Unified Approach for Weighted Sensitivity Design of PID Controllers with Smith Predictors

Abstract

This paper combines a Smith Predictor with an approach for graphically determining all Proportional-Integral-Derivative (PID) controllers in either continuous-time (CT) or discrete-time (DT) domains that meet performance specifications expressed in a form of a weight on the sensitivity transfer function using Hardy-Space (H∞) control. A Smith Predictor (SP) is often used when designing a controller for a system that exhibits a "relatively" large delay that may cause the system’s relative stability and/or performance to deteriorate. The PID controller gains, namely Proportional gain Kp, Integral gain Ki and Derivative gain Kd, will be determined graphically using only the frequency response of the systems’ components, i.e., plant with delay and SP structure. The inclusion of a SP along with a PID controller can significantly improve stability margins and/or performance when compared to relying solely on a PID controller. The improvement can be observed even if there is a mismatch between the actual process and its corresponding SP model. By using the delta operator, the same procedure can be applied to either continuous or discrete time systems, hence a unified approach. The stability boundaries of the PID controller will be determent graphically where within the boundaries, nominal stability is guaranteed and weighted sensitivity requirements are met.