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A novel nonlinear coupling control approach for overhead cranes: Theory and implementation

This paper presents a novel nonlinear control approach for underactuated overhead crane systems, which guarantees both fast trolley positioning and sufficient payload swing eliminating performances. The controller is applicable to both regulation control and trajectory tracking control. Via the utilization of a payload position-like signal, the nonlinear coupling behavior between the actuated trolley horizontal motion and the unactuated payload swing is artificially enhanced. Specifically, by constructing an elegant error signal, the controller is put forward, and the overall crane dynamics is transformed into an interconnected system consisting of two subsystems with respect to (w.r.t.) the constructed error signal and the payload swing, respectively. Subsequently, both subsystems are proven to be input-to-state stable (ISS); by invoking the small gain theorem, we further show that the overall interconnected system is ISS, all of which are supported by Lyapunov techniques. LaSalle's invariance theorem is utilized to prove that the system state is driven to the equilibrium point. Numerical simulation results are included to demonstrate the feasibility and superior performance of the proposed method over existing methods, and its robustness against external disturbances.