Model-free and finite-time sliding-mode tracking control based on a second-order adaptive disturbance observer

In practical engineering, many control issues face the challenge of being unmodelable, rendering model-based control methods inapplicable. To address this problem, an enhanced model-free and finite-time control framework incorporating a disturbance observer and sliding-mode control is put forward. Firstly, a second-order adaptive disturbance observer is constructed using tracking error. It is capable of responding in real-time to the system's tracking dynamics and adaptively estimating the lump disturbance, achieving collaborative improvement in estimation and tracking performance. This observer offers advantages a simple structure, few parameters, and wide applicability. Secondly, based on an established auxiliary strategy, a sliding-mode control law is designed using the virtual estimation state error of the proposed observer. This design simplifies the controller structure, ensures global sliding-mode robustness, and avoids sliding-mode chattering and high-frequency switching of the controller. Thirdly, a model-free and finite-time controller is developed by incorporating the lumped disturbance (estimated by the designed second-order adaptive disturbance observer) into the proposed sliding-mode control law through compensation, and its finite-time exponential convergence is theoretically proven. Finally, the effectiveness and superiority of the proposed method are verified through comparative experiments.