DC brushless generator mathematical model

[medo79]

Dear all,
I am looking for the mathematical model for DC brushless generator in laplace form. Could you tell me where could I find this model in any textbook?

 

[waross]

Like a homopolar generator using conduction through the bearings and a pool of molten metal such as mercury in place of brushes???

http://en.wikipedia.org/wiki/Homopolar_generator

Bill
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"Why not the best?"
Jimmy Carter

 

[cswilson]

It all depends on how sophisticated a model you want to get. If you want a very basic model from "input" to "output" without considering much the internal mechanisms of the motor, you have a very simple model in Laplace form that is essentially the same as that for a brush DC motor, except that the electrical inputs are given as AC (RMS) quantities.

From RMS current input to torque output is just a gain term Kt (torque constant).

From torque to acceleration is just another gain term 1/J, where J is the rotor's moment of inertia. If the load is stiffly coupled to the motor (enough so you can ignore the dynamics of your coupling), this term should be 1/(Jm+Jl), where Jm is the motor rotor inertia and Jl is the load inertia as reflected back through any gearing.

From acceleration to velocity is a simple integration, 1/s in Laplace form.

If you have a voltage input, the transfer function from voltage to current is 1/(Ls+R), where L is the inductance and R is the resistance (both must be expressed so that they provide the proper relationship in RMS terms). Also, the back EMF voltage (which is Ke times the velocity output) must be subtracted from the input voltage.

In most of these stages, the units can be tricky! The units provided in catalogs are usually not the same as you want for analysis.

If you want to go past this and analyze the individual phases, you immediately introduce all sorts of non-linear terms that cannot be handled in simple Laplace transforms.

Curt Wilson
Delta Tau Data Systems