A partially saturated nonlinear controller for overhead cranes with experimental implementation

The present paper exploits a partially saturated nonlinear control law for underactuated crane systems, which is achieved by converting the crane model into an objective (or equivalently, desired closed-loop) system. The proposed method guarantees “soft” trolley start by incorporating a smooth saturated function into the control law. More specifically, we first establish an objective system with guaranteed signal convergence and stability performance; then based on the structure of the objective dynamics, a partially saturated control law is derived straightforwardly by solving one partial differential equation, without performing any partial feedback linearization operations on the original crane model. The convergence and stability performance of the objective (i.e., closed-loop) system is guaranteed with Lyapunov techniques and LaSalle's invariance theorem. To validate the practical performance of the proposed method, we implement hardware experiments to illustrate that the new method achieves superior performance with reduced control efforts.