Question:
Jerk limitation or mean value filtering:
Which method for equalising the curves of position setpoints is more suitable in terms of positioning behaviour and achievable drive performance?
Answer:
It depends! Both filtering methods have their advantages and disadvantages.
Both methods aim to avoid abrupt changes in the course of acceleration/deceleration. Jumpy changes always produce a wide spectrum of frequencies (Fourier), so the individual natural frequency of the machine, which is always present, will also be there. Thus, the whole system is excited to oscillate with the natural frequency.
A filter method is particularly effective when only the natural frequency of the machine is filtered out of the spectrum or damped.
Jerk limitation:
Setting: Jerk limitation (Jerkmax) = 𝑎𝑚𝑎𝑥 * f0 | [m/s³] = [m/s²] [1/s]
| f0: Natural frequency of the machine
| amax: Max. Acceleration/deceleration achieved during the respective positioning movement.
- Target and over-grinding positions are reached exactly. Setpoint generation does not cause any time delay.
- The same applies to synchronous movements of several axes.
Disadvantages:
The frequency spectrum shifts for movements over short distances if the full acceleration amax is not achieved in the travel profile (so-called triangular operation).
The natural frequency f0 of the machine is correspondingly less damped and the occurrence of vibrations can increase.
- To avoid the excitation of vibrations in triangular operation, the jerk limitation must be adjusted, see formula.
Average filter:
Setting: Average filter time (TFilter) = 1 / f0 | [s] = 1 / [1/s]
| f0: Natural frequency of the machine
Advantages:
- Easy to parameterise, only tuning to the natural frequency f0 of the machine required.
- Parameterisation not dependent on the acceleration curve of the respective positioning movement.
Disadvantages:
- The movement takes place with a time delay due to the influence of the filter. The target position is only reached after a filter time has elapsed.
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In the case of over-ground movements (positioning profile with final speed), the specified positions are not hit exactly.
- Synchronous movements of several axes are only possible to a limited extent, because the progressions of position and speed are not calculated absolutely, but result from filtering. In such applications, the same filter settings must be used.
Comparison of the two methods using the example of a machine with a natural frequency of 1 Hz:
With mean value filter, in triangular operation (amax is not reached) the vibration-exciting amplitude for the natural frequency of 1 Hz remains at zero. With jerk limitation, a clear amplitude at 1 Hz is set in delta operation.
The amplitude in the example is almost as high as in the unfiltered case (blue curve).Figure: Fig 6 from white paper with additions
Keywords: controller setting, control characteristics, performance, stability limit, vibration excitation
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