Gantry crane control of a double-pendulum, distributed-mass load, using mechanical wave concepts

H Habibi,W O'Connor

doi:10.5194/ms-4-251-2013

Abstract

Abstract. The overhead trolley of a gantry crane can be moved in two directions in the plane. The trolley is attempting to control the motion of a suspended, rigid-body, distributed mass load, supported by a hook, modelled as a lumped mass, in turn connected to the trolley by a light flexible cable. This flexible system has six degrees of freedom, four variables describing the flexible, hanging load dynamics and two (directly controlled) input variables for the trolley position. The equations of motion are developed and the crane model is verified. Then a form of wave-based control (WBC) is applied to determine what trolley motion should be used to achieve a reference motion of the load, with minimum swing during complex manoeuvres. Despite the trolley's limited control authority over the complex, flexible 3-D dynamics, WBC enables the trolley to achieve very good motion control of the load, in a simple, robust and rapid way, using little sensor information, with all measurements taken at or close to the trolley.

Highlights

In a typical problem of crane control, the challenge is to achieve controlled motion of the load, simultaneously moving it to follow a desired trajectory while actively controlling the swing
The most dynamically advanced developments in crane controllers in 3-D assume point mass loads, or at most, a rod-like body hanging from the trolley
The double-pendulum, distributed mass, gantry crane model assumed in this work has non-trivial dynamics, and represents a considerable advance on the simple pendulum model often used

Summary

Introduction

In a typical problem of crane control, the challenge is to achieve controlled motion of the load, simultaneously moving it to follow a desired trajectory while actively controlling the swing. The reference inputs are requested motions to the system, that is, desired controlled motions of the load These inputs could be desired crane positions or velocities over time. (Specifying one, implicitly specifies the other.) Here it is assumed that the reference inputs are position control requests for the load motion over time. The most dynamically advanced developments in crane controllers in 3-D assume point mass loads, or at most, a rod-like body hanging from the trolley. The trolley position variables xT and yT are considered as input variables, used to control the attached flexible system, so four equations of motion are required. With the crane model behaving as expected, the WBC ideas are developed and used to control the swinging load by controlling the trolley motion

Wave-based approach to crane control

Results

Conclusions