Robust design of Smith predictor for a delay margin based on maximum sensitivity

Abstract

Using direct synthesis method, the controller in the Smith predictor structure is designed as a proportional-integral (PI) controller for first order plus time delay (FOPTD) model and proportional-integral-derivative (PID) controller for second order plus time delay (SOPTD) model. The tuning parameter in the direct synthesis method is evaluated based on the maximum sensitivity (peak value of the sensitivity function) of the closed loop. Delay margin is recommended as the robustness measure for delay compensators because the delay compensators are more sensitive for delay uncertainties. In this work, a simple analytical formula is developed for selection of the tuning parameter corresponding to the delay margin. Nominal and robust control performances are achieved with the designed controller. Three examples have been considered to show the advantages of the proposed design method.