Tracking control design for a multi-degree underactuated flexible-cable overhead crane system with large swing angle based on singular perturbation method and an energy-shaping technique

Abstract

A flexible-cable overhead crane system having large swing is studied as a multi-degree underactuated system. To resolve the system dynamics complexities, a second order singular perturbation (SP) formulation is developed to divide the crane dynamics into two one-degree underactuated fast and slow subsystems. Then, a control system is designed based on the two-time scale control (TTSC) method to: (a) transfer the payload to a desired location and decrease the payload swing, by a nonlinear controller for slow dynamics; and (b) suppress transverse vibrations of the cable, by a linear controller for fast dynamics. The nonlinear controller is designed based on an energy shaping technique according to the controlled Lagrangian method. To demonstrate the control system effectiveness, an example of the flexible cable crane systems with a lightweight payload is considered to perform simulations. In addition to the proposed control system, two other controllers; namely, a linear controller based on the linear–quadratic regulator method and a TTSC based on the approximate SP model and partial feedback linearization, are applied to the system for comparison. Also, by applying a disturbance force to the trolley and considering 10% uncertainty in crane parameters, the control performance against disturbances and parameter uncertainties is investigated.

Spatial transportation of the beam on a bifilar fastening

“…A very simplified model for moving a point load by a trolley of an overhead crane is the elliptical pendulum model used in works [7][8][9][10][11][12][13][14][15][16].…”

Swing Characteristics and Vibration Feature of Tower Cranes under Compound Working Condition

“…Fatehi et al proposed a second-order singular perturbation formulation. e formulation can divide the crane dynamics into two onedegree actuated fast and slow subsystems [18]. Chin et al modelled a boom crane as a spherical pendulum and a rigid system with two degrees of freedom.…”

Influence of structural elasticity on transshipment dynamics of dual-trolley overhead crane

“…For instance, the wire rope was considered as elastic body with continuously distributed mass in Refs. [7][8][9][10][11] However, it was characterized by spring and damper in Refs. [12][13][14][15] In addition, it was modeled as a series of rigid segments connected by hinges in Rong et al 17 In recent years, there have been lots of literatures concerning on the structural elasticity of crane.…”

“…Masoud 2 developed an analytic approximation of the oscillation frequency of the hoisting mechanism of a quayside container crane, in which the elasticity of the hoisting cables were taken into consideration. Fatehi et al [7][8][9] has dealt with the modeling and control problems of an overhead crane with a flexible cable. A dynamical model including both transverse vibrations of the flexible cable and large swing angles of cable was developed.…”