Minimum Time Control of a Gantry Crane System with Rate Constraints

TL;DR

This paper develops minimum time control strategies for a gantry crane considering rate constraints and uncertainties, ensuring minimal residual vibrations through robust optimal control profiles validated experimentally.

Contribution

It introduces a robust optimal control framework for gantry cranes that accounts for modal uncertainties and validates the approach with experimental results.

Findings

Optimal bang-off-bang control profiles are derived for different displacements.

Switching behavior in control profiles varies with displacement magnitude.

Robust control profiles effectively reduce residual vibrations in experiments.

Abstract

This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated.