An Improved Sliding Mode Differentiator Combined with Sliding Mode Filter for Estimating First and Second-order Derivatives of Noisy Signals

This paper proposes a new sliding mode differentiator combined with a sliding mode filter for estimating first and second-order derivatives of noisy signals. The proposed differentiator can be seen as a version of Slotineet al.'s sliding mode observer extended with an additional non-Lipschitz property, which is intended to realize a faster reaching to the sliding mode. It behaves as a noise-reduction filter that is composed of first, second and third-order low-pass filter in the sliding mode, but also employs the filter that is composed of second, third and fourth-order low-pass filter out of the sliding mode. Moreover, the differentiator effectively removes impulsive noises by combining a sliding mode filter and its discrete-time implementation is based on the implicit (backward) Euler discretization, which does not result in chattering and realizes the exact sliding mode. Experiments show that the proposed algorithm has a better balance between the noise attenuation and small phase lag than the linear-filtered Euler differentiation and previous sliding mode differentiators. It was validated through experiments using optical encoder signals of industrial robots