Using Singular Perturbation Method for Controlling a Crane System with a Flexible Cable and Large Swing Angle

Abstract

This paper aims to develop an advanced control system for an overhead crane with transverse vibrations of flexible cable while considering large angle of the cable swing. The control objective is to move the payload to a desired position and at the same time, to reduce the payload swing and to suppress the cable transverse vibrations only by applying a directional (horizontal) driving force to the trolley. The crane system with cable vibrations and large swing angle is categorized as a multi-degree under-actuated system whose characteristics impose serious challenges when applying control methods. One reasonable way to overcome the challenges is to separate the degrees of under actuation. To do so, singular perturbation approach is used to divide the dynamical system into a fast subsystem for cable vibrations (with flexible un-actuated coordinates) and a slow subsystem for trolley motion and cable swing (with one degree of under actuation). Based on two-time scale control method, a composite control system is designed. Accordingly, the control system consists of a linear controller for fast dynamics (for vibration suppression) and a nonlinear controller for slow dynamics (for reducing cable swing and controlling the payload motion). Simulations are performed to demonstrate the effectiveness of the control system for an illustrative example of the crane systems with flexible cable moving a lightweight payload.