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Can you help me with a state space representation of the electrical network below:

schematic

simulate this circuit – Schematic created using CircuitLab

I'm representing this network in a (mathematical) state space form. I'm struggeling with solving the first order differential equation representation of C2:

dUc2/dt = Ic2 = IL2 - IL3 - IC3

IL2 and IL3 are input variables of the state space model (U=LdI/dt) but IC3 is not an input variable and should be expressed in variables used in the input matrix (shown below). Can you help me with that?

The input variables: X = [Uc1 Uc2 Uc3 Uc4 IL1 IL2 IL3 IL4]

The final state space model will be implemented in Matlab to optimize the parameters based on measured results.

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  • \$\begingroup\$ The circuit lacks an electromotive force generator. \$\endgroup\$ Commented Apr 24 at 12:00
  • \$\begingroup\$ Hi, I know, that does not matter. You can specify starting conditions for all the components. Capacitor C1 will be charged at t=0. \$\endgroup\$ Commented Apr 24 at 12:57
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    \$\begingroup\$ At a glance there appear to be eight state variables. Unless some reduction can be made, you have a very laborious problem if the solution has to be done by pen and paper \$\endgroup\$ Commented Apr 24 at 13:28
  • \$\begingroup\$ Can you help me? is not a question about electronics ... please ask about the problem, not about people's capability to help you ... how would a yes answer be useful to you? \$\endgroup\$ Commented Apr 24 at 16:51
  • \$\begingroup\$ Are you interested in transient behavior or the steady-state response? If it's steady-state, it might be better to represent everything in terms of impedances -- for example, R1 and L1 form a high-pass filter, as do R2 and L2. Then L3 and C3 form a "tank", as well as L4 and C4. Then you can plot the frequency response -- from your simulation, you get peak gain at 100 kHz. \$\endgroup\$ Commented Apr 24 at 18:13

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