非线性微分-代数子系统的逆系统的构造

Construction of Inverse System for Nonlinear Differential-algebraic Equations Subsystems

对于一类非线性微分-代数(Differential-algebraic equation,DAE)子系统,将非线性常微分方程(Ordinary differ- ential equation,ODE)系统的逆系统方法进行了完全扩展,首先对此类非线性DAE子系统提出的物理背景和系统特性进行了详细阐述,然后给出了非线性DAE子系统的逆系统定义,包括单位右逆系统和α阶积分右逆系统,接下来提出一种递归算法,利用此算法给出了被控系统可逆的充要条件,并构造了物理可实现的控制器,实现了非线性DAE子系统的线性化解耦,最后基于本文所提出的控制方法,研究了电力系统同步发电机组励磁汽门综合控制的线性化解耦问题。

For a class of nonlinear differential-algebraic equation （DAE） subsystems, the method of inverse system for nonlinear ordinary differential equation （ODE） systems is expanded completely in this paper. At first, the background and the particularities of such systems are expatiated. Then, the definitions of inverse system （including unit right inverse system and a-order right inverse system） are put forward. A recursive algorithm is given, based on which the sufficient and necessary conditions for the invertibility of the nonlinear DAE subsystems are presented. After that, a feasible controller design scheme is proposed to decouple and linearize the nonlinear DAE subsystems. At last, the linearization for excitation and valve coordinative control of one turbo-generator set within power systems is studied based on the control method presented in this paper.