I have been learning about AC servos for a project. As i look through the torque speed curves, I get stuck. I understand how to use them, but I am baffled by the shape.

I was always taught that there is a linear relationship between torque and speed. If you look at torque speed curves for DC motor this is clear. The power supplied to the motor is equal to the product of torque and speed. The result is this proportional relation.

For these AC servos, we do not see this. There is a constant (or nearly constant) torque region across a range of lower speeds. Then we get the linear drop off after exceeding the torque and speed rating of the motor. Why are there two curves that determine the servo behavior? This does not make sense to me from a first principles perspective. How would you model this and what equations govern the slope of these regions? What I learned in my undergrad does not seem to apply.

If I find a servo that satisfies my power, torque, and inertia requirements, is it awful that I am not driving the system anywhere near the rated speed? For example, 230 RPM instead of 3500 RPM? Something about that feels wrong.

  • $\begingroup$ This would be much better answered by those on EE Stack Exchange. $\endgroup$
    – DKNguyen
    Jan 11 at 23:41

1 Answer 1


I was always taught that there is a linear relationship between torque and speed.

Only for permanent magnet brushed DC motors. Other types of motors have other curves.

Technically, even raw brushless DC motors do not have a linear relationship between torque and speed either. That is because the motor used in a brushless DC motor drive system is actually a permanent magnet synchronous motor (normally thought of as an AC motor.) These synchronous motors can be driven open-loop directly from a 3 phase power supply and when they are, they are constant speed devices. However, they obviously have physical limits and beyond their torque capability they lose synch with the line and no longer operate properly. These synchronous motors may be optimized for sinusoidal phase currents or trapezoidal phase currents. Optimization for sinusoidal phase currents allows for best efficiency when operating directly off a three phase power supply or a sine-wave output variable speed drive, whereas optimization for trapezoidal phase currents allows for best efficiency when operating off a 6-step commutation which requires simpler electronics than a sine-wave drive.

But when paired with a closed-loop drive to commutate them, their torque speed curve becomes like that of a brushed DC motor, and a brushless DC motor is born. The drive is assumed in the behaviour.

In a similar way, induction motors have humpedback torque speed curves that vary from motor to motor based on design objective:

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AC servo drives are paired with induction motors and use a control algorithm called "field oriented control" or "vector-oriented control. The mathematical basis behind them is something called a Park transform or D-Q coordinate transform. Very mathy. If you want to know how to model it, that's how. It was only mentioned in undergrad.

It basically takes the motor phase currents and mathematically weeds out the two currents buried inside the motor on top of each other that determine motor operation, and tells you what you need to do with the phase currents to get a desired result in these two currents. This lets you decouple torque from speed so you don't have to be a slave to the strange torque-speed curves above. I think it's sort of like how in a motor with a separate field and armature winding you have more freedom because you can control both the field excitation current and the armature current, except in an induction motor you don't have explicit windings for each and the currents for both run all over each through the same phases.

The purpose of this is to linearize the torque-speed curve of the induction motor which allows it to be used as a servo to achieve constant torque over the range of operating speeds (so-called constant torque control). But obviously, the motor has physical limits, so the constant torque characteristic can't hold forever and past some limit, it begins to falter and that's why the curve drops off.


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