Slow Traverse and Standing Error on a Positioner
A single-axis actuator uses a 24 V brushed dc motor rated 3600 rpm at 24 V no load, a 30:1 gearbox and a 5 mm-pitch leadscrew; total travel is 150 mm. Feedback is a potentiometer over the full stroke feeding a 12-bit ADC (0–5 V mapped to 0–150 mm). The controller is proportional-only. A commanded full-stroke move, which the mechanics should complete in about 15 s, takes 26 s and shows a steady following error of about 3 mm. When the axis stops, a standing error of 0.40 mm remains, identical whether the axis approaches the set point from the positive or the negative direction. Terminal voltage at the drive is 24.0 V and the motor current during the move is far below the drive's 5 A limit. The amplifier is linear, not PWM.
1. Calculate the expected and the observed traversing speed. Given the current reading, what does the shortfall implicate, and what single measurement separates the candidates?
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Expected speed
- Screw speed: 3600 rpm / 30 = 120 rpm
- Linear speed: 120 rev/min × 5 mm/rev = 600 mm/min = 10 mm/s
- Traverse time for 150 mm: 15 s (matches the quoted figure)
Observed speed: 150 mm / 26 s = 5.8 mm/s, i.e. 58 % of expected.
For a shunt dc motor, speed is essentially set by back EMF, V − I·Ra. With I small, V − I·Ra ≈ V, so 58 % of rated speed implies roughly 0.58 × 24 = 14 V across the armature, not 24 V.
Judgement: low current rules out mechanical binding, excess friction or torque saturation - any of those would drive current up, not down. So the missing 10 V is being lost electrically, either in the drive's output stage/cabling or because the motor is not the rated unit / the gearing is not 30:1.
The measurement that separates them: put a meter directly across the motor terminals while it is moving. About 14 V means the loss is between the drive terminals and the motor (series element, connector, undersized wiring, or an amplifier that cannot swing to its rail). A full 23–24 V means the motor or the gearbox is not what the drawing says, and the fault is mechanical/naming, not electrical.
2. Calculate the feedback resolution and compare it with the 0.40 mm standing error. What does the comparison, and the fact that the error is independent of approach direction, tell you?
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Resolution: 150 mm / 4096 counts = 0.037 mm per count.
The 0.40 mm standing error is about 11 counts, roughly thirty times the quantisation step. So the error is not an ADC rounding effect, and no amount of filtering or averaging at the ADC will remove it. Note also that the same comparison applies to the 3 mm following error - the loop is not being limited by feedback resolution at all.
Direction independence: if the fault were backlash in the gearbox or leadscrew, approaching the same set point from opposite directions would give errors of opposite sign (the classic backlash signature, and its magnitude would equal the lash). The error here is identical from both directions, so lash is excluded.
What remains is a stiffness limit of the loop: in a proportional-only system the error must be non-zero to generate the torque that holds the axis against friction and stiction. A 0.40 mm error that is stable, repeatable and direction-independent is the textbook signature of finite loop gain plus coulomb friction.
3. How would you confirm that diagnosis on the machine, and what change would remove the standing error?
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Confirming test
- Read the motor current at rest. A proportional loop holding against friction must still be commanding torque, so a standing armature current of a few hundred milliamps while the axis is stationary confirms that the loop is producing torque through the error.
- Raise the proportional gain in steps and record the standing error. If the error falls roughly in inverse proportion to gain until it hits the resolution floor or the axis starts to hunt, the loop stiffness is the cause.
- Apply a small manual disturbance and watch the recovery: a slow, sluggish return with a persistent offset is friction plus low gain; a sharp oscillatory return means gain is already at the stability limit.
Correction Add integral action (or a small feed-forward/integral term) so that the loop can build holding torque at zero error - this removes the standing error without demanding more gain from a system that may not have the phase margin for it. Reducing friction (lubrication, alignment, preload) attacks the other half of the product. Increasing gain alone is the wrong first move: it will shrink the offset but push an already marginal loop toward oscillation, and it does nothing about the 58 % speed shortfall, which is a separate electrical fault and should be fixed first.