Feedforward vs. Feedback Fixed-Parameter H2 Control of Non-Stationary Noise

Abstract

Stationary random noise can be modelled as a wide-sense stationary white noise filtered by a minimum phase filter. Such filter can be used to design an optimal control filter minimising variance of the signal being the effect of the noise and the secondary sound interference. However, in many environments the noise is subject to change. For instance, some of the noisy devices are switched on and off, speed of some rotors or fans changes, etc. As a result contribution of different frequency components may significantly vary in time. Solving the optimisation problem to update control filter is rather avoided in on-line systems. In adaptive approach there are problems with convergence or some unpleasant transient acoustic effects. In this paper, the fixed-parameter approach to control is appreciated. Dominating frequency components/bands can usually be distinguished for the acoustic environment. Then, the idea of generalised disturbance defined by a frequency window of different type can be applied. If a reference signal, correlated with the disturbance to be reduced is available in advance, a feedforward structure can be applied, and otherwise, a feedback structure is used. Spectral and inner-outer factorisations are employed in order to cope with non-minimum phase character of the acousto-electric plant. Efficiency of the proposed approach for both control structures is verified based on the data obtained from an active personal headset. The generalised disturbance based control systems are confronted with the classical Wiener control systems designed for the given disturbance.