多输入的二阶广义分布参数系统的控制综合问题  

The control synthesis problem for the second order singular distributed parameter system with multiple inputs

作　　者：刘锋[1] 葛照强[2] 史国栋[3] 

机构地区：[1]江苏技术师范学院数理学院,常州213001 [2]西安交通大学应用数学系,西安710049 [3]常州大学信息科学与工程学院,常州213164

出　　处：《中国科学：信息科学》2012年第11期1445-1458,共14页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:60674018);江苏省高校自然科学基金(批准号:08KJD510003)资助项目

摘　　要：广义分布参数系统具有广泛的实际背景.如复合材料中的温度分布,电缆中的信号传播,电磁耦合超导线路中的电压分布,飞行器姿态控制等问题研究中都会出现这样的系统.极点配置与反馈稳定性是这类系统研究的重要方面.本文应用泛函分析及算子理论讨论了Hilbert空间中多输入的二阶广义分布参数系统的极点配置与反馈稳定性问题,获得了这类系统极点可配置与可镇定的一些充分条件,并利用复分析、复级数、有界线性算子的广义逆等方法建立了反馈控制律的构造性表达式.本文结论不仅具有重要的实际意义,而且对广义分布参数系统的控制综合问题研究具有重要的理论价值.Singular distributed parameter system is widely applicable, for example, to the studies of the temper- ature distribution of composites, signal propagation in electrical cables, voltage distribution of electromagnetically coupled superconductive circuits, and aerocraft attitude control. Pole assignment and feedback stability are two important research aspects of the system. This paper, first of all, defines the pole assignment and feedback stability for the second order singular distributed parameter system with multiple inputs in Hilbert space, the subnegative definite operator, and the generalized inverse of the bounded linear operators, and presents some relevant properties; and then, it systemizes the second order singular distributed parameter system with multiple inputs into the first order singular distributed parameter system with multiple inputs by using the suitable trans- formation, which makes the two systems be of the same generalized eigenvalues, and discusses the pole assignment and feedback stability problems of the first order singular distributed parameter system with multiple inputs via functional analysis, operator theory and subnegative definite operator. Based on it, some sufficient conditions of the pole assagnment and stability of the second order singular distributed parameter system with multiple inputs in Hilbert space are obtained. It establishes the constructive expressions of the feedback control laws by using complex analysis, complex series and the generalized inverse of the bounded linear operators. The research results are not only of practical significance, but of important theoretical values for studying the control synthesis problem of the singular distributed parameter system

关 键 词：极点配置 反馈稳定性 广义分布参数系统 多输入 HILBERT空间 

分 类 号：O231[理学—运筹学与控制论] O177[理学—数学]