Robust PID control using a Smith predictor for time delay systems

Abstract

Time delays are unavoidable in many mechanical and electrical systems. The presence of delay typically imposes strict limitations on achievable feedback performance in both continuous and discrete systems. The presence of the delay complicates the design and analysis of a control system as it makes continuous systems infinite dimensional, and it significantly increases the dimensions in discrete systems. This work will propose a method to determine all PID controllers that stabilize the closed-loop system and satisfy weighted sensitivity, robust stability or robust performance constraints for stable time delay systems with a Smith predictor using the frequency response of the system. The Smith predictor works to eliminate the time delay from the characteristic equation and so improves the range of PID controllers that stabilize the system. A comparison between the range of PID controllers with and without Smith predictor is given in this work. This work also proposes a method for finding all PI-PD controllers that stabilize an unstable system with a modified version of the Smith predictor.