H¦0¦0 control of acoustic noise

Abstract

The application of H0|0 control techniques to study global acoustic noise reduction in a one-dimensional duct is considered. The acoustic problem is formulated as an unbounded control system on an infinite-dimensional Hilbert space. A sequence of approximating finite-dimensional control systems is shown to coverage to the solution of the well-posed infinite-dimensional problem under certain conditions. The finite-dimensional control problem is solved using Nevanlinna-Pick interpolation. The question of the achievable level of global acoustic noise reduction in the one-dimensional duct is then addressed. Both feedback and feedforward design are examined. Optimal placement of the controller actuator location and controller sensor location is discussed, as well as the effect of the number and location of performance points in relation to the actuator and sensor. Numerical results indicate that uniform stabilizability of approximations is not necessarily for controller design. Results also indicate that behaviour of the zeros of the approximations, as well as the poles, is important for H0|0 controller design.