The thesis is concerned with the active control of randomly vibrating structures by means of feedback control, with particular emphasis on reducing the sound radiation from such structures. A time domain model of the structural and radiation dynamics of an actively controlled plate has been developed, based on the theory of radiation filters for estimating the sound radiation from multimodal vibrations. This model has then been used in simulations of optimal feedback control, with special emphasis of the stability margins of the optimal control scheme. Two different methods of designing optimal and robust discrete-time feedback controllers for active vibration control of multimodal structures have been compared. They have been showed to yield controllers with identical frequency response characteristics, even though they employ completely different methods of numerical solutions and result in different representations of the controllers. The Internal Model Control structure combined with optimal filtering is suggested as an alternative to state space optimal control techniques for designing robust optimal controllers for audio frequency vibration control of resonant structures.
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Department of Acoustic Technology, Technical University of Denmark, 1999