The effect of structured uncertainty in the acoustic plant on multichannel feedforward control systems

Algorithms used for multichannel adaptive feedforward control, such as the multiple error LMS algorithm, require a model of the cancellation paths, which a control engineer would refer to as the plant, to update the signals driving the secondary sources. Uncertainties in this plant model or in the physical plant can lead to instability or suboptimal performance. This paper describes the effect of practically realistic uncertainties in both estimated and physical plant on the stability and performance of such a control algorithm. The system used here has 32 error sensors and 16 secondary sources and is designed to control a pure tone of 88 Hz. We consider the structured uncertainties due to changes in the error sensor locations, changes in the secondary source locations, and the excitation frequency. Results of preliminary experiments and numerical simulations show that these uncertainties have very different effects on the stability and performance of the control system. The singular value decomposition of the transfer matrix is used to discuss the characteristics of each type of plant error in the principal coordinates of the system.