We take the series RLC block located in ’artemis/SSN/SSN Components/SSN Series RLC’ for our explanations.
The Series RLC state-space equations are well-known:
In the model, these matrices are built using Simulink:
Note: The order of the states (vC and iL) is inverted from the equations. Both representations are correct.
The continuous-time domain matrices Ac Bc Cc, with a null D matrix, are then discretized using both Trapezoidal and Backward Euler rule of integration. The resulting discrete A matrix Ad depends on the discretization method used. The same comment also applies to the discrete B matrix. C and D matrices are not affected by discretization. h is the discretization time step.
This is done in the following subsystem, with Ts being the discretization time step.
In the model, this is again made using only Simulink blocks: