Lower Bounds on Delay Margin of Second-Order Unstable Systems

This paper examines the delay margin achievable by using PID controllers for linear time-invariant (LTI) systems subject to variable, unknown time delays. We derive explicit lower bounds on the delay margin of second-order unstable delay systems achievable by PID control, which provide a priori the ranges of delay over which a second-order delay plant is guaranteed to be stabilizable by a PID controller, and more generally, by a finite-dimensional LTI controller. Analysis shows that our results are less conservative in most cases than lower bounds obtained elsewhere using more sophisticated and general LTI controllers. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.