An online modelling method for secondary path of two distinct variable step-size strategies based on the filtered-x least square (FXLMS) algorithm is proposed. In this method, the variable step-size strategy with two distinct steps is used, and two variable step-size strategies are used before and after the secondary path modelling process converges, so that the convergence rate is guaranteed. At the same time, it can effectively avoid the fluctuation after the system converges and improve the

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... tability and modelling accuracy of the system. Due to the white noise, the signal of secondary path modelling will affect the control part. A white noise control strategy is proposed to adjust the white noise according to the change of the stepsize of the secondary path. On the premise of ensuring identification speed and precision, the influence of white noise on the control part is eliminated as far as possible. Compared to the existing methods, the simulation result shows that the proposed method can significantly improve the modelling accuracy of the secondary path while ensuring the convergence speed and has a better performance in vibration control effects.