Transfer function matrix of a Multiple input DC-DC converter

I am trying to find the transfer function of the following multiple input boost converter:

I replaced S4 with a diode and this is what the simulink module looks like:

This is what the switch wave forms should look like:

I am mostly focused on Switch 3 which controls the boost operation of the converter, I am trying to control it using a PI controller but in order to tune the controller I need a transfer function. Since the system is a MISO system it means I need a transfer function matrix that relates each of the 4 input to the output, but I am not sure how to extract this. Do I use a step function on each of the inputs? What steps should I take in order to extract the transfer function matrix and tune the PI controller?

Any feedback would be greatly appreciated.

Answer 1

[Paul]

Does linearize work on Simulink Simscape models?

Answer 2

[Mohamad Nazir]

Hi Mohammad, you can probably use Model Linearizer app (https://fr.mathworks.com/help/slcontrol/ug/modellinearizer-app.html) on Simulink to get a linearized model (state-space or transfer function) for each I/O then design your controller.

However, may I suggest the trial & error method? I think you can simply add a PID controller and start with a gain of zero for Integral and Derivative terms and 1 for Proportional term, then increase/decrease it until you get oscillations, divide the gain by 2 then start increasing integral/derivative term until you get the desired reference tracking.