An active vibration control system with decoupling scheme for linear periodically time-varying systems

For the active vibration control (AVC) of periodically time-varying systems, the filtered-x least mean squares (FXLMS) method is widely applied. Many AVC systems based on FXLMS employ two coupled adaptive processes - online modeling or identification and controller updating - to track the parametric change and realize the real-time updating of the control signal. Errors in one process can affect the other. When one process converges, it takes several steps for the other process to converge. After they both converge, it is difficult to tell whether the controller is optimal or not. Therefore, it is difficult to evaluate the influence of the coupling effect and perform a rigorous derivation. In this study, the new AVC system adopts adaptive identification and non-adaptive control to avoid the coupling effect, and the necessary condition for decoupling is obtained. This condition guarantees that the optimal controller can be obtained the moment the system identification process converges, and meanwhile boosts the convergence of the identification process. The robustness of the identification process with the self-tuning mechanism and the optimization of the controller are proved by rigorous derivation. A simple but representative numerical verification is presented to verify the effectiveness of the proposed AVC system.