Discrete time feedback control of sound radiation

The solution of the discrete time linear quadratic Gaussian (LQG) optimal control problem is applied to problems in the feedback control of sound radiation. The solution used requires the identification of suitable recursive models of both the plant to be controlled and shaping filter from which the unwanted disturbance is assumed to originate. The traditional formulation of the problem involves the minimisation of the mean squared error signal derived directly from the plant output. This formulation is extended here in order to deal with the minimisation of the sum of the mean squared error signals evaluated at a number of error sensors placed at locations other than at the output of the plant to be controlled. The analysis is thus appropriate for the design of controllers whose objective is the minimisation of far field acoustic pressure radiated by a vibrating surface.