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I am trying to determine the state-space model of the circuit shown below. Also shown are the KH equations. Those equations I put in a Solver (Mathcad), however the result does not seem correct. For example, the solver tells me that the derivative of \dot X is 0. Can anyone explain what I am doing wrong?

enter image description here

Daiz
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  • My impression is that the issue arises because the equation M_II does not comprise any derivatives – Daiz May 06 '22 at 16:30

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Figured it out I think. So for anyone who is interested: Kirchhoff equations are not guaranteed to be linearly independent, which is a problem for converting the circuit into state-space. Usually, meshes of capacitors or nodes of inductors cause such issues (see M_II, a mesh of caps). To get rid of the problem, I expressed the current of C_sr as follows:

$$ I_{C,sr}=C_{sr}\dot{X}_2 - C_{sr}\dot{X}_4 \\ C_{sr}\dot{X}_3=C_{sr}\dot{X}_2 - C_{sr}\dot{X}_4 \\ \dot{X}_3=\dot{X}_2 - \dot{X}_4 $$

Notice that the 3rd state will effectively disappear; no other state depends on it anymore.

Daiz
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