18 April 2007 Lyapunov stability of periodically modulated cosine drivers for resonance tuning of harmonic oscillators
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Abstract
Resonance tracking control of harmonic oscillators whose natural frequency is unknown is investigated from a Lyapunov stability perspective. In particular, a periodically-modulated cosine driver (PMCD) is investigated for this purpose. The proposed resonance tuner is time-synchronized with periodic sampling of the harmonic oscillator's output to ensure that an analytical relationship exists between the drive frequency and the tracking error. This relation defines a class of discrete time nonlinear systems whose origin, is shown to be asymptotically stable.
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J. B. Aldrich, S. Sherrit, X. Bao, M. Badescu, Y. Bar-Cohen, Z. Chang, "Lyapunov stability of periodically modulated cosine drivers for resonance tuning of harmonic oscillators", Proc. SPIE 6523, Modeling, Signal Processing, and Control for Smart Structures 2007, 65230B (18 April 2007); doi: 10.1117/12.716403; https://doi.org/10.1117/12.716403
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