High-order sliding mode-based robust active disturbance rejection control for uncertain fractional-order nonlinear systems

In this paper, a new fractional-order (F-O) Active Disturbance Rejection Control (ADRC) scheme is proposed for nonlinear F-O systems with uncertainties. The proposed approach combines backstepping control with a High-Order Sliding Mode Extended State Observer (H-OSMESO). This observer provides accurate finite-time estimations of both the system states and multiple disturbances and uncertainties without exhibiting chattering. This enhancement improves the disturbance rejection ability and the tracking performance. An ADRC scheme using a H-OSMESO remains unexplored for F-O systems control. We start by designing a H-OSMESO to obtain the extended state and system state estimates. The extended state includes external disturbances and uncertainties (total disturbance). It is proven that the ESO (Extended State Observer) converges in finite time. The estimates of the total disturbance and states are then used to construct a backstepping control law to track the desired references while compensating for the total disturbance. The closed-loop system stability is demonstrated using the Lyapunov function. Finally, the robustness and effectiveness of the proposed ADRC scheme are demonstrated by simulating two numerical examples. These results are then compared with other available approaches.