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 ...