Nonlinear adaptive algorithm for active noise control with loudspeaker nonlinearity

Low frequency noise is an environmental pollution which affects human psychologically and physiologically. Low frequency noise of excessive amplitude could cause hearing loss, negative social behaviours, sleep and cardiovascular diseases. There are two methods to cancel or control noise which are active and passive methods. Passive method involves the use of enclosures, barriers and silencers but is ineffective at low frequency noise (below 500Hz). An active method which has received much attention is the use of Active Noise Control (ANC) system which involves an electro acoustic system that cancels unwanted noise using the principle of superposition. Adaptive algorithms are prevalently applied in the design of nonlinear active noise control (ANC) system. The most important nonlinearity in ANC is the saturation effect produced by the electro-acoustical sensors and transducers. The dominant saturation nonlinearity in the transducers is the loudspeaker which can be represented by a Wiener model. An effective solution to mitigate such nonlinearly distortion is to employ the Nonlinear Filtered-X Least Mean Square (NLFXLMS) algorithm. The controller compensates the nonlinearity using a model of the saturation effect represented by Scaled Error Function (SEF). However, the NLFXLMS is limited by two practical issues such that the degree of nonlinearity has to be known in advance and the SEF cannot be evaluated in real time. In this work, the NLFXLMS algorithm is modified by incorporating Tangential Hyperbolic Function (THF) to model the saturation effect of the loudspeaker. The proposed THF-NLFXLMS algorithm models the Wiener secondary path and applies the estimated degree of nonlinearity of the nonlinear secondary path in the control algorithm design. The results show that the Wiener secondary path with saturation nonlinearity represented by SEF can be modelled by THF with a certain degree of accuracy and yield a good estimate of the degree of nonlinearity can be obtained. The performance of the proposed algorithm is comparable with the benchmark NLFXLMS and superior to the conventional FXLMS with the proposed algorithm