Nonlinear coupling control laws for an underactuated overhead crane system

In this paper, we consider the regulation control problem for an underactuated overhead crane system. Motivated by recent passivity-based controllers for underactuated systems, we design several controllers that asymptotically regulate the planar gantry position and the payload angle. Specifically, utilizing LaSalle's invariant set theorem, we first illustrate how a simple proportional-derivative (PD) controller can be utilized to asymptotically regulate the overhead crane system. Motivated by the desire to achieve improved transient performance, we then present two nonlinear controllers that increase the coupling between the planar gantry position and the payload angle. Experimental results are provided to illustrate the improved performance of the nonlinear controllers over the simple PD controller.

I. Introduction

Precise payload positioning by an overhead crane (especially when performed by an operator using only visual feedback to position the payload) is difficult due to the fact that the payload can exhibit a pendulum-like swinging motion. Motivated by the desire to achieve fast and precise payload positioning while mitigating performance and safety concerns associated with the swinging motion, several researchers have developed various controllers for overhead crane systems. For example, Yu et al. [29] utilized a time-scale separation approach to control an overhead crane system; however, an approximate linearized model of the crane was utilized to facilitate the construction of the error systems. In [27], Yashida et al. proposed a saturating control law based on a guaranteed cost control method for a linearized version of the crane system dynamics. Martindale et al. [18] utilized an approximate crane model to develop exact model knowledge and adaptive controllers while Butler et al. [2] exploited a modal decomposition technique to develop an adaptive controller. In [3], Chung and Hauser designed a nonlinear controller for regulating the swinging energy of the payload.