controllers and in particular, the fundamental limits of delay within which a PID controller may robustly stabilize the delay processes.
Dan Ma received the Ph.D. degree from Northeastern University in 2007, Shenyang, China, in Control Theory and Control Engineering. Since 2006, she has been with School of Information Science and Engineering, Northeastern University, Shenyang, where she is appointed an Associate Professor. She was a Postdoctoral Fellow at Northeastern University from 2008 to 2010, a Guest Professor with Department of Electrical Engineering, University of Notre Dame, South Bend, Indiana, USA, in 2012, and a Research Fellow at Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China, in 2017. Her main research interests include network-based control systems, switched systems, and time-delay systems. She is a member of CAA Youth Committee, and a member of TCCT Technical Committee on Nonlinear Systems and Control.
