9.1 Background

As we show in this chapter, the IMC structure can be rearranged to the standard feedback structure.

Question: Why do we care about IMC, if we can show that it can be rearranged into the standard feedback (PID) structure?

Answer: Because the process model is explicitly used in the control-system design procedure. The standard feedback structure uses the process model in an implicit fashion; that is, PID tuning parameters are often "tweaked" based on a transfer function model, but it is not always clear how the process model affects the tuning decision. In the IMC formulation, the controller, q(s), is based directly on the "good" part of the process transfer function. The IMC formulation generally results in only one tuning parameter, the closed-loop time constant (l, the IMC filter factor). The IMC-based PID tuning parameters are then a function of this closed-loop time constant. The selection of the closed-loop time constant is directly related to the robustness (sensitivity to model error) of the closed-loop system. Also, for open-loop unstable processes, it is necessary to implement the IMC strategy in standard feedback form, because the IMC suffers internal stability problems.

The reader should realize that the IMC-based PID controller presented in this chapter will not give the same results as the IMC strategy when there are process time delays, because the IMC-based PID procedure uses an approximation for dead time, while the IMC strategy uses the exact representation for dead time.