Real time nonlinear filtered-x lms algorithm for active noise control

Active noise control (ANC) is an effective noise reduction method capable of reducing unwanted low frequency noise (typically below 500Hz) electronically. In practical ANC applications, nonlinearity effects degrade the performance of conventional linear control algorithm. The nonlinearity sources could originate from the noise process, primary and secondary acoustical propagation paths, or from the transducers consisting of loudspeaker, microphone or amplifier. The saturation of the loudspeaker amplifier is considered as the main source of nonlinearity in many ANC systems. In the nonlinear ANC literature, various nonlinear algorithms have been introduced. These nonlinear algorithms were employed to improve noise reduction performance. The performance of these algorithms is usually compared with the standard linear filtered-x least mean square (FXLMS) algorithm. A review of these algorithms has shown that the nonlinear FXLMS (NLFXLMS) algorithm produces high level of cancellation while keeping the computational complexity low. However, unlike the other algorithms, NLFXLMS cannot be implemented in real time. The NLFXLMS algorithm is a stochastic gradient algorithm that incorporates the derivative of a nonlinear plant model which is represented by the scaled error function (SEF) in the controller design. The SEF has been extensively used to model the saturation nonlinearity. A major drawback of using the SEF function lies in its theoretical nature such that for a finite integration limit, the SEF become non-elementary integral and requires infinite series or numerical methods for evaluation. In addition,the identification of the exact SEF parameter used to scale the strength of saturation nonlinearity becomes impractical. Consequently, the practical applicability of the NLFXLMS algorithm is limited by this drawback. In this work, a new method of modelling the saturation effect of the amplifier based on tangential hyperbolic function (THF) of the nonlinear part of a Hammerstein model structure is proposed. The THF is derived to represent a wide range of nonlinear distortions and replace the SEF with a certain degree of accuracy. The advantage of replacing the SEF with the THF is the ability of the latter to be realised in a nonlinear modelling scheme. Subsequently, the THF modelling scheme can be incorporated into an established real time NLFXLMS algorithm termed THF-NLFXLMS algorithm. The developed THF-NLFXLMS algorithm is tested by means of simulation and implemented experimentally using FPGA-based real time controller for a nonlinear ANC application. The application involves the reduction of a traffic noise that affects the pressure field in a bedroom. The ANC architecture implemented is a single channel internal model control (IMC) based feedback ANC system. Simulation and experimental results have shown that the developed THF-NLFXLMS achieves additional noise reduction of 19% from that being achieved by the linear FXLMS algorithm.

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