Causality in systems of active reduction of vibration and noise

"This task was carried out in three steps. The first one concerned a theoretical analysis of the influence of a compensation signal and the geometry of an active reduction system on its efficiency. The second step consisted in developing specialist software and using it for simulation tests. The third step of the task consisted of measurements at a test stand. They involved measurements of the space distribution of the efficiency of active noise reduction systems in an acoustic wave guide. A system of active reduction with a controller that uses an algorithm of least mean squares was used. On the basis of the obtained results it was confirmed that when a compensated signal is not deterministic - but its band is restricted - it is possible to achieve the effect of active reduction at the observation points for which the system is not causal. At the same time, one needs to consider a gradual degradation of the technical parameters of the active reduction system as the parameters of the signal generated by the compensated source become less predictable. This means that in the case of sources of noise that emit deterministic signals, when designing systems of active reduction, it is possible to neglect the aspect of causality; whereas in the case of sources of noise that emit random signals, it is necessary to fulfil the condition of causality."