Discrete-time Algorithms of a Parabolic Sliding Mode Filter: a Comparative Review

This paper compares two chattering-free discrete-time algorithms of a parabolic sliding mode filter, which has become one of the most important components of the active disturbance rejection control, for removing noise. One is an algorithm derived by using the isochronic region (IR) method, and the other one is an algorithm derived by using the backward Euler (BE) discretization method. Numerical example results show that the BE method realizes exact arrival of the filter's state to the sliding surface and the target state, whereas the IR method produces overshoot. In addition to that, the phase lag of the BE method is smaller than that of the IR method.