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In this physics, dynamical systems, and control engineering tutorial, you will learn
(1) How to automatically derive state-space models of nonlinear systems starting from the equations of motion. You will learn how to completely automatize the derivation process by using Python and Python's symbolic computation library called SymPy.
(2) How to simulate the derived nonlinear state-space model in Python. You will also learn how to simulate the state-space model for arbitrary control inputs.
As a test case, we use a nonlinear inverted pendulum on a cart system. For brevity, in this tutorial, we call this system the cart-pendulum system. This system is a very important example of a non-trivial nonlinear system that is often used as a benchmark of different control and estimation algorithms.
The state-space model of the cart-pendulum system has four state variables. For this system, the derivation of the nonlinear state-space model from the equations of motion is not trivial and if a person is doing the derivations by hand, most likely he or she will make an error. Motivated by this, we created this tutorial that explains how to completely automatize the derivation process and how to easily simulate the nonlinear dynamics of this system in Python. Everything explained in this video tutorial can be generalized to more complex dynamical systems, such as UAVs, mobile robots, robotic arms, etc.
