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.

Tracking of periodic oscillations in an underactuated system via adaptive neural networks

“…Taking into account that the ideal weights W f and W g are constants, equations (19) and (20) can be written in terms of the estimation errorsW f andW g , as follows…”

Tracking Control and Vibration Reduction of Flexible Cable-Suspended Parallel Robots using a Robust Input Shaper

“…However, the stability of the system can be achieved by approximation of the cables dissipation energy using Rayleigh viscous damping function. The dynamics of the exible system can be investigated by dividing the dynamic equations into the slow and fast dynamics using singular perturbation techniques [23,24]. In order to express the exible system equations in the form of singular perturbations, the state u and the small parameter " are de ned:…”

Dynamic Responses of an Overhead Crane’s Beam Subjected to a Moving Trolley with a Pendulum Payload

“…Meanwhile, flexible cables were researched sufficiently for cable elevator systems [13], but elevators just rose and descended vertically. Fatehi et al [14] proposed an advanced control system for an overhead crane when there are transverse vibrations in the flexible cables and when considering large angles of cable swing. e payload swing and the transverse vibrations of the cables could be simultaneously reduced and suppressed, respectively, by applying a horizontal driving force to the trolley.…”