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Technical Briefs

Reduction in the Number of Gain-Scheduling Parameters Using Dimensional Transformation

[+] Author and Article Information
Haftay Hailu

 Honeywell Aerospace, Torrance, CA 90504

Sean Brennan

Department of Mechanical and Nuclear Engineering,  The Pennsylvania State University, 318 Leonhard Building, University Park, PA 16802sbrennan@psu.edu.

J. Dyn. Sys., Meas., Control 130(3), 034505 (May 12, 2008) (6 pages) doi:10.1115/1.2907396 History: Received March 18, 2005; Revised October 19, 2007; Published May 12, 2008

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Controller and plant both scheduled to varying parameters

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Figure 2

A graphical representation of the LPV simplification process

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Figure 3

Schematic of the gantry system

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