线性跟踪系统Lyapunov函数性质及其应用

The Nature of the Lyapunov Function and Its Application in the Linear Tracking System

研究了线性跟踪系统Lyapunov函数性质,并基于该性质进行控制系统设计研究,给出控制器结构和Lyapunov函数取值估计;首先,以经典三回路为基础建立线性闭环跟踪系统微分方程;在完成系统数学模型的基础上,给出线性跟踪系统Lyapunov函数对时间的一阶导数为非负,二阶导数为非正,即线性跟踪系统Lyapunov函数最大值不是在系统的初始状态而是稳定状态这一论点;进而基于该Lyapunov函数性质对控制系统进行设计和Lyapunov函数取值进行研究;最后通过仿真验证,仿真结果表明所提出的线性跟踪系统Lyapunov函数性质、控制器设计和Lyapunov函数取值估计是正确的。

The nature of the Lyapunov function of the linear tracking system is researched,given the structure of the controller and the estimated value of the Lyapunov function based on the nature.First,the linear differential equation of the closed-loop tracking system is established based on the classic three-loop autopilot structure;based on the Lyapunov function,given the theorem： the first derivative of a linear tracking system is non-negative,the second derivative is non-positive,and the maximum of the Lyapunov function is in steady state not in the initial state of the system.Then the control system is designed and the maximum of the Lyapunov function is evaluated based on the nature of the Lyapunov function.Finally simulation results show that the nature of the Lyapunov function of linear tracking system,the controller and the Lyapunov function value are correct.