# Step response of high-powered servo motor

I'm involved with a project that will need a servo motor to generate a high torque and a high speed in a short amount of time. Using typical speed/torque graphs and taking into account a certain gear ratio, it's possible to find a (small, and expensive) variety of motors that suit our specifications. One example chosen at random might be this servo motor.

One thing that worries me, however, is whether the motor we select can accelerate in the time we're asking for (<1sec); as far as I know, speed/torque graphs are measured assuming steady state operation.

What would be the parameters to look for to estimate whether a given motor will have the transient behaviour we require? In other words, is it possible to approximate the step response of such a motor?

(Edit: after I wrote this question I realised it is probably necessary to specify what sort of motor control I'd be using; i.e., torque control, speed control, or position control. Ideally it would be good to have the step response of the torque output under a range of loads since the others would follow from that. As discussed in the answers, this might be impossible to know from a data sheet.)

The parameters you want to look for are moment of inertia and torque. Looking at the datasheet at the link you provide, page 5, you can find a table: what you are looking for is the second and the third column. The equation of your interest is $\tau=I\alpha$, that is the "rotational equivalent" of $F=ma$. Solving for $\alpha\text{: }\alpha=\frac{\tau}{I}$. Calculating alpha you can have a rough estimate of the time your servo needs to speed up to full rpm. Keep in mind two things:

• You will need to add upp the moment of inertia of your sistem
• You can probably set up the speed up time in the controller so it might be slower than expected for this reason

For example, looking at the first row: $$\tau=0.32\ Nm\text{, }I=0.037\ kgcm^2= 3.7\cdot10^{-6}kgm^2\text{, so }\alpha=8.65\cdot10^3\frac{rad}{s^2}$$ If you want to speed up to the rated speed, that is $\omega=3000\text{rpm}=3000\cdot \frac{2\pi}{60}\frac{rad}{s}=314.2\frac{rad}{s}$, you can easily compute $t=\frac\omega\alpha=\frac{314.2\frac{rad}{s}}{8.65\cdot10^3\frac{rad}{s^2}}=36.3ms$

That's not that much isn't it? Again, I am assuming that the acceleration is costant with speed, which may or may not be true.

I suggest you to calculate the moment of inertia of the system you want to drive and then contact the manufacturer and ask them which servo will allow you to respect the speed up constraint that you have.

• Thanks, this goes some way towards answering the question. Can you be sure that the "rated torque" will be constant from the very moment the motor powers up, though? I guess that was the main concern I had, since we can simulate everything else. – Will Robertson Apr 25 '14 at 8:37
• No, I am not sure. I think that the rated torque is a minimum value and your system will actually take less time to speed up, but that's just what I think. You should really call the manufacturer. – Vladimir Cravero Apr 25 '14 at 8:45