Nonlinear Tracking Control of 3-D Overhead Cranes Against the Initial Swing Angle and the Variation of Payload Weight

In this brief, we propose a nonlinear tracking control method of 3-D overhead crane systems which works well even in the presence of the initial swing angle and the variation of payload weight. Besides the practical importance of the overhead cranes, this study is also theoretically interesting because four variables (trolley and girder positions, two swing angles) should be controlled using two control inputs (trolley and girder forces). To control such an underactuated system as cranes, a simple proportional-derivative (PD) controller has been normally used. Unlike the conventional regulation control, the newly proposed nonlinear tracking control law further improves the performance and robustness, which is based on the feedback linearizing control by using the swing angular rate as well as the swing angle. The proposed nonlinear tracking control law eliminates the nonlinear characteristics of the system and achieves the satisfactory position control and swing suppression, even when the initial swing angle and the variation of payload weight exist. We present the stability analysis and simulation results to demonstrate the practical application of our scheme.

I. Introduction

Crane systems have been widely used in industrial fields. Position control and swing suppression of payloads are needed for crane control. The behavior of the payload shows similar characteristics of an inverted pendulum as it uses flexible cables for suspending the payload, and the dynamics of a crane system are similar to those of an inverted pendulum. Like the inverted pendulum, the crane system is also an underactuated system in that the number of variables to be controlled (the payload position and the swing angle) is by nature less than that of control inputs (the forces driving the trolley and the girder). Since the crane system shows a stable behavior around its desired equilibrium point as opposed to an inverted pendulum, there have been numerous studies done on the simple proportional-derivative (PD) control law. In practical applications, however, it is necessary not only to have a fast position regulation toward the desired position in an economic sense, but also to suppress the swing motion of the payload since a severe payload swing can cause a payload damage or an accident, and also hinder an accurate placement of the payload. Accordingly, much research has been done on the overhead crane systems.