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Technical Briefs

A New Approximation Algorithm of Fractional Order System Models Based Optimization

[+] Author and Article Information
Li Meng1

School of Information Science and Engineering,  Northeastern University, Shenyang 110004, China; School of Information Engineering,  Shenyang University, Shenyang 110044, Chinamengliinsy@126.com

Dingyu Xue

School of Information Science and Engineering,  Northeastern University, Shenyang 110004, Chinaxuedingyu@ise.neu.edu.cn

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(4), 044504 (May 07, 2012) (7 pages) doi:10.1115/1.4006072 History: Received August 04, 2011; Revised December 25, 2011; Published May 04, 2012; Online May 07, 2012

This paper proposes a new approximation scheme which is an extension to the well-established Charef’s approximation method for fractional order systems. The method relaxes the constraints on the locations of the pole-zero pairs of the approximate system, which provides more flexibility and space for approximate system to approach the original system as close as possible. The approximate system based on an optimization process performs not only a good magnitude fitting but also a good phase fitting. The benefits from using the proposed scheme are illustrated by numerical examples in frequency domains.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Bode plots of (1 + s/ω c )−α and Charef’s approximation

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Figure 2

Bode plot of (1 + s/ω c )−α and the proposed approximation

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Figure 3

Comparison of Bode diagrams of (1 + 0.2s)−0.5 and the three approximate systems

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Figure 4

Comparison of Bode diagrams of (1 + s/1.3)−0.6 (1 + s/6.2)−0.3 and the two approximate systems

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Figure 5

Comparison of Bode diagrams of (1 + (s/5)0.6 )−0.5 and the two approximation systems

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Figure 6

Comparison of Bode diagrams of [25/(s2  + 8.5s + 25)]0.2 and the two approximation systems

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Figure 7

Comparison of Bode diagrams of [590570/(s2  + 461.0913s + 590570)]0.2 and the two approximation systems

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Figure 8

Comparison of Bode diagrams of [25/(s2  + 6.5s + 25)]0.2 and the three approximation systems

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Figure 9

Comparison of Bode diagrams of [25(s2  + 8.5s + 25)]0.7 and the two approximation systems

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Figure 10

Comparison of Bode diagrams of (1 + s/10)−(0.6+j0.3) and the two approximation systems

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