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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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Appendix 8.1: Derivation of Closed-Loop Relationships for IMC

Refer again to Figure 8-12. Recall that the feedback signal is

and the signal to the controller is

The controller output or process input is

which can be rearranged to

Now, we realize that

and we find

or

which can be written

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