Wang Kai, Xu Wei
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China.
Sensors (Basel). 2024 Feb 29;24(5):1600. doi: 10.3390/s24051600.
This paper is concerned with the stability analysis and design of the -DOF (-degree-of-freedom) mass-chain vibration systems containing both semi-active and passive mechanical controllers. Based on Lyapunov's stability theory, sufficient conditions are derived for the -DOF vibration system containing a semi-active switched inerter and a passive mechanical network with the first-order admittance to be globally asymptotically stable. Furthermore, the optimization designs of a quarter-car vibration control system and a three-storey building vibration system are conducted together with the derived stability results, and the instability cases contradicting the stability conditions are presented for illustration. The optimization and simulation results show that the combination of semi-active and passive mechanical controllers in vibration systems can clearly enhance system performances in comparison with the conventional semi-active or passive control. The novelty of this paper is that the stability problem of a general -DOF vibration system that simultaneously contains a semi-active controller and a first-order passive controller is investigated for the first time, where such a system combines the advantages of both semi-active and passive mechanical controllers. The investigations and results can provide an essential foundation for further exploring the stability problems of more general systems, and can be applied to the controller designs of many vibration systems in practice.
本文关注包含半主动和被动机械控制器的-DOF（自由度）质量链振动系统的稳定性分析与设计。基于李雅普诺夫稳定性理论，推导了包含半主动开关惯量器和具有一阶导纳的被动机械网络的-DOF振动系统全局渐近稳定的充分条件。此外，结合推导的稳定性结果对四分之一汽车振动控制系统和三层建筑振动系统进行了优化设计，并给出了与稳定性条件相悖的不稳定情况进行说明。优化和仿真结果表明，与传统的半主动或被动控制相比，振动系统中半主动和被动机械控制器的组合能够显著提高系统性能。本文的新颖之处在于首次研究了同时包含半主动控制器和一阶被动控制器的一般-DOF振动系统的稳定性问题，该系统兼具半主动和被动机械控制器的优点。这些研究和结果可为进一步探索更一般系统的稳定性问题提供重要基础，并可应用于实际中许多振动系统的控制器设计。
