Robust Stabilization of Time-Delay Systems using PID Controller with a Smith Predictor

Time delays in the feedback complicate the analysis and design of the closed-loop system. The use of a Smith predictor in combination with a Proportional Integral Derivative (PID) controller is a well-known technique for dealing with these delays in stable systems. However, many authors have questioned the robustness of this approach when the model of the plant is not known exactly. In this paper, the authors tackle this problem directly by determining all PID controllers working in combination with a Smith predictor that robustly stabilize the closed-loop system. The use of a Smith predictor tends to increase the size of the set of all robustly stable PID controllers in the controller parameter space. A numerical example is used to compare the set of robustly stabilizing PID controllers with and without a Smith predictor.