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.
823420 We investigate the feasibility of a variable-geometry truss (VGT) based architecture for suppressing payload pendulations in ship-mounted cranes. The VGT assembly is conceived to be retrofitted onto the boom tip of ship-mounted cranes. A simplified planar model is developed. A control point along the cable hoisting the payload is constrained to move along a straight path with a given control input (acceleration) imparted via the actuators embedded in the VGT assembly. Control laws based on either linear quadratic or fuzzy control methodologies are developed in order to minimize an assigned cost functional. Their effectiveness is compared through extensive numerical simulations. The performance of the VGT architecture and associated control laws is analyzed when the crane is subject to the most severe combination of resonant excitations: a primary resonant roll excitation at the natural frequency of the controlled system, and a principal-parametric resonant heave excitation, both corresponding to sea state three and higher. The proposed strategy exhibits enough control authority over the system dynamics, greatly reducing the severe and undesirable resonant pendulations caused by the ship motions in a broad-band frequency range. Moreover, its disturbance-rejection capabilities are exerted with feasible control efforts, which are localized in the segment of the crane where they are needed.15( 2380 Cranes, variable-geometry truss, linear quadratic control, fuzzy control, nonlinear resonance, nonlinear active control
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