This paper investigates the problem of optimally locating passive vibration isolators to minimize unwanted vibration caused by exogenous disturbance forces. The stiffness and damping parameters of the isolators are assumed to be known, leaving the isolator locations, which are nonlinearly related to system states, as unknown optimization variables. An approach for reformulating the nonlinear isolator placement problem as a linear time-invariant (LTI) feedback control problem, by linking fictitious control forces to fictitious measured outputs using a nonzero feedforward term, is proposed. Accordingly, the isolator locations show up within a static output feedback gain matrix which can be optimized, using methods from optimal control theory, to minimize the H2 and/or H∞ norms of transfer functions representing unwanted vibration. The proposed framework also allows well-established LTI control theories to be applied to the analyses of the optimal isolator placement problem and its results. The merits of the proposed approach are demonstrated using single and multivariable case studies related to isolator placement in precision manufacturing machines. However, the framework is applicable to optimal placement of passive isolators, suspensions, or dampers in automotive, aerospace, civil, and other applications.
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February 2017
Research-Article
A Linear Feedback Control Framework for Optimally Locating Passive Vibration Isolators With Known Stiffness and Damping Parameters
Jihyun Lee,
Jihyun Lee
Department of Mechanical Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
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Amir H. Ghasemi,
Amir H. Ghasemi
Department of Mechanical Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
Search for other works by this author on:
Chinedum E. Okwudire,
Chinedum E. Okwudire
Department of Mechanical Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
e-mail: okwudire@umich.edu
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
e-mail: okwudire@umich.edu
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Jeffrey Scruggs
Jeffrey Scruggs
Department of Civil and Environmental Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
Search for other works by this author on:
Jihyun Lee
Department of Mechanical Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
Amir H. Ghasemi
Department of Mechanical Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
Chinedum E. Okwudire
Department of Mechanical Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
e-mail: okwudire@umich.edu
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
e-mail: okwudire@umich.edu
Jeffrey Scruggs
Department of Civil and Environmental Engineering,
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
University of Michigan–Ann Arbor,
2350 Hayward,
Ann Arbor, MI 48109
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 26, 2016; final manuscript received September 4, 2016; published online October 27, 2016. Assoc. Editor: Patrick S. Keogh.
J. Vib. Acoust. Feb 2017, 139(1): 011006 (11 pages)
Published Online: October 27, 2016
Article history
Received:
January 26, 2016
Revised:
September 4, 2016
Citation
Lee, J., Ghasemi, A. H., Okwudire, C. E., and Scruggs, J. (October 27, 2016). "A Linear Feedback Control Framework for Optimally Locating Passive Vibration Isolators With Known Stiffness and Damping Parameters." ASME. J. Vib. Acoust. February 2017; 139(1): 011006. https://doi.org/10.1115/1.4034771
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