State space modelling of a Mechanical System with Synchronous Motor

Hi Everyone,

I am about to build a state-space equations for a mechanical steering system connected to PMSM, in order to analyze its control performance. The original differential equations governing the system are as follow:

• MECHANICAL DYNAMICS = 3 second order differential equations (I will be having 6 states )

• ELECTRIC DYNAMICS = 2 equations of current in d and q reference frame. (I will be having 2 states)

I wanna control the motor current according to a reference signal coming from a driver input torque.

• Should I make a state space for each mechanical and electrical syatem, then join them together?
• or can Its enough to control q-axis current and add it directly to mech. sys? .... In this case. ., with this Iq I will be having 7 states in my model.

Thank you

Answer 1

[Sabin]

For such a system it is not common to combine all equations into a single model. It might end up with a very complex nonlinear model that is useless for controller design. Moreover, if you plan to have a cascade control structure is better to have separate models for inner and outer loops.

You can take a look at one of our examples in Simscape Electrical, showing an Electric Power Assisted Steering. Hope this helps.

[Ali Bashabsheh]

Thank you,

I already went through this example. My contribution in this project will be in a control proposal, hence its not easy (or not allowed) to modeify the controller in this example.

You mentioned "if you plan to have a cascade control structure is better to have separate models for inner and outer loops"; do you think I can have a state-space model like the following, and still design a good controller:

or you suggest I break it into smaller structures, then combine together? I am quite confused about it!

Thanks