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Technical Briefs

Design of Gain-Scheduled Strictly Positive Real Controllers Using Numerical Optimization for Flexible Robotic Systems

[+] Author and Article Information
James Richard Forbes1

Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto, ON, M3H 5T6, Canadaforbes@utias.utoronto.ca

Christopher John Damaren

Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto, ON, M3H 5T6, Canadadamaren@utias.utoronto.ca

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(3), 034503 (Apr 21, 2010) (7 pages) doi:10.1115/1.4001335 History: Received April 24, 2009; Revised February 08, 2010; Published April 21, 2010; Online April 21, 2010

The design of gain-scheduled strictly positive real (SPR) controllers using numerical optimization is considered. Our motivation is robust, yet accurate motion control of flexible robotic systems via the passivity theorem. It is proven that a family of very strictly passive compensators scheduled via time- or state-dependent scheduling signals is also very strictly passive. Two optimization problems are posed; we first present a simple method to optimize the linear SPR controllers, which compose the gain-scheduled controller. Second, we formulate the optimization problem associated with the gain-scheduled controller itself. Restricting our investigation to time-dependent scheduling signals, the signals are parameterized, and the optimization objective function seeks to find the form of the scheduling signals, which minimizes a combination of the manipulator tip tracking error and the control effort. A numerical example employing a two-link flexible manipulator is used to demonstrate the effectiveness of the optimal gain-scheduling algorithm. The closed-loop system performance is improved, and it is shown that the optimal scheduling signals are not necessarily linear.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Planer two-link flexible manipulator

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Figure 2

Gain-scheduled feedback control system

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Figure 3

Optimal scheduling signals with η1=η2=10, η3=1

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Figure 7

Optimal gain-scheduling control system response with η1=η2=η3=1

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Figure 8

Optimal gain-scheduling control system response error with η1=η2=η3=1

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Figure 4

Optimal gain-scheduling control system response with η1=η2=10, η3=1

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Figure 5

Optimal gain-scheduling control system response error with η1=η2=10, η3=1

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Figure 6

Optimal scheduling signals with η1=η2=η3=1

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