This page is part of a serie of articles on how to write the model of an inverted pendulum. We strongly recommand to read the previous pages for a better understanding.

Based on the previous result, it is now possible to write the state space model of the system. Let's define \(X\) the state of the system:

$$ X=\begin{pmatrix} x_1 \\ \Theta_2 \\ \dot{x_1} \\ \dot{\Theta_2} \end{pmatrix} $$

The state space representation is:

$$ \dot{X}=\begin{pmatrix} \dot{x_1} \\ \dot{\Theta_2} \\ \left[A^{-1}.B\right] \end{pmatrix} $$

- Ball and beam model
- Dynamic model of an inverted pendulum (part 1)
- Dynamic model of an inverted pendulum (part 2)
- Dynamic model of an inverted pendulum (part 3)
- Dynamic model of an inverted pendulum (part 4)
- Dynamic model of an inverted pendulum (part 5)
- Modelling of a simple pendulum
- Equation of closed and open loop systems
- PI-based first-order controller

Last update : 02/11/2021