状态反馈事件触发控制系统的分析与设计

Stability Analysis and Design of a State-Feedback Event-Triggered Control System

针对线性系统状态反馈事件触发控制在工程应用中仅使用单一动态门限或静态门限存在Zeno现象的缺点,提出了动静门限相结合的事件触发机制。将闭环控制系统建模为脉冲系统模型,应用脉冲系统理论,导出了确保控制系统稳定的触发机制参数确定定理,得到了便于实现触发机制门限参数设计的线性矩阵不等式条件。针对确保系统稳定的触发机制门限参数可在一个区间内选择的特点和静态门限分量大小影响系统稳态区域大小的特点,进一步提出了变门限触发机制,可使系统在稳态情况下自动将静态门限分量减小,显著减小稳定区域,提升事件触发控制的稳态性能,从而可实现精确控制。定量仿真表明,变门限触发机制可以在通信资源消耗量几乎相同的情况下将稳态范围缩小到固定门限方法的12.3%。

In practical engineering systems,event-triggered control only using dynamic or static threshold may cause Zeno behavior.In order to avoid the Zeno behavior,an event-triggering mechanism composed of static and dynamic threshold is proposed.The event-triggered control system is modelled in the form of impulsive system.Impulsive system theory is employed to deduce the stability theorem,which can be used to determine the parameters of event-triggering mechanism,and also a useful linear matrix inequality（LMI）form is given.Based on the characteristics of the event-triggering mechanism and relationship between the static threshold and steady state performance,a variable threshold event-triggering mechanism is proposed.When the system works in a steady state,this mechanism can decrease the static threshold automatically to reduce the steady state region and improve the steady state performance,which means the mechanism can be used in high-accuracy control.Quantitative simulation results show that,compared with the fixed threshold event-triggering mechanism,this variable threshold event-triggering mechanism can reduce the steady state region to 12.3percent with the same consumption of communication resources.