| In daily life,the problems of low frequency noise in ducts exist in domestic appliances like range hood,air conditioner,vacuum cleaner.By traditional passive noise control method,the performance is poor in controlling low frequency noise,and the heat dispersion function could be decreased.A major challenge of applying active noise control on those appliances is that the noise transmitting duct is short.As a result,the output of secondary source is transmitted back to the reference sensor.This contaminates the quality of reference signal and deteriorates the stability and performance of active control system.On the other side,short distance between reference sensor and secondary source will cause the lack of causality,which will deteriorate the performance.This paper will analysis the performance of feedforward active noise control system in short duct from two perspectives,including acoustic feedback and causality.Based on the concept of equivalent secondary path,this paper uses the phase deviation between the equivalent secondary path and the real secondary path to analyze the convergence behavior of the system with acoustic feedback.If the phase deviation exceeds 90 degrees at some frequencies,the control filter is difficult to converge around those frequencies.The noise reduction performance decreases,and the system may become unstable.Simulations are carried out to evaluate the performances of 4 approaches for solving the acoustic feedback induced problems,which includes the method of using a unidirectional microphone,the method of using the Filtered-u LMS(FuLMS)algorithm,the feedback neutralization method and the online modeling method.The spectral factorization method is used to analyze the system causality.The transfer function is divided into minimum-phase part and all-pass part.Then,the optimum causal filter is derived,and the error signal is decomposed into causal part which can be controlled by causal filter,and non-causal part.Simulations based on pure delay transfer functions show that the noise reduction level will decrease with wider bandwidth noise.The simulations based on measured transfer function illustrate that the reflection of duct-wall will generate peak value of group delay in some frequencies of secondary path,which will influence the performance of active noise control system.Finally,experiments were carried out in a short duct,the performance of solutions for solving acoustic feedback in real duct system was compared.The results show that the unidirectional method is the most convenient method,but the directivity is poor in low frequency range.The FuLMS algorithm has low computational load,however the convergence is hard to be guaranteed.The feedback neutralization method has the best performance but has weak robustness when the system is time variant The online modelling method doesn’t require an extra filter,but its performance is slightly worse than other solutions due to complicated adjustment parameters.In addition,the primary noise bandwidth and the location of reference sensor were changed to get different system causality,experiment results confirm that with the increase of noise bandwidth or the distance between primary source and reference sensor,the noise reduction level of error sensor will decrease.This paper discussed active noise control system in short duct from the perspective of acoustic feedback and non-causality.The stable criterion under acoustic feedback and relation between non-causality parameters and noise reduction level are derived and validated through experiments. |
