Absolute vibration suppression (AVS) is a control method for flexible structures. The first step is an accurate, infinite dimension, transfer function (TF), from actuation to measurement. This leads to the collocated, rate feedback AVS controller that in some cases completely eliminates the vibration. In case of the 1D wave equation, the TF consists of pure time delays and low order rational terms, and the AVS controller is rational. In all other cases, the TF and consequently the controller are fractional order in both the delays and the "rational parts". The paper considers stability, performance and actual implementation in such cases.
Yoram Halevi, "Fractional order absolute vibration suppression (AVS) controllers," Proc. SPIE 10172, A Tribute Conference Honoring Daniel Inman, 1017204 (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 29, 2017; Published: 10 April 2017); https://doi.org/10.1117/12.2257918.
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