Fixed-time observer-based back-stepping controller design for tower cranes with mismatched disturbance

As a common means of transportation, tower cranes are widely used on various occasions. However, they are often affected by various external disturbances, especially mismatched disturbances, such as wind disturbance, which seriously reduces the work efficiency and safety of the system. In order to solve the above problems, this paper proposes an optimized back-stepping controller based on fixed-time disturbance observer in the presence of unexpected disturbances. The reason why the back-stepping method has been so favored in the study of underactuated systems is its unique design methodology, which searches for a positive definite Lyapunov function for iteration. Firstly, the crane system model is rewritten in cascade form, which is used to simplify the design of the subsequent back-stepping controller as well as the observer. Secondly, the conventional back-stepping method is optimized and finite-time convergence control is introduced to improve the transportation efficiency. Then, in the presence of mismatched disturbances, a finite-time disturbance observer is proposed to estimate and compensate for the sudden disturbances to minimize the impact on crane operations. Finally, the effectiveness of the proposed method is verified experimentally.