Robust controller design based on double-layer nonlinear disturbance observers and sliding mode control for nonlinear systems with mismatched disturbances and uncertainties

The nonlinear disturbance observer (NDOB) has good disturbance estimation performance in various nonlinear systems. However, for existing robust controller designs based on NDOBs, there are few studies that can adaptively adjust the anti-disturbance performance of the controller. Moreover, most existing controllers based on NDOBs use a single NDOB for disturbance estimation in the controller design process. In order to improve tracking performance of the controller based on NDOB, this paper elaborates on a novel controller design method that includes double-layer NDOBs with cascaded or embedded design ideas. Firstly, for nonlinear systems with unmatched disturbances and uncertainties, the first-layer NDOB is used to estimate the composite-lumped disturbance in the nonlinear system. Then, the sliding mode surface based on the tracking error variables containing disturbance estimation values is defined. Next, by taking the time derivative of the sliding mode surface, a first-order derivative equivalent linear system containing unknown terms is obtained, and the second-layer NDOB is constructed to estimate the unknown terms. Finally, a robust tracking controller based on sliding mode control is designed, which includes the disturbance estimation values provided by the double-layer NDOBs. Under the proposed control technique, the semi-global ultimately uniformly bounded stability of the closed-loop system has been proven through stability analysis of candidate Lyapunov functions. The simulation demonstrated the effectiveness, robustness, and good adaptability of the proposed control technology. Simulation comparison results verified that using the double-layer NDOBs in controller design is beneficial for improving the disturbance suppression performance and tracking performance of the controller.