Frequency domain analysis of electrical model

[jonschumacher]

I would like to perform a frequency domain analysis of a linear electrical model composed of components from the standard library. As a result, I would like to obtain a Bode plot. Normally, one would transform the differential equations into the Laplace domain, calculate the transfer function and determine amplitude and phase for the selected frequencies. I find it hard to find any documentation on solving problems in frequency instead of time domain. I would really appreciate any hint on how to do this within ModelingToolkit.

Regards,
Jonas

[baggepinnen]

The way forward here is to provide functionality for linearization, i.e.,

• Simplify the system to a form with identity mass matrix (no algebraic equations left) (Reduce system to DAE index 0 in the presence of unbound inputs #1325)
• Linearize the system from input u to output y, i.e., transform

x' = f(x, u)
y  = g(x, u)

to

x' = Ax + Bu # + f(x0, u0)
y  = Cx + Du # + g(x0, u0)

where A,B,C,D are matrices. After this,
https://juliacontrol.github.io/ControlSystems.jl/latest/lib/timefreqresponse/
https://juliacontrol.github.io/ControlSystems.jl/latest/lib/plotting/
covers most things related to frequency-domain analysis.

References:

• Modelica linearize
• Modia linearize