A pragmatic controller for a gantry crane

Abstract

A gantry crane presents a control problem with ten state variables. The undamped swinging of the load has led earlier researchers to apply cumbersome control strategies. The essence of pragmatic control is gleaned from autopilot designs of half a century ago. The control is designed as a set of ‘nested loops’, where the innermost loop takes the form of a velocity loop wrapped around a motor to give crisp velocity control. Target values are derived from states in the outer loops, to be applied to a succession of inner loops. These target values are subjected to constraints. Thus in the case of the crane, the horizontal position of the load can be considered to be the two outermost variables. In this study, from the load position error, two target velocity components are calculated and subjected to limits. The velocity error leads in turn to a target acceleration of the load and subsequently, to the target displacement that takes place between the horizontal coordinates of the hoist and the load. In this paper, the pragmatic control technique is demonstrated with the aid of a JavaScript and MATLAB software programs using a state-space model.