Mechatronics Q & A: When is it OK to break mismatch rules?

Dec. 13, 2007
Q: I design servocontouring applications using both linear motor and rotary/ball-screw methods, and the inertia mismatch issue has always been a concern for me.

I’m familiar with the importance of maintaining an inertia mismatch of 5:1 or less for ball-screw contouring applications. On the other hand, my motion-control vendor says this rule has been “broken” by high-performance, fast sampling controllers, in conjunction with high-resolution feedback systems.

I understand that higher inertia mismatch reduces system bandwidth. But is it possible that mismatch is less relevant in more and more instances because of newer, high-performance motion components that recently have become available?

A: Excellent question. Yes, it is true that reducing rotor inertia increases bandwidth, and high bandwidth is the bane of low-performance amplifiers. If the amplifier has a bandwidth or gain limitation, the associated phase lag causes an issue with control. Should you get to 180° of phase shift with positive gain, you have an oscillator. A system that is oscillating out of control will have a phase shift lagging by 180° in the feedback while the gain is at or above 0 dB, the reference for no gain.

I have been successful with inertial mismatches as high as 20:1 on a belt-coupled motor with high-bandwidth amplifiers. But when obsolescence dictated a change in such systems, we had to overcome significant challenges. In one case the system had used an analog tachometer for feedback, but the new drive needed a resolver. The subsequent delays in a resolver-to-digital conversion were simply unacceptable for the performance we wanted. As soon as the gain was high enough to handle the customer’s requirements, the system became unstable.

All in all, as the bandwidth and performance of the amplifiers rise, performance depends less and less on rotor inertia.

One method of overcoming the challenges of inertia mismatch is to use motors that directly couple to the load. Direct-Drive Rotary (DDR) motors can significantly reduce inertia mismatch concerns, letting users simply consider the load as part of the motor-rotor inertia.

In high-gain situations, however, even a direct-drive coupling has compliance, Here the amplifier must handle loads that can be as high as my personal record of 1,600:1. At this level of inertia mismatch, use of a sine/cosine encoder, along with fast interpolation techniques, dictate the use of an amplifier with high performance.

— Lee Stephens

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