Design of fractional order non-linear active noise control systems

Active noise control (ANC) systems, which works on the principle of destructive superposition has become a popular choice for noise control in the recent past. ANC systems, which employs a filtered-x least mean square (FxLMS) algorithm, fails to effectively mitigate noise in the presence of non-linearities in the ANC system. A few non-linear ANC systems have been lately designed to overcome this limitation. In addition, it has been reported that the fractional order least mean square (FLMS) algorithm can provide improved convergence over conventional least mean square (LMS) algorithm when applied for system identification. In an endeavour to improve the convergence in non-linear ANC scenarios, this paper attempts to design a non-linear ANC system trained using a fractional order adaptive algorithm, derived using a Riemann-Liouville differintegral operator. We have employed the even mirror Fourier non-linear filter (EMFN) as the non-linear network and the results obtained show improved convergence over conventional non-linear ANC schemes. Secondly, it has been observed that there is a dilemma in choosing the right fractional order i.e. positive fractional order give faster convergence but degrades steady state performance, however negative fractional order converges slow and having improved steady state performance. In order to overcome this difficulty of choosing the right fractional order, a convex combination of two fractional order controllers has been further proposed and tested. The new convex combination scheme has been shown to not only provide enhanced convergence speed, but also deliver improved steady state error.