Stabilization of feedback-type active control systems in finite ducts.

Abstract

Use of feedback-type control architectures in active noise cancellation can be very difficult due to the extreme sensitivity of this approach to instability, but are sometimes advantageous because the need for the reference sensor is eliminated. Instability results when the feedback loop time delay causes an additional phase shift of 180° at some frequencies allowing high-gain positive feedback to occur. The classical approach to this problem is to design a compensation filter which reduces the feedback gain to less than unity at the frequency(s) where the loop delay causes instability. In a finite-length duct, the feedback instabilities are found to be related to the transducers and the distance between them as well as their positions within the duct. The potential for instability is present whether adaptive or fixed active noise control is done using a feedback-type controller. The compensation filter design is determined directly from the physical parameters of the finite waveguide and the transducers. However, the performance of the feedback controller is restricted by the compensation filter.