Chapter 9. The IMC-Based PID Procedure

In Chapter 8 we developed a transparent framework for control-system design: the IMC structure. One nice thing about the IMC procedure is that it results in a controller with a single tuning parameter, the IMC filter (l). For a system that is "minimum phase," l is equivalent to a closed-loop time constant (the "speed of response" of the closed-loop system). Although the IMC procedure is clear and IMC is easily implemented, the most common industrial controller is still the PID controller. The purpose of this chapter is to show that the IMC block diagram can be rearranged to the form of a standard feedback control diagram. We find that the IMC law, for a number of common process transfer functions, is equivalent to PID-type feedback controllers.

After studying this chapter, the reader should be able to do the following:

• Design an internal model controller, then find the equivalent feedback controller (IMC-based PID) in standard form; derive and use the results presented in Table 9-1

• Use an approximation for time delays in order to find a PID-type control law; compare the performance of various IMC-based PID controllers for time-delay processes; use Table 9-2

• Use Table 9-3 to find PID-type controllers for unstable processes

The major sections of this chapter are as follows:

9.1 Background

9.2 The Equivalent Feedback Form to IMC

9.3 IMC-Based Feedback Design for Delay-Free Processes

9.4 IMC-Based Feedback Design for Processes with a Time Delay

9.5 Summary of IMC-Based PID Controller Design for Stable Processes

9.6 IMC-Based PID Controller Design for Unstable Processes

9.7 Summary