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Active control of the reflection of waves in beams

We present some theoretical and experimental results related to the problem of developing active systems for the control of flexural waves in beams. Two types of feedforward control systems were implemented in the Laboratory. The first system was an implementation of an ideal compensator which modifies the reflection matrix at the boundary of a beam to generate a perfect anechoic termination. The transfer functions for the compensator were identified using an optimum sensor arrangement, with the disturbance waves generated with a shaker attached midways along the span of the beam, and the secondary waves generated by means of two PZT actuator pairs located near the active boundary. For the second system the filtered-X-LMS algorithm (XLMS) was used to adaptively identify the parameters of a compensator. We show how, under certain conditions, the XLMS algorithm converges to the structure of the ideal compensator. We also show how the parameters of the adaptive compensator, as well as the parameters of the plants, can be identified using an estimate of the reflected waves provided by an observer using measurements from a compact array of sensors. We report experimental results in which good attenuation levels were achieved over a wide frequency band.