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

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3.4. Transfer Functions

A transfer function relates inputs to outputs in the Laplace domain. In particular, the Laplace domain relationship between a manipulated input and output is called a process transfer function.

Consider an nth order differential equation,

Equation 3.22a

Since we are assuming that the model is based on deviation variables, and that the system is initially at steady state, the initial conditions are

Equation 3.22b

Taking the Laplace transform of each term,

Solving for Y(s), we find

The ratio of polynomials is called the ...

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