Nonlinear Systems in Python

Most of the Python Control Systems package tools we’ve used will not work for nonlinear systems. For instance, nonlinear systems cannot be defined with control.tf(), control.ss(), and control.zpk(). Similarly, the simulation functions control.forced_response(), control.initial_response(), and control.step_response() do not work for nonlinear systems.

There are two common ways of defining and simulating nonlinear systems in Python. The first uses the SciPy package’s integrate module’s functions such as solve_ivp(). The second uses the Control Systems package, which has nonlinear state-space model reprsentations. For simulating nonlinear systems, the Control Systems package actually calls the SciPy package’s integrate module’s functions. Because we have already been using the Control Systems package for linear system models, we will us its nonlinear facilities, as well. However, it should be mentioned that the package’s documentation for nonlinear systems is a bit sparse.