9.6. IMC-Based PID Controller Design for Unstable Processes
The IMC procedure must be modified for unstable processes. Rotstein and Lewin (1991) have used the procedure developed by Morari and Zafiriou (1989) to find IMC-based PID controllers for unstable processes. The modification to the procedure shown in Sections 9.2 and 9.3 is to use a slightly more complicated filter transfer function.
Find the IMC controller transfer function, q(s), which includes a filter, f(s), to make q(s) semiproper. An additional requirement is that the value of f(s) at s = pu (where pu is an unstable pole) must be 1. That is,
Morari and Zafiriou (1989) recommend ...