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Research Papers

Nonlinear PD Control of a Long-Span Cable-Supporting Manipulator in Quasi-Static Motion

[+] Author and Article Information
Jingli Du, Hong Bao, Chuanzhen Cui, Xuechao Duan

Key Laboratory of Electronic Equipment Structure Design of Ministry of Education,  Xidian University, Xi’an, Shaanxi 710071, China

J. Dyn. Sys., Meas., Control 134(1), 011022 (Dec 06, 2011) (9 pages) doi:10.1115/1.4004784 History: Received October 16, 2010; Revised June 22, 2011; Published December 06, 2011; Online December 06, 2011

This paper addresses modeling and control of a cable-supporting manipulator serving as the feed supporting structure of a large radio telescope. The manipulator consists of six long cables so that their curves must be considered. The end-effector is prone to vibration due to the long-span cables even if cable lengths can change perfectly just as they are expected. To deal with this problem, a feedback controller in the workspace is devised, in which the effects of both the cable length error and the pose error of the end-effector are taken into account. A controller is first devised for the resultant cable wrench exerted on the end-effector. Then the incremental relationship between the cable end force and the cable length together with the displacements of the end-effector is deduced. Combining this relationship, we convert the controller into a nonlinear one with cable length increment as the control output, which can be readily utilized in the manipulator. Numerical examples and experiments carried out on a field model of dimension 50 m validate the positioning precision of the manipulator and we can conclude the feasibility of the proposed feed supporting system.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of the FAST

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Figure 2

Cable-supporting manipulator of the FAST 50 m model

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Figure 3

Mechanical analysis of a sagged cable

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Figure 4

Control strategy of the cable-supporting manipulator

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Figure 5

Part of the finite element model of the cable-supporting manipulator

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Figure 6

Position and orientation motions in and about x axis

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Figure 7

Differentiations of the motion in and about x axis

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Figure 8

Position and orientation tracking error for slewing line motion

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Figure 9

Position and orientation tracking errors in slewing line motion

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Figure 10

Position and orientation tracking errors in tracking motion

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Figure 11

Position and orientation errors of the fine-tuning Stewart platform

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