Nonlinear coupling control method for underactuated three-dimensional overhead crane systems under initial input constraints

Abstract

In this paper, we present an enhanced coupling nonlinear control method for three-dimensional overhead crane systems under initial input constraints. The proposed control method can achieve superior control performance and strong robustness with respect to system parameter variations and external disturbances. Moreover, it guarantees ‘soft’ trolley start by introducing hyperbolic tangent functions into the controller. More precisely, we enhance the coupling behaviour between the trolley movement and the payload swing by fabricating two composite signals, based on which an energy-like storage function is established. Then, a nonlinear coupling control method under initial input constraints is derived directly. Lyapunov techniques and LaSalle’s invariance theorem are successfully adopted to find the asymptotic stability solution while satisfying the initial input constraints. Strict mathematical analysis of the control scheme with initial input constraints is provided as theoretical support for the superior performance of the controller. Simulation and experimental results are conducted to show the superior performance and strong robustness of the proposed control method.