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Dynamic model of an inverted pendulum (part 6)

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.

State space representation

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:

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

See also

Last update : 02/11/2021