目的:针对一类具有时变时滞的非线性系统,设计状态控制器实现闭环系统输出对参考轨迹的H∞跟踪。创新点:利用统一模型表示所研究的时变时滞非线性系统,修正参考模型使其更具一般性,引入缩放系数提高系统的跟踪精度。方法:采用一个由线性时滞动态系统和有界静态非线性项组成的统一模型来描述所要研究的时变时滞非线性系统。完成系统建模后,首先给出参考轨迹跟踪的定义,以修正后的跟踪模型为参考轨迹,采用状态反馈法实现闭环控制(图1)。并对闭环系统的H∞性能进行分析,基于此分析结果推导得到以线性矩阵不等式形式表示的跟踪控制器参数所满足的条件。该条件可以确保闭环系统H∞意义下跟踪给定的参考信号。在控制器设计中引入缩放系数以提高跟踪精度。图2和图4分别给出跟踪控制器对正弦信号和方波信号的H∞跟踪;图3和图5则分别表示在正弦参考信号和方波参考信号输入下,缩放系数的变大对提高跟踪效果的具体影响。结论:针对一类具有时变时滞的非线性系统,以修正后的跟踪模型为参考轨迹,设计状态反馈控制器实现闭环系统输出对参考轨迹的H∞跟踪,并可通过增大缩放系数提高跟踪效果。 OBJECTIVE: To design a class of nonlinear systems with time-varying delays, a state controller is designed to achieve the H∞ tracking of the reference trajectory of the closed-loop output. Innovation point: The unified model is used to represent the nonlinear system under time-varying delay, the reference model is modified to make it more general, and the scaling factor is introduced to improve the tracking accuracy. Methods: A unified model consisting of a linear time-delay dynamic system and a bounded static nonlinear term is used to describe the nonlinear system to be studied. After completing the system modeling, the definition of reference trajectory tracking is given firstly. The modified tracking model is used as the reference trajectory and the closed-loop control is implemented by the state feedback method (Figure 1). The H∞ performance of the closed-loop system is analyzed. Based on the analysis results, the conditions of the tracking controller parameters expressed in terms of linear matrix inequalities are derived. This condition ensures that the given reference signal is tracked in the H∞ closed-loop system. Introduce a scaling factor in the controller design to improve tracking accuracy. Figure 2 and Figure 4, respectively, given tracking controller for sinusoidal signals and square wave H∞ tracking; Figure 3 and Figure 5, respectively, that the sine reference signal and the square wave reference signal input, the scaling factor increases to improve Track the specific effects of the effect. CONCLUSION: For a class of nonlinear systems with time-varying delay, the modified tracking model is taken as the reference trajectory. The state feedback controller is designed to achieve the H∞ tracking of the reference trajectory of the closed-loop output of the closed-loop system and can be improved by increasing the scaling factor Track the effect.