A novel block backstepping-based trajectory tracking control with zero dynamics stability for underactuated overhead cranes

For underactuated overhead cranes, the load swing angle is not actuated, which makes the control difficulty greatly increased. In order to achieve the goal of anti-swing, many researches have been developed. However, an extremely superior control technology, called backstepping, has not been applied to overhead cranes. In this paper, a block backstepping-based trajectory tracking control scheme for 2-DOF overhead cranes is proposed for the first time. Firstly, a new variable transformation with state coupling function is designed to achieve swing suppression and thereby improve transient performance. Then, in order to enhance steady-state performance, an integral state is introduced into the designed Lyapunov candidate function. Finally, a trajectory tracking controller is proposed by backstepping. Meanwhile, a novel parameter tuning method is developed using pole placement, which saves time and effort in control parameter tuning. Note that the proposed scheme only utilizes backstepping technology and does not use other techniques for additional processing. Via zero dynamics analysis and Lyapunov stability theorems, the stability is rigorously proved. The advantages and robustness of the proposed scheme are explained by the following experimental results: settling time of the trolley is about 5 s, and the steady-state error remains within $0.5\%$. The load swing angle enters the range of [$-0.5$ deg, $0.5$ deg] in about 4 s.