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TECHNICAL BRIEFS

A Problem With the LQ Control of Overhead Cranes

[+] Author and Article Information
Zhonghua Wang, Brian W. Surgenor

Department of Mechanical and Materials Engineering, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

J. Dyn. Sys., Meas., Control 128(2), 436-440 (Nov 20, 2004) (5 pages) doi:10.1115/1.2196419 History: Received April 21, 2004; Revised November 20, 2004

The control of an overhead crane is a classic optimum control problem, and its solution can be found in most textbooks on the subject of automatic controls. However, there is a design issue with respect to the relative mass of the cart and the suspended payload. If this problem is ignored, then the results of an analysis can be misleading and the response can be unstable. Based on a stability analysis, a design recommendation for optimal asymptotic linear quadratic (LQ) controllers with fixed gains is presented to avoid this problem. The results are validated by both simulation and experiment.

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Figures

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Figure 1

Model parameters for an overhead crane

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Figure 2

Value of element A43 and controller gain K4 as payload mass is varied

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Figure 3

Laboratory-based overhead crane apparatus

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Figure 4

Simulated responses for 0.1kg and 2.2kg payloads within initial gain set

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Figure 5

Simulated responses for 0.1kg, 2.2kg, and 32kg payloads with modified gain set

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Figure 6

Experimental response for 2.2kg payload with initial gain set

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Figure 7

Experimental response for 2.2kg payload with modified gain set

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Figure 8

Experimental response for 32kg payload with modified gain set

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