Application of Kautz Models for Adaptive Vibration Control
Abstract Both for active noise control (ANC) and active vibration control (AVC) the well known F-X-LMS-algorithm can be used. This approach requires a proper model of the path from the actuator to the error sensor, preferably received with an on-line identification. In the field of ANC adaptive finite impulse response (FIR) filters work well for this task, but for lightly damped mechanical systems with long impulse responses FIR filters with up to several thousand coefficients would have to be used. One alternative are adaptive IIR filters, but these can get unstable while adapting or the adapting process can get stuck in local minima. In this work, adaptive Kautz models are introduced, which need some a priori knowledge about the poles of the system. On the other hand, they represent an infinite impulse response while maintaining the transversal structure of the adaptive filter. This is reached by generalization of the FIR filter, for which the delay operator is substituted by discrete allpass filters, the Kautz filters. The adaptive filter bank is implemented by means of the straightforward LMS algorithm in the Matlab/Simulink environment. As an example, system identification with Kautz models and their usage in AVC for a simple mechanical system will be studied.