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A Frequency-Domain Approach to Optimal Fractional-Order Damping

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Abstract

In this paper, we will consider the single term optimal fractional-order damper for an otherwise undamped oscillator. First, we will find the single term damper that minimizes the time domain integral of the squared step error (2-norm) and the integral of the time-weighted squared error (Hilbert–Schmidt–Hankel norm). Next we will consider a more intuitive frequency domain approach that insures the maximally flat magnitude response. Time and frequency domain plots are given for comparison with the integer-order solutions. Further improvements in performance are shown to be possible using multiple active fractional-order dampers.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Akron, Akron, OH, 44325–3904, U.S.A.

    Tom T. Hartley & Carl F. Lorenzo

Authors
  1. Tom T. Hartley
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  2. Carl F. Lorenzo
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Correspondence to Tom T. Hartley.

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Hartley, T., Lorenzo, C. A Frequency-Domain Approach to Optimal Fractional-Order Damping. Nonlinear Dyn 38, 69–84 (2004). https://doi.org/10.1007/s11071-004-3747-7

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  • DOI: https://doi.org/10.1007/s11071-004-3747-7

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