自适应陷波器滤波X－LMS算法稳定性分析

提出主动噪声控制系统稳定性分析的一种新方法．控制器采用自适应陷波器滤波Ｘ—ＬＭＳ算法，为改善系统的稳定鲁棒性和加速算法的收敛，利用声学通道的相位特性设计了补偿滤波器．通过建立状态空间模型对系统进行性能分析，经过旋转变换，将时变系统转化为等价的线性时不变系统，从而可以便利地利用控制理论进行稳定性分析

Stability Analysis of Filtered-X LMS Adaptive Notch Filter for Active Noise Control

Boucher et al in 1991 stidied the effect of errors in the plant model on the stability of an active noise control system. For the multichannel case (for example ,aircraft noise aircraft control), the method of Ref.4] can give a Probability of stability. In this paper we propose a different mpthod and, when extended by us to the multichannel case, it can indicate whether the system is stable or not by determining certain eigenvalucs of the system.This paper presents the basic steps, which are used for the stability analysis of a single channel tem in this paper and for a multichannel system5]. These basic steps are :1. Compensating filter needs by filtered-X LMSalgorithm is designed in such a way as to stabilize the system despite the exdistence of the acoustic channel. Errors of parameters in such a filter unavoidably exist and the question is whether such errous will cause instability.2. The errous of Compensating filter can be described as the uncertain parameters in state space equation which ,mathematically expressed ,is eq(13)3 Starting from eq (13) and introducing a rotation matrix,system into a discrete time invariant system, which is eq.(22).values.4. Eq .(22) can be used to determine the needed eigenvalues