Control of friction oscillator by Lyapunov redesign based on delayed state feedback  

作　　者：Zhicong Li Qi Wang Haiping Gao 

机构地区：[1]School of Science, Beihang University,Beijing 100083, China [2]School of Science, Hebei University of Science and Technology,Shijiazhuang 050018, China

出　　处：《Acta Mechanica Sinica》2009年第2期257-264,共8页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (10672007)

摘　　要：The stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated by proposing a controller design method. Firstly a sufficient condition of the stability for the nominal system with delayed state feedback is derived by constructing a Lyapunov-Krasovskii function. The delayed feedback gain matrix is calculated by applying linear matrix inequality method. Secondly on the basis of the delayed state feedback, a continuous function is designed by Lyapunov redesign to ensure that the solutions of the friction oscillator system are ultimately bounded under the overall control. Moreover, the ultimate bound can be adjusted in practice by choosing appropriate parameter. Accordingly friction-induced vibration or instability can be controlled effectively. Numerical results show that the pro- posed method is valid.The stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated by proposing a controller design method. Firstly a sufficient condition of the stability for the nominal system with delayed state feedback is derived by constructing a Lyapunov-Krasovskii function. The delayed feedback gain matrix is calculated by applying linear matrix inequality method. Secondly on the basis of the delayed state feedback, a continuous function is designed by Lyapunov redesign to ensure that the solutions of the friction oscillator system are ultimately bounded under the overall control. Moreover, the ultimate bound can be adjusted in practice by choosing appropriate parameter. Accordingly friction-induced vibration or instability can be controlled effectively. Numerical results show that the pro- posed method is valid.

关 键 词：TIME-DELAY Nonsmooth system Linear matrix inequality （LMI） Dry friction oscillator Ultimate boundedness 

分 类 号：O175.13[理学—数学] TP13[理学—基础数学]