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

Abstract

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.

H∞ control of periodic piecewise vibration systems with actuator saturation

“…However, since the two processes, that is, system modeling and controller updating, are coupled, it may result in accumulated errors, amplified vibration and destabilized systems (Kim and Swanson, 2005). Moreover, the convergence of the two processes may not be synchronous; it is hard to tell whether the controller is optimal after both of them converge (Wang and Mak, 2014). A control strategy including adaptive identification combining with nonadaptive control was proposed in Wang and Mak (2014), which decouples the two processes, and the optimal controller can be guaranteed when the identification process converges.…”

“…Moreover, the convergence of the two processes may not be synchronous; it is hard to tell whether the controller is optimal after both of them converge (Wang and Mak, 2014). A control strategy including adaptive identification combining with nonadaptive control was proposed in Wang and Mak (2014), which decouples the two processes, and the optimal controller can be guaranteed when the identification process converges. However, this kind of active vibration control calls for fast online processing, which leads to a high cost.…”

Simulation and experiment on the performance of a passive/active micro-vibration isolator

“…Due tod ðzÞ ¼ d ðzÞ ÀHðzÞ À HðzÞ À Á uðzÞ, there isd ðnÞ ¼ d ðnÞ whenHðzÞ ¼ HðzÞ. Thus, the identification precision of the FIR model is of great significance to guarantee the control performance of the system (Rustighi et al, 2011;Zhang et al, 2012;Wang and Mak, 2014).…”

Multi-frequency micro-vibration control with hybrid adaptive control algorithm

“…Active vibration control (AVC) is commonly used to suppress the low-frequency vibration as the passive vibration control techniques are ineffective in many applications. Filtered x least mean square (FxLMS) algorithm is popular in single-frequency narrowband AVC system as its rapid convergence and easy to use (Wang and Mak, 2016). In fact, vibration disturbance often contains several narrowband frequency components.…”