9.4. IMC-Based Feedback Design for Processes with a Time Delay
In order to arrive at a PID equivalent form for processes with a time delay, we must make some approximation to the dead time. (Please note that we do not use an approximation for dead time when implementing the “pure” IMC strategy developed in Chapter 8. We are doing this only for the IMC-based PID procedure presented in this chapter; this is only done to yield a PID-type controller.) We use either a first-order Padé approximation for dead time or neglect dead time entirely and use the first-order transfer function results.
First-Order + Dead Time
Since first-order + dead time is the most common representation of chemical process dynamics, the PID equivalent form developed here is ...