Process Control: Modeling, Design, and Simulation

3.9. Poles and Zeros

There are a number of different ways to represent process transfer functions. The “polynomial” form is

Equation 3.49

The values of s that cause the numerator of Equation (3.49) to equal zero are known as the “zeros” of the transfer function. The values of s that cause the denominator of Equation (3.49) to equal zero are known as the “poles” of the transfer function.

The “pole-zero” form is

Equation 3.50

and complex poles (or zeros) must occur in complex conjugate pairs.

The “gain-time constant” form is the one that we use most ...