Non-linear optimisation problems in active control

The work described in this thesis is concerned with the nonlinear optimisation problems encountered in the application of active sound control. These are mainly to do with the optimal locations of transducers in an active control system; loudspeakers and microphones in the examples presented in this thesis. Two natural algorithms are used to perform this optimisation. Their properties are briefly reviewed and the modifications required to use them in this context are discussed. Measurements and predictions are also described of the acoustic transfer impedance in an enclosure, with or without a Helmholtz resonator attached. Also the performance is studied of active sound control systems under the constraint that the control signal inputs to loudspeakers is limited, and the optimal transducer positions under these circumstances are considered. Finally the algorithms developed and verified in the laboratory enclosure are applied to a set of data measured in a helicopter and used to suggest a practical control system which gives acceptable performance with a minimum number of practically sized loudspeakers and microphones.