Active noise control with weak nonlinearities in the secondary path

In this paper, we address the problem of adaptive control of a nonlinear noise process in the presence of a weakly nonlinear secondary path. This problem is common in many cases of Active Vibration Control (AVC) and Active Noise Control (ANC) where the secondary path nonlinearity is due to the presence of a weak nonlinear actuator. Our proposed configuration turns out to be subsumed by a method called the filtered-A LMS algorithm proposed by Klippel [1]. In that paper, Klippel attempted to linearize a weakly nonlinear plant (main or primary path) using an adaptive inverse control method so that the nonlinear plant will track an input signal. He certainly did not consider our configuration or usage. Thus some effort to connect these two algorithms is required. Furthermore, we also determine that as the nonlinear secondary path becomes linear, and there is thus only a nonlinear primary path, the filtered-A LMS algorithm and our configuration gives the so-called Volterra filtered-x LMS (VFLMS) algorithm [2] developed by Tan and Jiang. In this paper, we connect the algorithms. Detailed implementation information is provided. Extensive simulations show that the algorithm works well for our AVC problem.