Tracking Control of an Underactuated Gantry Crane using an Optimal Feedback Controller

Abstract

Gantry cranes have attracted a great deal of interest in transportation and industrial applications. To increase the effectiveness of gantry cranes, the control of such systems is considered vital. This paper is concerned with tracking the control of an underactuated gantry crane using an optimal feedback controller. The optimal control strategy takes into account a performance index, including integrated time and absolute error criterion. To do this, nonlinear dynamic equations of the system are derived using Lagrange’s Principle. The minimum tracking error of the trolley and the minimum oscillation of the hoisting line are assumed as design  parameters, and the best gains of the feedback controller are achieved. Finally, some tracking simulations are performed which demonstrate the capability of the simple proposed method in the optimal tracking control of a gantry crane.