Adaptive Cancellation of Time-Varying Disturbances

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The object of this project is to develop control algorithms for the cancellation of periodic disturbances whose frequency content varies significantly over time. Typical applications include active noise and vibration control, although the problems under consideration are generic and the algorithms are applicable in many other contexts. Two classes of algorithms are considered. They have been studied before for restricted cases and have shown promising results. The algorithms are particularly valuable because of their simplicity and because of the tools available to design them for specific performance goals. In the project, the algorithms will be developed so that they will become applicable to the most general problems with multivariable system and with disturbances having multiple harmonic components. An important intermediate goal will be the analysis of the robustness properties of adaptive algorithms using little known but powerful results of linear time-invariant system equivalence. These results will enable a precise quantification of the robustness margins of the algorithms, and may lead to new strategies for robust design. Another goal is the development of new algorithms for the estimation and tracking of the parameters of periodic signals using multiple sensors. The algorithms will be tested in active noise control or active vibration control experiments.