Discrete-time super-twisting fractional-order differentiator with implicit euler method

This brief proposes a discrete-time fractional-order differentiator based on the super-twisting algorithm for second-order systems. The differentiator achieves higher performance with respect to the classical ones of integer order in terms of convergence time and robustness. It relaxes the classical boundedness condition required to be satisfied by the second-order derivatives of the functions in conventional differentiators. The numerical integration is performed by an implicit Euler discretization technique based on the Fractional Adams-Moulton method, which significantly suppresses the chattering. The significance of the proposed differentiator is demonstrated through a simulation example, comparing with the classical ones.