金属加工控制微分方程的广义拟近似解研究  

Study on Generalized Quasi Approximate Solution of Differential Equation of Metal Processing Control

作　　者：陈艳君[1] 陈婷婷[1] 

机构地区：[1]南昌大学科学技术学院,江西南昌330029

出　　处：《世界有色金属》2015年第12期96-97,共2页World Nonferrous Metals

摘　　要：金属加工是一个精细化系统控制工程,金属加工控制采用的是二阶超稳定常微分方程控制方法,对该类微分方程的广义你近似解的稳定性分析,提高金属加工控制的稳定性,为解决系统的稳定性控制问题提供数学理论基础。采用向量Lyapunov函数方法进行金属加工控制的泛函分析,得到了金属加工控制中二阶超稳定常微分控制方程超稳定解。给出了广义拟近似解稳定性定理,进行数学推导和证明。分析表明,金属加工控制的二阶超稳定常微分方程的广义拟近似解的渐进稳定的,提高了金属加工的精密控制的可靠性。Metal processing is a fine system control engineering, metal processing control is the two order of the stability of ordinary differential equations, the stability of the differential equation for the stability of the approximate solution to improve the stability of the metal processing control, to provide a theoretical basis for the stability of the system. Using the functional analysis of the Lyapunov function method to control the metal processing, the super stable solutions of the two order super stable ordinary differential equations are obtained. The stability theorem of the generalized quasi approximate solution is given, and the mathematical derivation and proof are given. The analysis shows that the asymptotic stability of the two order of the control of the metal processing is asymptotically stable, which improves the reliability of metal processing.

关 键 词：金属加工控制 稳定性 微分方程 

分 类 号：O231[理学—运筹学与控制论]