Adaptive fuzzy backstepping hierarchical sliding mode control for six degrees of freedom overhead crane

Most overhead crane control studies attempt to position the payload accurately and minimize its horizontal swing without considering axial oscillation. The axial vibration caused by the lifting rope’s elasticity significantly affects the actuators’ reliability and the system’s overall performance over time. In this paper, a novel overhead crane model is developed to describe an actual crane’s behavior more closely by further considering the effect of axial payload oscillation. Furthermore, an adaptive fuzzy backstepping hierarchical sliding mode controller is designed to guarantee precise movements and reduce vibrations of payload in both horizontal and vertical directions under complex conditions, such as unknown external disturbances and cable elasticity. Three inputs consisting of the trolley-moving force, the bridge-pulling force, and the payload-hoisting torque stabilize six outputs simultaneously, including trolley motion, bridge travel, hoisting drum rotation, two payload swings, and axial payload oscillation. The controller is first designed using the backstepping hierarchical sliding mode control strategy. This controller’s parameters are then adjusted online using a fuzzy logic system, ensuring system states’ stability on the sliding surface. The system’s stability is analyzed and proved mathematically by LaSalle’s principle. Several simulations on MATLAB/Simulink have been conducted with constant or trapezoidal reference signals, with and without external disturbances. These simulation results show the proposed method’s effectiveness, such as motion precision, minor load swings, and minimal axial oscillation.