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
This is often written in the form
where (obviously a0 ≠ 0)
and the parameters are as follows: ...