Unified approach for graphically designing PID controllers with Smith predictors for time-delay systems

Abstract

This paper combines a Smith Predictor with an approach for graphically determining all Proportional-Integral-Derivative (PID) controllers in either the Continuous-Time (CT) or Discrete-Time (DT) domains that meet Gain Margin (GM) and Phase Margin (PM) specifications. Smith Predictors (SP) are often used when designing controllers for systems that exhibit “relatively” large delays that may cause the system's stability and/or performance to deteriorate. The PID controller gains, namely Proportional gain (K p ), Integral gain (K i ) and Derivative gain (K d ), will be determined graphically using only the frequency response of the system's 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 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 procedure outlined applies to both CT and DT systems, hence, the unified approach designation. Additionally, this procedure will ensure meeting predesign requirements in terms of gain and phase margins. The stability boundaries of the PID controller gains will be determined graphically where within the boundaries, nominal stability is guaranteed and stability margins requirements are met.