A servo axis that oscillated after auto-tune. The axis was a belt-driven XY table, 500 mm travel, 400W servo motor. The drive’s auto-tune ran for 5 minutes. It set the gain. At 1000 RPM, the axis was smooth. At 300 RPM, it oscillated (buzzing sound). The customer re-ran the auto-tune. Same result. The auto-tune set high gains to achieve fast response. But the belt was flexible. The high gains excited the belt’s natural frequency. The axis buzzed. This is about servo tuning and why flexible mechanics need different tuning than rigid ones.
The mechanics bandwidth
A servo axis has a natural frequency determined by the mechanical system. A ballscrew on a fixed-fixed support might have a natural frequency of 80 Hz. A belt-driven axis has a natural frequency of 15-30 Hz (the belt stretches and acts as a spring). The servo loop gain must be below the mechanical natural frequency. If the loop gain is set to 50 Hz on a belt with 20 Hz natural frequency, the loop oscillates. The buzz.
The auto-tune measures the natural frequency by injecting a small torque chirp. It should set the gain to 1/3 of the measured natural frequency. But the auto-tune assumes a rigid mechanical system. It measures the motor-side resonance (the coupling and rotor), not the load-side resonance (the belt and table). The motor-side resonance might be 100 Hz. The auto-tune sets gain at 50 Hz. But the load-side (belt) is at 20 Hz. The gain at 50 Hz excites the belt. The axis buzzes.
What was changed
1. Lowered the loop gain manually. The velocity loop gain was reduced from 50 Hz to 15 Hz. The buzz stopped. The axis was less responsive (slight overshoot on quick moves) but stable. The position loop gain was also reduced. The axis took 10% longer to settle. For a packaging machine, the settle time was acceptable. The buzz was unacceptable.
2. Added a notch filter. The drive has a notch filter that cancels a specific frequency. The belt resonance was at 22 Hz. The notch filter was set to 22 Hz with a bandwidth of 5 Hz. The filter attenuates the loop response at 22 Hz. The gain at 22 Hz dropped by 20 dB. The axis could run at 30 Hz loop gain without buzzing. The settle time improved. The notch filter is the standard solution for belt-driven axes.
3. Stiffened the belt. The original belt was a polyurethane timing belt with steel cords. Switching to a carbon-cord belt increased the axial stiffness by 3x. The natural frequency rose from 20 Hz to 35 Hz. The loop gain could be set to 25 Hz. The axis was faster and stiffer. The carbon-cord belt costs 2x the steel-cord one. For high-performance axes, it’s worth it.
The tuning process for flexible axes
For a flexible mechanical system (belt, long ballscrew, or linear motor with a light load), the tuning process differs from a rigid one:
- Measure the resonance. Use the drive’s resonance measurement (or inject a chirp). Find the load-side natural frequency. Write it down.
- Set the loop gain below resonance. Velocity loop gain at 1/3 of the measured resonance. If resonance is 20 Hz, set gain to 7 Hz. The axis will be sluggish but stable.
- Add a notch filter at the resonance. The notch filter allows the loop gain to be raised above the resonance without exciting it. Raise the gain until the axis is responsive but stable.
- Adjust the inertia ratio. If the load inertia is mismatched, the auto-tune sets wrong gains. Measure the reflected inertia. Set it correctly. The tuning will be more stable.
- Test at all speeds. Run the axis from 1 RPM to max speed. Listen for buzz. If buzz appears at a specific speed, that’s a resonance. Add a notch or lower the gain at that speed range.
The gain vs bandwidth tradeoff
| Mechanical system | Typical natural freq | Max loop gain | Tuning approach |
|---|---|---|---|
| Direct drive (rigid) | 200+ Hz | 100 Hz | Auto-tune fine |
| Ballscrew (short, fixed-fixed) | 80 Hz | 30 Hz | Auto-tune + fine-tune |
| Belt drive (steel cord) | 20-30 Hz | 7-15 Hz + notch | Manual + notch filter |
| Long ballscrew (1500 mm) | 15 Hz | 5 Hz + notch | Manual + low gain |
The tuning rule: auto-tune works for rigid mechanics, flexible systems need manual tuning. The buzzing axis wasn’t a bad auto-tune — it set 50 Hz gain on a 20 Hz belt resonance. Lower the gain to 1/3 of the measured resonance. Add a notch filter. For new designs, stiffen the mechanics (carbon-cord belt, short ballscrew) so the natural frequency is high enough. The auto-tune can’t fix a mechanical resonance — it can only work with what the mechanics provide.
