Adaptive gain parabolic sliding mode filter augmented with vibration observer

This paper presents a new sliding-mode-based noise filter for removing high frequency noise. It is based on Jin et al.'s (2012) parabolic sliding mode filter (J-PSMF). In the new filter, the gain of J-PSMF is adapted according to the level of noise in the input signal, which is defined by using Lecours et. al.'s (2016) vibration observer. Compared to both second-order linear low-pass filter (2-LPF) and J-PSMF, the new filter achieves better balance between noise mitigation and signal preservation. Due to implicit (backward) Euler discretization, the new filter does not suffer from chattering. The proposed filter was validated experimentally by using a DC servo motor equipped with an optical encoder. The proposed filter was implemented in a positioning system under PDD
²
(proportional, derivative and second derivative) control and shown that both noise attenuation and non-overshooting response are achieved simultaneously.