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

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3.11. Padé Approximation for Dead Time

As discussed in the previous section the transfer function for a pure time delay is eθs, where θ is the time delay. Some control system design techniques require a rational transfer function; the Padé approximation for dead time is often used in this case.

A first-order Padé approximation is

A second-order Padé approximation is

Example 3.8: Application of the Padé Approximations for Dead Time

Consider the first-order + dead time transfer function, where the time-delay dominates the time constant

The first-order ...

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