Position and velocity feedback low-pass filters

These filters are used to cope with distorted feedback signals that occur in the control loop. Typical distortions to consider are:

  • Encoder noise in the position signal - optical and good magnetic encoders usually have a low amplitude. 1st order filters with a 1000 Hz * cutoff are a good starting point.
  • Noise in the velocity signal - noise from the position signal is amplified due to differentiation. 1st order filters with a 500 Hz * cutoff are a good starting point.
  • Velocity signal distortions due to encoder nonlinearity. These distortions appear with a frequency of 1,2,4 x revolutions per seconds. The filter configuration depends on the particular setup.

Note

Setting the velocity filter more rejective than the position filter is one possible approach, see A practical guide to low-pass filter design for details how to set up filter parameters.

* The specified frequencies are just initial values that will not interrupt the motion control. Lower values should be found and set see A practical guide to low-pass filter design

The main parameters of the Low-pass filters are the cutoff frequency and the filter order:

  • The cutoff frequency determines the frequency at which the filter attenuates the signal to -3 dB of the amplitude. After that frequency, a roll-off region starts that further attenuates the signal.
  • The filter order determines the steepness of the roll-off region resulting in -20 dB a decade per filter order.
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As a summary, the cutoff frequency is when the filter starts attenuation and the order is how fast it attenuates from that point on.

Note

Filtering comes at a cost of a phase shift. The higher the filter order, the more delay is introduced to the filtered signal. This might significantly limit the maximum sharpness of the control loop.

A practical guide to low-pass filter design

  1. Determine the approximately required bandwidth of the signal. This can be done based on the reference profile specifications or roughly estimated using the control loop bandwidth from the minimum rise time to be realized when tracking a reference step:

    \[Bw \simeq \frac {0.35} {t_r} Hz.\]
  2. Ideally, the filtered signal shouldn’t be modified until this frequency: magnitude change and phase shift have to be as little as possible. Thus, the filter cutoff frequency should be approximately one decade (x10) higher.

  3. Examine spectral density plot of the target signal and determine the frequency range that has to be filtered out.

  4. Configure a 1st order filter. Note if noise amplitude significantly grows together with frequency. In this case, a second order filter should be used.

  5. Try to change cutoff frequency/filter order until appropriate balance between noise filtering and phase-shift/attenuation is reached.