(from matlab Example)
A cube rotating on its corner has an inertia tensor J and a damping force F of 0.2. The following system uses inputs as the driving torque and the outputs as angular velocity in a state-space model.
$$J = \begin{bmatrix}
8 & -3 & -3 \\
-3 & 8 & -3 \\
-3 & -3 & 8
\end{bmatrix}$$
$$F = 0.2\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}$$
The equation for the state-transition matrix is \(A=-J^{-1}F\), the input-to-state matrix is \(B=J^{-1}\), the state-to-output matrix is \(C=I\) and the feedthrough matrix is zero \(D=0\).
[[Angular Velocity]]
- StatespaceModelMATLAB
Backlinks:
[[State-Space Model of Rotating Body]]