Process Control: Modeling, Design, and Simulation

3.7. Second-Order Behavior

Second-order models arise from systems that are modeled with two differential equations (two states). In this section we separately consider transfer functions that do not have “numerator” dynamics and those that do.

Pure Second-Order Systems

Consider a linear second-order ODE, with constant parameters

Equation 3.35

This is often written in the form

Equation 3.36

where (obviously a₀ ≠ 0)

and the parameters are as follows: ...