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Research Papers

Augmented Controllable Region of Unstable Second Order Systems With Impulsive Actions

[+] Author and Article Information
Wookjin Sung

Department of Electrical Engineering, Sungkyunkwan University, Suwon 440-746, South Koreaece2744@gmail.com

Jiecai Luo

Department of Electrical Engineering, Southern University, Baton Rouge, LA 70813jluo@engr.subr.edu

Kwanho You1

Department of Electrical Engineering, Sungkyunkwan University, Suwon 440-746, South Koreakhyou@ece.skku.ac.kr

1

Corresponding author.

J. Dyn. Sys., Meas., Control 131(5), 051007 (Aug 18, 2009) (8 pages) doi:10.1115/1.3155008 History: Received November 22, 2007; Revised May 06, 2009; Published August 18, 2009

In this paper, we suggest how to enlarge the maximum controllable region for unstable linear systems with mixed control actions. Using the impulsive action as an alternating control input, it is shown how the collaborative control inputs (bang-bang and impulsive action) work to augment the controllable region of unstable second order systems. However, the weakness resides in the sensitivity to model uncertainty and the time-consuming work to construct the switch curves (bang-bang switch curve and impulse firing curve). We suggest an efficient way to approximate the switch curves. It overcomes the shortcomings from the use of original switch curves, which are constructed through time backward computation. Simulation results show how the approximate switch curves can be used to determine the optimal control values for an augmented maximum controllable region.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Switch curve and maximum controllable region for an unstable oscillator with ζ=−0.2 and no impulse actions, w(t)=0

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Figure 2

Switch curves and impulse firing curve with ζ=−0.2 and γ¯=0.5

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Figure 3

Enlarged maximum controllable region with γ¯=0.5

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Figure 4

Approximate bang-bang switch curve and impulse firing curve with ζ=−0.2 and γ¯=0.5

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Figure 5

Example of an unstable second order system: spring-mass-damper

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Figure 6

State trajectories driven by time optimal control input and impulse actions with ζ=−0.2 and γ¯=0.5

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Figure 7

State trajectory for an unstable oscillator with model uncertainty, ζ=−0.2 and Δ¯=0.5

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