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

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3.12. Converting State Space Models to Transfer Functions

A general state space model can be converted to transfer function form, using the following steps. Starting with the state space model

Take the Laplace transform of each term, assuming zero initial conditions

Solving for x(s), then y(s) (it should be noted that often D = 0)

where G(s) is a transfer function matrix. For example, the transfer function relating input j and output i is

or in ...

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