Active Vibration Control (AVC) based on the principle of destructive interference is an effective approach for suppressing low-frequency vibration in modern structures. This review paper presents a systematic review of adaptive filtering algorithms, especially Least Mean Squares (LMS), Filtered-x LMS (FxLMS), and Variable Step-size FxLMS (VSS-FxLMS) algorithms, used in piezoelectric smart structures. These algorithms play a crucial role in enhancing the performance and efficiency of AVC systems, allowing for better control and adaptation to varying vibration conditions. As the application of piezoelectric actuators and sensors for vibration suppression has expanded, adaptive algorithms have become essential for improving the convergence rate, stability, and precision of control. In particular, advancements in algorithmic design have focused on improving robustness under varying operating conditions and increasing the accuracy of suppression. The review highlights major algorithm developments, mathematical formulations, and performance comparisons, along with applications to piezoelectric beams, blades, and plates. While the VSS-FxLMS algorithm demonstrates improved robustness, comprehensive comparative studies across different applications remain limited. A numerical simulation is also presented to evaluate the convergence and vibration suppression performance. This work provides insights into current challenges, recent advances, and promising directions for future AVC system design. Specifically, it identifies the need for more research on real-time system integration, multimodal vibration reduction, and the scalability of adaptive algorithms for intricate, large-scale systems. The findings suggest that hybrid algorithms that incorporate the best features of each of the aforementioned approaches could greatly enhance future AVC systems.
Akbar et al. (Mon,) studied this question.