VF PWM for varying frequency reference function
The constraint for amplitude is the signal may reach but not exceed the sawtooth in a comparator.

Whenever your Amplifier saturates like in your scope wave, the loop incremental gain automatically goes to 0 since it is no longer can vary when saturated. Ie nonlinear. So on average the overall gain is effectively reduced for step response. Lead/lag compensation or Nyquist root analysis needs to correct that.

Other info

Navigation servo analysis gets complicated when you push the spectral boundary where PWM side bands introduce jitter or the integration of force into velocity into position for stabilization maneuvers creates excess delay from a 3rd order system from integration.  So the multiple forms of feedback with predictor-correction targets to minimize maneuver control spectrum,  and gryo+accelerometers in 3 axis and drift calibration are complex when non-linearity is added.  

Phase shift in the compensation network must not lag too much as delay must be much less than the inverse BW desired. This often leads to DSP’s with digital filters.


  Once the scope of a design broadens to optimize sensors , transfer functions and specs, then a math simulation can be useful. But you need to start with specs. PWM ought to be a linear function after you choose and optimize the spectrum and bandstop and bandpass requirements.