Stability-guaranteed adaptive algorithm and its application to active noise canceling

There are some cases where feedforward control can be utilized effectively, e.g., the active noise control and the vibration control of a building. When there exists an indetenninistic factor or a fluctuation, the adaptive filter must be introduced. The algorithm that adjusts the coefficient of the adaptive filter has mostly been based on the filtered-x algorithm. A problem in this approach, however, is that the stability is not guaranteed and the stepwidth of least-mean square (LMS) algorithm must carefully be determined. From such a viewpoint, this paper proposes the adaptive algorithm both in the time and the frequency domains, where an arbitrary stepwidth can be used, and the robust stability is guaranteed even if an additive noise is mixed. As the first step, the infinite impulse response (IIR) adaptive filter is considered, aiming at implementation of the controller in the time domain, and the properties of the adaptive algorithm are analyzed. Then, the adaptive algorithm in the frequency domain is proposed where the controller is implemented using the frequency-sampling filter and the stability is guaranteed. In contrast to the case of the design in the time domain, the implementation in the frequency domain has the advantage that the realization is ensured independently of the order or the structure. Finally, the usefulness of the proposed adaptive algorithm is demonstrated by numerical example and experiment in the active noise canceler.