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Motor Modeling 2:
Developing State Equations
Some basic electical and mechanical equations (w/ Laplace notion highlighted)
-
Eqn's matching
VOLTAGE
Eqn's matching
TORQUE
-
(C*V) = (1/s)*i
(C*V) = Q = [integral] i dt
Keep mindful of various notations for angle and angular velocity, etc:
Current will produce a torque:
...which must be balanced against the forces due to inertia (J) and friction (D):
The back EMF (voltage) generated is proportion to the angular velocity:
And finally, note that the BACK EMF CONSTANT (Ke) is in fact the SAME VALUE as the TORQUE CONSTANT:
(....but different units!)
...convert each to MKS units to see this.
gonzo@mit.edu
2.010 Tutorial #2, 21-Sep-00
(....but different units!)