The IMC-based PID procedure, like the IMC procedure from Chapter 8, can be based on either good setpoint tracking or improved disturbance rejection. Here, we first consider design for setpoint tracking.
The procedure outlined in Section 9.2 is illustrated by way of two examples: a first-order process and a second-order process. For clarity we drop the (~) notation on all of the process model parameters.
Find the PID-equivalent to IMC for a first-order process
Find the IMC controller transfer function, ...