A unified graphical approach for a PID controller design with a Smith predictor

Abstract

This dissertation will extend the graphical method to the unified domain to design a PID controller augmented with a Smith predictor so that the closed loop system with deadtime meets nominal stability (NS), nominal performance (NP), robust stability (RS) and robust performance (RP) design requirements. Next, this research will report on the effects of the presence of a feedback path transfer function on the analysis and the design of a PID controller with a Smith predictor to ensure that the closed loop system will meet nominal performance and robust stability and performance design conditions. This includes the study of parameter uncertainty in the feedback transfer function dynamics on the sensitivity and complementary sensitivity transfer functions for robust stability and robust performance design requirements Finally, the dissertation will provide the general solutions for different PID controller configurations for nominal stability, nominal performance, robust stability and robust performance. A Smith predictor is often used when designing a controller for a system that exhibits “relatively” large delay that may cause the system’s stability margins and/or performance to deteriorate. The inclusion of a Smith predictor along with a PID controller can significantly improve stability margins and/or performance when compared to systems relying solely on a PID controller. The improvement can be observed in terms of the expansion of the ranges of the PID controller gains even if there is a mismatch between the actual system model and its corresponding Smith predictor model.