A novel zero delay low pass filter: Application to precision positioning systems

In this paper, a nonlinear low-pass filter is presented, which produces significantly less phase lag than linear and some nonlinear filters. The proposed filter employs a saturation function to enhance the linear filter's performance. The gain and phase responses of the filter are derived analytically using a modified describing function, and the efficiency of the proposed method is examined through numerical examples. Based on the required cut-off frequency and noise to signal ratio, a rule of thumb is given to set the filter's parameters. In the frequency domain, simulation results show that the filter's gain response is near 0dB in the pass-band, and the noise attenuation rate is -40dB∕dec, while the phase lag is three times lesser compared to 2^nd order Butterworth low-pass filter. Moreover, comparing with Jin et al.'s parabolic sliding mode filter and feed-forwarded parabolic sliding mode filter the gain and phase of the proposed filter are closer to zero in the pass-band and before cut-off frequency. Furthermore, the filter's performance is also evaluated in case of different noise color and concluded that the proposed filter is superior to linear and nonlinear filters in case of white, blue, or purple noise Finally, the filter's effectiveness and the tuning guideline are validated by simulating a precision motion control system in the discrete-time domain.