一类时滞线性系统的变结构振动控制

VARIABLE STRUCTURE CONTROL OF A CLASS OF LINEAR TIME-DELAY SYSTEMS

应用自适应性和鲁棒性良好的变结构控制理论 ,研究时滞影响下机械和结构的振动问题 ,给出控制律的等速趋近律设计方法和系统稳定性与时滞量无关的判据 ,排除时滞带给系统稳定性分析的困扰。算例结果表明 ,所提出的变结构控制方法能有效地减小时滞振动系统的峰值响应 。

The stability of linear time-delay systems is usually analyzed by Lyapunov method in the field of mathematics and control. For this case, the system is asymptotically stable if all the infinite roots of system characteristic polynomial have negative real parts. However, it is difficult to carry out in practical applications. Variable structure control is a good way to design controller with self-adaptiveness and robustness. In this paper, it can be used to discuss the vibration problems of mechanism and structures with time-delay. The controller is designed by using the constant-speed approach law and the stability criterion independent of delay information, making the stability analysis of structure vibration with time-delay straightforward. The numerical simulation results demonstrate that the peak-response is reduced under the control and the stability is preserved.