Active control of nonlinear noise processes in a linear duct

TLDR: This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques: the low-frequency noise itself and the actuator in an ANC system has been shown to be nonminimum phase.

Abstract: This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller.