A novel method of designing stable feedback controllers for local control of sound

This paper investigates the performance and stability of a virtual microphone feedback controller for local control of sound through theoretical analysis, simulations and real-time implementation. In real-time implementation of practical systems we usually need to measure the frequency response of the controller before the controller is implemented, in order to ensure that the expected performance is achieved. If an unstable controller is used, we will not be able to measure the frequency response of the controller, which will make the implementation and maintenance of the controller more difficult. Therefore a novel method to design a stable feedback controller for a local control system is presented in this paper. The local control system is designed to attenuate a broadband disturbance at a point near the listener's ear, i.e. the virtual microphone, rather than at the control microphone, i.e. the physical microphone. The results showed that if a good performance was to be achieved the controller would be unstable. This is because the magnitude of the response of the virtual plant is lower than that of the physical plant. The feedback controller in this work is designed to minimize the noise at the virtual microphone, with a virtual plant response used in the performance objective. However the physical plant is used in the stability constraint. Therefore there is a trade-off between the performance and controller stability. The main contributions of the paper are to propose a novel method to design a stable feedback controller and analyze the performance and stability of a virtual microphone feedback controller for the local control of sound through simulations and real-time implementation.