Flatness-Based Backstepping Antisway Control of Underactuated Crane Systems under Wind Disturbance

A control method that combines trajectory planning and backstepping is proposed for the antisway problem of underactuated overhead cranes under wind disturbance. First, a set of flat outputs is proposed so that the crane system dynamics can be represented by each order of flat outputs. Sufficient relevant constraints are given to ensure that the trolley can arrive at the desired position in a limited time under variable rope lengths, and that the swing angle can be suppressed when the payload is lifted or lowered during operation. The planned trajectory is obtained by solving for the optimal parameters of the flat output. Next, to reduce the deviation caused by wind disturbance on the actual control of the trajectory, a tracking controller is designed. Because the system output space and flat output space are differentiable homeomorphisms, the backstepping controller constructed based on the flat output can indirectly control the system output, which makes the backstepping method applicable to underactuated cranes. The simulation results show that the proposed method is effective and has strong robustness.