The general control laws for pointwise controllers to dissipate vibratory energies of translating beams and strings with arbitrarily varying length are presented. Special domain and boundary control laws that can be easily implemented result as a special case. Sufficient conditions for uniform stability and uniform exponential stability of controlled systems are established via Lyapunov stability criteria. Numerical simulations demonstrate the effectiveness of the active controllers in stabilizing translating media during both extension and retraction. Optimal gains leading to the fastest rates of decay of vibratory energies of controlled systems are identified. It is shown that under the optimal control gains, translating media can be completely stabilized during extension and retraction.
Active Control of Translating Media With Arbitrarily Varying Length
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 2000; revised February 2001. Associate Editor: B. Yang.
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Zhu, W. D., Ni, J., and Huang, J. (February 1, 2001). "Active Control of Translating Media With Arbitrarily Varying Length ." ASME. J. Vib. Acoust. July 2001; 123(3): 347–358. https://doi.org/10.1115/1.1375809
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