## 1 Introduction
[PERSON] and [PERSON] [10] used the results of four wearings to establish the controller's objective function and constraints and then created an analog circuit controller. [PERSON] and [PERSON] [19] found that the low-frequency drastic changes in the secondary path when putting on and removing headphones could be identified using an adaptive filter, based on which a feasible weighting coefficient update rule was established through experiments. Leading companies like BOSE, SONY and Apple have adopted proximity sensors, offering quick and accurate responses in their ANC headphones to monitor the states of wearing and removal [20; 21; 22], and this approach can replace algorithmic detection from an engineering application perspective, reducing the algorithm's consumption of system power. For the latter case, Ti's engineer [PERSON] et al. [23] used the average result of 10 real subjects to obtain the secondary path transfer function and employed a smaller update coefficient to handle the greater variance. [PERSON] and [PERSON] [24] constructed different weighting coefficient constraints using real secondary path data from two dummy heads and six subjects wearing the headphones at three different angles and used the sequential quadratic programming (SQP) algorithm [25] to derive the FIR filter and compared the results. [PERSON] and [PERSON] [26] built an uncertainty model using the real part of 78 secondary path transfer functions tested on a single subject and also used the SQP algorithm to calculate the FIR filter. However, the implementation methods mentioned above use either analog circuits or FIR filters. Analog circuits have significant errors, and the FIR controllers will introduce additional delay and cannot meet the requirements of current ANC headphones. [PERSON] et al. [27] and [PERSON] et al. [28] implemented controller designs using the IIR filters and optimized them with the genetic optimization algorithm (GA) combined with the Nelder-Mead (NM) algorithm and differential evolution (DE) algorithm, respectively. In the former controller, the application of dual optimization increased the system complexity, while the latter controller based on the DE algorithm operates directly in continuous space, facilitating the global minimum search but bringing high computational demand [29]. The GWO [30] algorithm and its improved version, IGWO [31], as typical representatives of swarm intelligence algorithms, are characterized by their simple structure, minor parameter adjustment, and ease of implementation. The IGWO algorithm contains an information feedback mechanism, and a balance is achieved between local optimization and global search, thus offering good performance in both solution accuracy and convergence speed. In this paper, a method is proposed to design a feedback ANC headphone controller. A new secondary path uncertainty constraint is proposed based on the results of multiple wearing tests on real subjects and a dummy head. This constraint is applied in the process of optimizing the controller, so that new subjects can obtain stable noise reduction and moderate waterbed lift when using the headphone. In Section 2, a safety factor and a waterbed suppression factor are introduced into a proposed uncertainty constraint, which is integrated into the H2/H\(\infty\) framework to obtain a feedback control strategic function. In Section 3, the control strategic function is optimized using the IGWO algorithm to obtain the optimal controller composed of cascaded biquad IIR filters, and the noise reduction performance is simulated in two cases with or without the proposed uncertainty constraint. The reliability of the proposed method is validated based on the measured results of the experimental test. Finally, conclusions are drawn in Section 4.