An Open-Loop Pole–Zero Placement Method for Active Noise Control Headphones

Abstract

Active noise control headphones for hearing protection are effective in the low frequency range, and both analog and digital controllers are used widely. Considering the bandwidth of noise reduction, the analog controller is more beneficial due to its shorter delay compared with the digital one. Analog controllers with fixed circuit structures are preferable for practical implementation. However, fixed-order controllers with low complexity, such as a biquad filter, are difficult to design for a high reduction level. On the other hand, a high order one, getting from the $H_{\mathrm { {inf}}}$ -norm optimization, is costly due to a larger number of circuit components. In this paper, an $H_{\mathrm {2}}$ -norm optimization method that places the controller’s pole–zero locations to meet desired robustness and performance, is proposed. To determine an initial guess with an appropriate order of the controller, a loop-shaping method by loop transfer recovery (LTR) is introduced. The experimental results show the effectiveness of the method.