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

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Appendix 16.1: Derivation of the Step Response Formulation

From superposition of all previous inputs, the output at step k can be found from

However, assuming that all step response coefficients greater than step N are equal to the value at step N (this is only true for stable systems with a long model horizon), we can write

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