Plant matrix consideration in active control, adaptive sound field reproduction and time-reversal acoustics

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A large number of problems in acoustics and vibration of continuous domains involve a set of sources (or actuators) and a set of receivers (or sensors) distributed in the continuum. This is the case in active noise and vibration control, in adaptive sound field reproduction, in time-reversal mirrors and to some extent in inverse vibroacoustic problems, all areas in which I had some interest recently. Although traditionally investigated separately, all of these problems fundamentally rely on a few properties of the plant matrix, the matrix of linear transfer functions between each actuator and each sensor through the propagation medium. It is the purpose of this proposal to contribute to the advancement of multi-channel active control, multi-channel sound field reproduction and vibroacoustic time-reversal techniques, under the specific angle of exploiting and possibly optimizing the properties of the plant matrix. 1- In active noise and vibration control, we are especially interested in decentralized architectures, i.e. independent control loops between one actuator and one sensor. This leads to neglecting off-diagonal coefficients of the plant matrix and results in a much simpler and robust practical implementation. 2- The objective of sound field reproduction - to reproduce an extended wave field in an arbitrary environment using a set of reproduction sources- finds applications in music or audio reproduction. In this topic we want to improve sound field reproduction techniques in realistic and possibly changing environments using adaptive control techniques. 3- Time reversal acoustics is a fascinating and rapidly growing technique that uses a "mirror" - a set of reciprocal transducers - to observe, store and re-emit (after time inversion) an arbitrary wave field to create its time-inverted image. In this topic, we want to exploit the focusing properties of time reversal mirrors to pinpoint the vibration sources on an extended, complex structure, or the acoustic sources on an extended, complex radiator.