单输入单输出微分代数系统的多指标非线性控制方法

针对含隐函数的单输入单输出微分代数系统,提出多指标非线性控制设计方法,以确保各状态量均具有良好的动、静态性能。借助于哈特曼–格鲁勃曼(Hartman-Grobman)定理推证非线性微分代数系统对应的一次近似系统的特征根与输出函数中参数矩阵(c1,c2)之间的关系,从而揭示了该方法的实质。将该方法应用于非线性微分代数模型的发电机单机无穷大系统中,设计了一个多指标的非线性励磁控制律。仿真表明:该控制律既能增强系统的稳定性,又能提高发电机机端电压控制精度,使各个状态量快速地追踪其给定值。说明该方法能有效地解决微分代数系统的动、静态性能的协调问题。

Multi-index Nonlinear Control Design for SISO Differential Algebraic System

This paper proposed the multi-index nonlinear control design method for simple-input simple-output(SISO) differential algebraic system with implicit function(DASMINC) in order to ensure all states of the system have excellent dynamic and steady-state performances.By means of Hartman-Grobman theorem,this paper deduced the relationship between parameter matrix(c1,c2) and characteristic roots of linear approximate system to nonlinear differential algebraic system.Therefore,the essence of DASMINC is revealed.Applying the method to single machine infinite bus system,which belong to a nonlinear differential algebraic model,a multi-index nonlinear excitation control law was designed.Simulation results show that the control law can enhance the stability of the system,improve the regulative precision of generator terminal voltage,and make each state trace for their given values rapidly.It manifests that the proposed method can effectively coordinate the dynamic and the steady-state performances for nonlinear differential algebraic system.