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Research Papers: Design and Analysis

Simultaneous Optimal Design of the Lyapunov-Based Semi-Active Control and the Semi-Active Vibration Control Device: Inverse Lyapunov Approach

[+] Author and Article Information
Kazuhiko Hiramoto

Associate Professor
Department of Mechanical and Production Engineering,
Niigata University,
8050 Ikarashi 2-no-cho,
Nishi-ku, Niigata 950-2181Japan
e-mail: hiramoto@eng.niigata-u.ac.jp

Taichi Matsuoka

Lecturer
Member of ASME
Department of Mechanical Engineering and Informatics,
Meiji University,
1-1-1 Higashimita,
Tama-ku, Kawasaki 214-8571Japan
e-mail: matsuoka@meiji.ac.jp

Katsuaki Sunakoda

Technical Advisor
Member of ASME
Sanwa Tekki Corporation,
2703 Nakaokamoto-cho,
Utsunomiya 329-1192, Japan

e-mail: sunakoda@tekki.co.jp

1A professor emeritus of Department of Mechanical Engineering at Akita University, Japan.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 1, 2011; final manuscript received May 9, 2012; published online November 21, 2012. Assoc. Editor: Spyros A. Karamanos.

J. Pressure Vessel Technol 134(6), 061211 (Nov 21, 2012) (13 pages) doi:10.1115/1.4007033 History: Received July 01, 2011; Revised May 09, 2012

We address a simultaneous optimal design problem of a semi-active (SA) control law and design parameters in a semi-active control device for civil structures. The vibration control device (VCD) that is being developed by authors is used as the semi-active control device. The VCD is composed of a ball screw with a flywheel for the inertial resistance force and an electric motor with an electric circuit for the damping resistance force. A new bang–bang type semi-active control law referred to as inverse Lyapunov approach is proposed. In the inverse Lyapunov approach, the Lyapunov matrix in the bang–bang type semi-active control based on the Lyapunov function is searched so that the control performance of the semi-active control system is optimized. Design parameters to determine the Lyapunov function and those of the VCD are optimized with the genetic algorithm (GA). The effectiveness of the proposed approach is presented with simulation studies.

Copyright © 2012 by ASME
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References

Figures

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Fig. 1

Schematic diagram of the VCD

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Fig. 2

Assembly of the VCD [12-14]

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Fig. 3

Setup of the three-storey benchmark structure in NCREE, Taiwan

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Fig. 4

Model of the three-storey benchmark structure

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Fig. 5

Fifteen storey building with three VCD

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Fig. 10

Time histories of structural responses to JMA Kobe NS (1995) earthquake (t: 0–20 s)

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Fig. 11

Result for JMA Kobe NS (1995) earthquake

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Fig. 12

Result for JMA Kobe NS (1995) earthquake (peak values)

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Fig. 13

Time histories of variable damping coefficients of the VCD diVCD, i = 1, 2, 3 for JMA Kobe NS (1995) earthquake

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Fig. 6

Time histories of structural responses to El Centro NS (1940) earthquake (t: 0–20 s, upper: r15(t) = q15(t) − q14(t), Lower: a15(t)=q··15(t), NC: Without the VCD, SA (inverse Luyapunov): Semi-active control with inverse Lyapunov approach, SA (energy-based): Semi-active control with the method in Ref. [5], Pon: passive on)

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Fig. 7

Result for El Centro NS (1940) earthquake (RMS values, left: relative displacement between neighboring two storeys, right: absolute acceleration)

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Fig. 8

Result for El Centro NS (1940) (1995) earthquake (peak values)

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Fig. 9

Time histories of variable damping coefficients of the VCD diVCD, i = 1, 2, 3 for El Centro NS (1940) earthquake

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Fig. 14

Time histories of structural responses to Taft NS (1952) earthquake (t: 0–20 s)

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Fig. 15

Result for Taft NS (1952) earthquake (RMS values)

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Fig. 16

Result for Taft NS (1952) earthquake (peak values)

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Fig. 17

Time histories of variable damping coefficients of the VCD diVCD, i = 1, 2, 3 for Taft NS (1952) earthquake

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Fig. 18

Power spectrum densities of the earthquake waves

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