FxLMS (Filtered-x Least Mean Square) algorithm is widely used in the field of AVC (active vibration control) for its good convergence and strong adaptability. However, the convergence rate and steady-state error are mutually restricted for the fixed step FxLMS algorithm. Increasing step size to accelerate the convergence rate will result in larger steady-state error and even cause control divergence. In this paper, a new DVSFxLMS (error signal Differential term feedback Variable Step size FxLMS) algorithm is proposed by establishing nonlinear function between and error signal, while using differential term of the error signal as the feedback control function. Subsequently, a DVSFxLMS controller is designed to carry out the AVC simulation and experiments on cantilever beam with PSA (piezoelectric stack actuator). Simulation and experimental results show that the proposed DVSFxLMS algorithm has faster convergence rate and smaller steady-state error than the traditional FxLMS algorithm, which also has strong antinoise ability and adaptive control ability to quickly track the variable external disturbance.

中文翻译：

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压电主动振动控制的误差信号微分项反馈增强型可变步长FxLMS算法

FxLMS（滤波x最小均方）算法因其良好的收敛性和较强的适应性而在AVC（主动振动控制）领域中得到广泛使用。但是，对于固定步长FxLMS算法，收敛速度和稳态误差相互制约。增加步长以加快收敛速度​​将导致更大的稳态误差，甚至导致控制偏差。通过建立非线性函数之间的非线性函数，提出了一种新的DVSFxLMS（误差信号微分项反馈可变步长FxLMS）算法。误差信号，同时将误差信号的微分项用作反馈控制功能。随后，设计了DVSFxLMS控制器，以利用PSA（压电堆栈致动器）对悬臂梁进行AVC仿真和实验。仿真和实验结果表明，与传统的FxLMS算法相比，所提出的DVSFxLMS算法具有更快的收敛速度和较小的稳态误差，还具有较强的抗噪能力和自适应控制能力，可以快速跟踪可变的外部干扰。