combined free speed of 3 motors

[James Kuszmaul]

Originally Posted by Ether

I'm having trouble extracting an interpretation of the above. Could you explain what you mean? Perhaps give an example?

If you had two different motors, both attached to something (perhaps a shooter wheel), and you wanted to create an optimal controller for the wheel (given some cost function), then I doubt (although I may be wrong) that that optimal controller would have you always apply the same voltage to the motors. Hence, it is suboptimal to make this simplification, although there certainly may be situations where it is convenient, and therefore valuable, to make the simplification (such as if you were limited for space on your Digital Sidecar and wanted to be able to use a y-cable to control two different motors).

Originally Posted by Ether

I thought that's what I did in the attachment to the original post. At what point in the derivation do you disagree?

To be clear, the derivation assumes the motors will be used to drive a load (like a drivetrain or heavy arm for example) with a reflected inertia much larger than the rotor inertia, so the dynamic contribution of the rotor inertia can be ignored.

I see how you would be driving a large load (in my equations, the moment of inertia was primarily a place holder for such a load), but I do not see how a derivation of a formula for the free speed logically leads to the idea that all the single motor formulas must be valid.
I agree that you can calculate a stall torque, stall current, free speed, resistance, and free current for the motor combination, but just because those numbers may be meaningful does not necessitate that the single motor equations are true.
In other words, just because you have formulas for combined stall torque, stall current, free speed, resistance, and free current, why is it that these equations are still valid for values of V, I, omega, and Torque other than those at stall torque and free speed:
V = I*R + omega / Kv
Torque = Kt * I
I may be missing something, but I have not seen any proof that these equations continue to hold, and I like to see proofs .