Superposition of the uncertainties in acoustic responses and the robust design of active control systems

The use of virtual sensing allows the frequency range of a local active noise control system located close to a listener's ears to be extended beyond what is possible when only controlling from remote physical sensors, particularly if head tracking is also used to determine the position of the virtual sensors. As the frequency range is extended, however, the uncertainties in the acoustic responses become more significant, and the design of multichannel adaptive controllers that are robustly stable to these uncertainties becomes more important. In order to fully characterise the uncertainties, a very large number of measurements would, in principle, need to be taken, due to the combination of all the possible changes in the acoustic environment. For uncertainties due to the simultaneous change in position of several objects within the acoustic environment, however, it is shown that the uncertainties can be accurately predicted by the superposition of these uncertainties, due to the change in position of the objects individually. This allows the uncertainty that is due to the change in position of a number of objects to be rapidly evaluated from a limited number of experiments and considerably simplifies the controller design process, which is illustrated here for an active headrest system using two different virtual sensing techniques.