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.