Sliding-Mode Disturbance Observer-Based Control for Fractional-Order System with Unknown Disturbances

Abstract

This paper concentrates on the disturbances estimation and attenuation problem of a general class of the fractional-order systems. For this purpose, this paper proposes a fractional sliding-mode disturbance observer (FSMDO)-based control scheme, which is capable of mitigating the unknown disturbances asymptotically. Meanwhile, by incorporating a novel fractional sliding-mode controller into the proposed control scheme, the asymptotical convergence of trajectory tracking errors is guaranteed. The developed control scheme owns three attractive highlights: (1) it is suitable for the general fractional-order systems, including nonlinear systems and incommensurate systems; (2) the proposed FSMDO can estimate the unknown exogenous disturbances and system uncertainties timely and precisely; (3) nominal performance can be retained by compensating the observed disturbances in a feedforward manner, and thus, the robustness of the system can be strengthened. Illustrative examples are provided to show the availability and superiority of the presented FSMDO control method in terms of robust control. As compared with the conventional methods, the dynamic control performance of the closed-loop system can be improved.