Abstract
This paper concerns the real-time estimation of wave amplitudes and their subsequent use as a cost function in adaptive active control of bending vibrations in a beam. The amplitude of the wave propagating downstream from the control location is estimated by filtering the outputs of an array of sensors. Minimizing this wave amplitude has significant advantages over the more conventional approach in which velocity at some point is minimized. Expressions for the ideal frequency responses of the wave filters are found for the case of an array comprising two sensors in the far field. These filters are non-causal. FIR implementations designed using direct and time-delay methods are described, the latter offering some substantial advantages. Practical performance considerations are discussed, including filter length, frequency range, effects of near fields, group delays, accuracy and cross-sensitivity. Simulations and experimental measurements are performed and compared.
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