The application of self-tuning control strategies to the active reduction of sound

The generalised minimum variance (GMV) strategy is proposed for the active reduction of sound, and it is shown that, under certain constraints, the more usual adaptive filtering control strategy is a special control law of the GMV strategy. Using both theoretical derivations and simulation experiments it is shown that the GMV strategy is a valuable extension of the usual strategies. Adaptive filtering appears to be suitable for a restricted class of disturbance signals. If the disturbance signal consists of a measurable part and a Gaussian noise part, the performance of the adaptive filtering controller is very good. The rate of convergence may be slow, as the acoustic process poles can be poorly damped. If the stochastic noise contribution to the disturbance signal is non-Gaussian, however, the performance of the adaptive filtering system seriously deteriorates. In that case feedback control should be applied. The GMV strategy is capable of reducing a measurable disturbance by feedforward control and a stochastic disturbance by feedback control. In general, the GMV control with both feedforward and feedback yields a much better performance than a pure feedback or an adaptive filtering strategy. A complication with the GMV control strategy, however, is to find an appropriate choice for the weighting polynomials in the cost function, when the secondary acoustic process is nonminimum phase. If necessary, these polynomials can also be used to place the closed-loop poles at well-damped positions