时滞不确定采样控制系统的鲁棒稳定性

Robust stability of sampled-data control systems with uncertain time-delays

中文关键词  鲁棒稳定性  采样控制系统  连续时间时滞  频率响应  时滞不确定性

英文关键词  robust stability  sampled-data control systems  continuous-time delay  frequency response  delay uncertainty

中文摘要

      本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法. 因为采样系统的对象是连续时间的, 所以对象中的时滞也应该是按连续时间来处理. 文中指出, 一个整数倍时滞是稳定的采样系统, 可能会因为有并不很大的连续时间时滞而失稳. 定义了一个新的变量w(t), 用来描述这个不确定连续时间时滞带来的动特性. 将w(t)的反馈回路分成与时滞无关和有关的两个部分, 并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法. 用修正z–变换法和仿真验证了这个由图解解析所求得的解. 本方法既可用于采样系统, 也可用于一般的连续时间系统.

英文摘要

      We propose a quantitative method for analyzing the robust stability of sampled-data systems with uncertain time-delays. Because the sampled-data systems are obtained from continuous-time systems by sampling, the time-delay in the sampled-data system must also be treated in the continuous-time system. It is pointed out that a stable sampled-data system with a time-delay equal to the integer-multiple of the sampling period may be destabilized by a small continuous time-delay. A new variable w(t) is defined to describe the dynamic response caused by the uncertain continuous timedelay. The feedback loop of w(t) is then divided into two parts. One depends on the uncertain time-delay, and the other is independent of the time-delay. A special frequency response method is proposed to determine the existence of the periodic solution of the system caused by the uncertain time-delay. The graphic-analytical solution is then verified by the modified z-transform method and by simulation. The proposed method can also be used for robust stability analysis of continuous-time systems with time-delays.