Lower Bounds on Delay Margin of Second-Order Unstable Systems

Abstract

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.