If the mechanical system has a resonance (for example a natural frequency) or if the system contains another source of distortion at a known frequency, exciting this particular frequency with the output of the torque controller may result in unwanted oscillations. This filter can be used to remove a specified frequency band around the resonance.
In practice, there is a certain challenge in usage of notch filters. If the resonance frequency is too low, introducing a notch filter will impair the control signal by adding a phase delay. It is therefore recommended to use notch filters only for high frequency resonances. *
* The frequency depends on both the central frequency and the rejection width. Generally, it should be higher than 50 Hz.
A practical guide to notch filter design:
Find resonances of the system. This can be done by observing a frequency response during the system identification procedure: Check the velocity reaction to a specific torque input frequency.
Decide which resonance should be compensated and identify the width of excitation frequencies.
Record the reference behavior of the system before applying the notch filter.
Configure the filter with the obtained parameters.
Check the resulting performance of the setup and optimize the filter parameters.
The smaller the width of the rejection band, the more ripples are in the surrounding frequencies amplitudes. However, the area of the phase shift is smaller as is the signal attenuation at the rejection band. It is recommended to use a rejection band width of at least 8 Hz in order to avoid overshoot.
The bigger the width of the rejection band, the smoother is amplitude transition around the central frequency. Additionally, the attenuation is bigger. This happens due to the second order of the filter which has limited attenuation per decade. However, the phase delay region is bigger.
Center frequency and bandwidth of notch filter