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In the conventional hybrid active noise control (CHANC) algorithm, the filtered-x least mean square (FXLMS) algorithm is used in both feedforward and feedback structures. However, the FXLMS algorithm does not process the reference signal and the error signal before updating the weight vector, which leads to the inadequate robustness of the CHANC algorithm in the impulsive noise environment. To solve this problem, the maximum versoria criterion is incorporated into the HANC (MVC-HANC) algorithm in this paper. Firstly, the MVC-HANC algorithm employs a novel nonlinear function to compress the error signal. Secondly, the proposed algorithm uses the modified sigmoid function to constrain the reference signal. To further improve the noise attenuation performance, the MVC-HANC algorithm uses a novel exponential function to adjust the step-size adaptively. Simulation and experiment results demonstrate that the proposed algorithm has the better attenuation performance than the conventional HANC algorithm.