Fractional-Order Nonlinear Disturbance Observer Based Control of Fractional-Order Systems

The robust control for a class of disturbed fractional-order systems is presented in this paper. The proposed controller considers a dynamic observer to exactly compensate for matched disturbances in finite time, and a procedure to compensate for unmatched disturbances is then derived. The proposed disturbance observer is built upon continuous fractional sliding modes, producing a fractional-order reaching phase, leading to a continuous control signal, yet able to reject for some continuous but not necessarily differentiable disturbances. Numerical simulations and comparisons are presented to highlight the reliability of the proposed scheme.