Hello Pamela,
I think a classical linearization of the PMSM in the time domain around those variables is simply too non-linear of a system for a basic linearizaiton analysis to be useful. The results you are getting confirms this. The issue is that this model is being analytically linearized based on the physics equations in a specific moment of time. This is not a good thing in AC systems, particularly with a motor attatched. The rotor angle, electrical phase, and every other variable are playing into this calculation, so the linearization while technically accurate, is not useful over an extended time frame because as soon as the electrical phase, or rotor angle change, your dynamic equations have changed. You'd have to linearize around all of the different operating points using this approach and basically just end up with the original model you started with. To abstract out much of the system behavior without using phasor techniques, you could try using a frequency response estimation and then fitting a transfer function to that system using system identification. This would give you a behavioral representation of the variables that you are interested in while abstracting out the AC nature of the electrical network. It would have limited accuracy aorund the operating point you linearize at as it true for all linearizations.
Phasor works because the underlying mathematical model is highly linear when converted to Phasor, so linearizing it doesn't change the behavior much. In general, if you are using classical linearizaiton techniques on an AC circuit, you would want to work with phasors.
Regards,
Joel
