Filtering

Overview

A digital filter removes unwanted components from the signal which passes through it.

This feature can be used for example as:

  • Position Feedback filters - Reduce encoder noise. 1st, 2nd or 3rd order low-pass filters are supported.
  • Velocity feedback filters - Reduce noise and effects of encoder nonlinearity in the velocity signal. 1st, 2nd or 3rd order low-pass filters are supported.
  • Loop shaping filter - Suppress excitation of resonance frequencies in the output of the motion control loop or in the input of the torque control loop. 2nd order notch filters are supported.

Any signal can be decomposed into a sum of sine waves with different frequencies. Some of them might negatively affect the control loops. It is possible to attenuate these unwanted frequencies by properly configuring a corresponding filter.

Configurable filters are implemented for the signals that are considered the most important for motion control.

../../../../../../_images/control_filters.png

Methods

Definitions

  • s - Laplace-domain frequency parameter
  • fc - Cutoff frequency of the low-pass filter or central frequency of the Notch filter, defined in Radians/s *
  • fw - Full width of the rejection band of the Notch filter [fc - fw /2 ,fc + fw/2], defined in Radians/s *
  • \({\zeta}\) - damping ratio

*Radians are used for internal calculation, user input is in [Hz]

Low-pass filters

../../../../../../_images/low_pass_filter_diagram.png

First Order Low-pass

A 1st order Butterworth filter is used for the continuous filter:

\[LP1(s) = \frac {f_c} {s +f_c}\]

Second Order Low-pass

A 2nd order Butterworth filter is used for the continuous filter:

\[LP2(s) = \frac {f_c^2} {s^2 + 1.41 f_c s + f_c^2}\]

Third Order Low-pass

A 3rd order Butterworth filter is used for the continuous filter:

\[LP3(s) = \frac {f_c^3} {(s + f_c)(s^2 + f_c s + f_c^2)}\]

Torque loop input shaping filter

../../../../../../_images/notch_filter_diagram.png

The following equation was used to design the torque loop input shaping filter:

\[BS2(s) = \frac {s^2 +f_c^2} {s + f_w s + f_c^2}\]