高超声速飞行器基于特征模型的自适应姿控系统稳定性分析

Stability analysis of a hypersonic vehicle controlled by the characteristic model based adaptive controller

文中研究了高超声速飞行器基于特征模型的全系数自适应姿态控制系统的稳定性问题,提出了一种通过计算有限个矩阵导出1范数或无穷范数来分析系统稳定性的方法,克服了特征模型时变和参数辨识给稳定性分析造成的困难.首先利用泰勒展开,获得高超飞行器姿态动力学输入输出描述的离散化方程.该组方程具有二阶特征模型的形式,可以分析出系统处于一个工作点附近时特征模型参数的取值范围.当使用线性反馈控制器,并引入一定保守性的情况下,可以将闭环系统看作一类由区间时变参数决定的时变对象.对于这样的一类对象,文中给出了其指数稳定的充要条件.最后利用前述结果,给出了判断高超声速飞行器基于特征模型的自适应控制系统稳定的充分条件,并通过一个算例来说明该方法的应用.

The closed loop attitude stability of a hypersonic vehicle controlled by the characteristic model-based all-coefficient adaptive controller is studied in this paper,and an algorithm based on the computation of induced matrix 1-norm or∞-norm is proposed.First of all,the Taylor series expansion is applied to discretize the inputoutput description of the attitude dynamics of the vehicle.The obtained diffierence equations have the same structure as characteristic model;thus the intervals which contain all possible values of certain characteristic model parameters are obtained.When the linear feedback controller is used in the feedback loop,with some conservation,the closed loop system is viewed as a class of interval time-varying systems defined by a number of free time-varying parameters.These free parameters take values from predefined intervals.The sufficient and necessary condition for the stability of this class of system is given.Finally,a sufficient condition for the stability of hypersonic vehicle attitude control loop is proposed and demonstration example is presented.The method proposed checks up the stability of the closed loop system by evaluating a finite number of matrix norms, and overcomes the difficulties brought by the time-varying nature of the characteristic model and parameter estimation.