Load Transfer Control for a Gantry Crane with Arbitrary Delay Constraints

Abstract

This paper describes a method to move the load of a gantry crane to a desired position in the presence of known, but arbitrary, motion-inversion delays as well as cart acceleration constraints. The method idea is based on a phase-plane analysis of the linearized model. In order to limit residual pendulation at the goal position, the method is extended to account for quadratic and cubic nonlinearities. The method of multiple scales is used to determine an approximate solution to the nonlinear equations of motion, thus providing a more accurate measure of the frequency of the oscillations. The nonlinear approach is very successful in limiting residual oscillations to very small values (less than 1 degree of amplitude), offering a reduction, with respect to the linear case, of as much as two orders of magnitude. Finally, this method offers a rationale for the future development of a controller for suppression of load oscillations in ship-mounted cranes in the presence of arbitrary delays.

A Graphical Approach to Input-Shaping Control Design for Container Cranes With Hoist

“…Input-shaping techniques are very sensitive to changes in system parameters, time delays, external disturbances, and they require "highly accurate values of the system parameters" to achieve satisfactory system response [6]. While a good design that uses a nonlinear frequency approximation of the payload oscillations can significantly improve the performance of input-shaping controllers [7], [8], it is much harder to alleviate the controller's sensitivity to changes in the length of the hoisting cable.…”

Effect of hoisting cable elasticity on anti-sway controllers of quay-side container cranes

“…Dadone and VanLandingham [10] derived a nonlinear approximation of the payload oscillation period using the method of Multiple Scales. Using numerical simulation, they compared the residual oscillations due to single-step inputshaping strategies based on their approximation, a simplified form of that approximation, and the linear approximation of the oscillation period.…”

Optimal delayed control for an overhead crane

“…Actually Erneux et al [6] gave conditions of stability for the control proposed by Pyragas applied to an overhead crane; In this note we present a methodology to obtain the optimal delay for the control law proposed by Pyragas. On the other hand, open loop schemes do not require the measurement of the load angle, in this context input shaping techniques [17] are the most popular which has proven effective on cranes for reducing oscillations [15]. Another open loop approach is optimal control, which calculates the motion trajectory off line based in the mathematical model of the system [4], [5]. Commonly open loop techniques can not handle disturbances, and sometimes is preferable work in conjunction with some feedback control.…”