What signal to use for identifying control-to-output TF of resonant converter? Is it required to have a transfer function when PI tuner is present?

I have a resonant converter (DC-AC) built on Simulink and I want to find out its control to output (current) transfer function using the system Identification toolbox in MATLAB/Simulink. I have three main questions, since the converter is PWM based:

1. Do I use the sine wave chirp signal as an input or use a square/rectangular wave version of the chirp signal or some other signal?

2. Do I actually need system Identification (and the open loop transfer function), if I have the MATLAB control system toolbox and PID tuner and I can design a z-domain (digital) PID controller without the System Identification Toolbox?

3. How can I tell whether my converter can be appropriately modelled by linear system dynamics?

I cannot find any specific information related to this topic other than this - https://www.mathworks.com/matlabcentral/answers/25674-square-wave-chirp

Thanks.