Fast Numerical Implementation for Variable Order Fractional Calculus Operator Based on Polynomial Fitting Method in Time Domain

摘要

The numerical implementation of fractional calculus is an important factor in applying the fractional calculus theory to engineering application. In most existing research, the order in model or controller is constant, so it is relative easy to implement the fractional calculus because its coefficients are constant values. But in many application fields the order is variable, which bring difficulty to achieve the real-time implementation of fractional calculus. In this paper, based on the impulse response invariant discretization(IRID) and polynomial fitting, a fast numerical implementation for variable order fractional calculus operator is proposed, and the simulation results illustrate the effectiveness of the proposed method.