In the field of active vibration control (AVC), it is difficult to use the classical filtered-x least mean squares (FxLMS) algorithm to solve the instability problem of active control system caused by the time-varying secondary path when the multiple channel coupling and the secondary path model are complex. Therefore, this paper proposes a new cost function based on the simultaneous perturbation stochastic approximation notch-filtering (SPSAN) algorithm. The proposed algorithm possesses two key characteristics: first, it eliminates the need for secondary path identification, and second, it extends single-channel algorithms to multiple channel ones. The proposed algorithm considers the energy of each harmonic vibration at each controlled point in the case of multi-channel coupling, and based on the goal of minimizing the total energy of the system. The proposed cost function to address the AVC problem in the case of multiple channel coupling. Theoretical analysis shows that compared to the single-channel case, the noise term of the SPSAN algorithm is smaller than that of the conventional cost function, despite the increase in the noise term when estimating the optimal control filter using this cost function. In addition, the multi-channel coupled SPSAN algorithm has smaller static error and faster convergence. Simulation and experimental results show that the proposed multiple channels coupled SPSAN algorithm can estimate the optimal control filters even with time-varying secondary path, and effectively suppresses the vibration of the seawater pump piping system.

中文翻译：

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主动振动控制中具有改进成本函数的多通道 SPSA 算法


在主动振动控制（AVC）领域，经典的滤波x最小均方（FxLMS）算法很难解决多通道耦合时二次路径时变引起的主动控制系统不稳定问题次要路径模型复杂。因此，本文提出一种基于同时扰动随机近似陷波滤波（SPSAN）算法的新成本函数。该算法具有两个关键特征：首先，它消除了辅助路径识别的需要；其次，它将单通道算法扩展到多通道算法。该算法考虑多通道耦合情况下各控制点各简谐振动的能量，以系统总能量最小化为目标。所提出的成本函数用于解决多通道耦合情况下的 AVC 问题。理论分析表明，与单通道情况相比，尽管使用该成本函数估计最优控制滤波器时噪声项有所增加，但SPSAN算法的噪声项仍小于传统成本函数的噪声项。此外，多通道耦合SPSAN算法静态误差更小，收敛速度更快。仿真和实验结果表明，所提出的多通道耦合SPSAN算法即使在二次路径时变的情况下也能估计出最优控制滤波器，并有效抑制海水泵管道系统的振动。