Explicit bounds for guaranteed stabilization by PID control of second-order unstable delay systems

Abstract : In this paper we derive explicit lower bounds on the delay margin of second-order unstable delay systems achievable by PID control, which provide a priori a guaranteed range of delay values over which a second-order delay plant can be stabilized by a PID, and more generally, a finite-dimensional LTI controller. This is done by deriving lower bounds on the delay margin achievable by PD controllers, whereas this margin constitutes a lower bound on that achievable by PID controllers. Analysis shows that in most cases our results can be significantly less conservative than the lower bounds obtained elsewhere using more sophisticated, general LTI controllers. © 2018 Elsevier Ltd