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Load Transfer Control for a Gantry Crane with Arbitrary Delay Constraints

The Bradley Department of Electrical and Computer Engineering, MC 0111, 340 Whittemore Hall, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Hugh F Vanlandingham

The Bradley Department of Electrical and Computer Engineering, MC 0111, 340 Whittemore Hall, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

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.

Key Words: Crane control • gantry cranes • method of multiple scales • input shaping

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