Hierarchical Backstepping Fast Terminal Sliding Mode Control Strategy With GPIO For Double Pendulum Cranes

In the field of cranes, the double pendulum effects may occur when the payload is large, and the hook mass is a non-negligible factor. Under these effects, the dynamic model of the system will be more complex, which brings many difficulties to the design of the controller. To achieve trolley positioning, suppress double pendulum effects, and improve anti-disturbances ability, this article presents a hierarchical backstepping fast terminal sliding mode control strategy for the double pendulum cranes. First, to design the observers and controller, the double pendulum crane system is divided into three subsystems. A generalized proportional integral observer (GPIO) is designed for each subsystem, which can estimate potential model uncertainties and unknown external disturbances of the system. According to the estimates of the GPIO, we design a first layer fast terminal sliding surface for each subsystem, and equivalent control law is designed using the idea of backstepping. Meanwhile, using the advantages of backstepping control makes the structure of the system more clear and brings convenience to the design of the Lyapunov function. Based on the first layer of sliding surfaces, we design a second layer sliding surface. Then, an ultimate control law is designed to ensure the stability of the entire system. In the end, the effectiveness of this control strategy is validated through simulation results on MATLAB/Simulink.