考虑饱和的发电机单机无穷大系统有限增益镇定

摘要：研究了一类具有饱和及外部干扰的发电机单机无穷大系统的鲁棒增益镇定问题.首先基于哈密顿能量理论将电机系统模型转化为广义耗散 哈密顿系统模型,然后运用静态输出反馈得到闭环哈密顿系统.在某增长条件下,证明了闭环系统可以达到渐近稳定和有限增益镇定, 同时得到了有限增益的估计值.仿真结果验证了所提方法的有效性.     

分析动力学的广义哈密顿原理

本文定义了三类新的可能运动，由此得到推广的拉格朗日函数；还定义了三种广义哈密顿作用量、由此建立了广义哈密顿原理。     

线性脉冲哈密顿系统的分岔分析和控制

通过将非线性形式的脉冲引进到线性哈密顿系统里,离散映射、利用中心流形理论和分岔理论讨论了线性脉冲哈密顿系统的复杂动力学性质.理论上分析了系统周期-1解的存在和稳定的条件、flip分岔的分岔条件,设计了一个线性脉冲控制器控制系统的动力学行为,给出了能验证理论分析结果的数值结论.     

基于端口耗散哈密顿系统的电机控制方法

为了满足永磁同步电机高精度、高动态性能的控制要求,提出了一种基于端口耗散哈密顿系统的电机控制方法.采用系统互联和阻尼结构配置的方式对永磁同步电机控制系统进行了设计,建立了d-q坐标系下的永磁同步电机数学模型,构造了端口耗散哈密顿系统的能量函数,利用IDA-PBC方法对电机速度控制器进行了设计.仿真结果表明,提出的控制策略只需要调节两个参数即可实现对电机的速度控制,减少了系统复杂性,利用负载扰动观测器作为前馈补偿,降低了噪声影响,加快了系统的响应速度,提高了系统运行的稳定性.     

异步电动机哈密顿控制系统的建模与仿真

采用哈密顿系统理论对异步电动机进行建模与速度控制。应用端口受控哈密顿系统理论,建立了异步电动机的非线性PCH数学模型及仿真模型,设计了系统的控制器和负载转矩观测器,分析了系统平衡点的稳定性。在Matlab/Simulink中,搭建异步电动机哈密顿控制系统的仿真模型。仿真结果表明,所提出的方案对负载扰动具有很强的鲁棒性。     

再生哈密顿回路的边数条件

为了缩小最短哈密顿回路的搜索空间,从而提高TSP算法的搜索效力;并依据图论中邻点交叉边的性质,对哈密顿回路内边进行全面分析和统计,给出和证明了再生哈密顿回路的边数条件P(n),这在图论中是未曾有过的.进而证明了最短哈密顿回路必至少含有前P(n)条小边之一的结论.该结论可广泛应用于TSP搜索算法中,减少搜索时间.     

基于能量成型的永磁同步直线电机控制研究

针对永磁同步直线电机(LPMSM)速度控制问题,从能量成型的观点出发,将其看作能量转换装置,采用端口受控耗散哈密顿(PCHD)理论推导出LPMSM系统的端口受控哈密顿模型.在哈密顿结构基础上利用互联和阻尼配置,给出闭环系统期望的哈密顿函数,对速度控制器进行了设计.设计中直接采用哈密顿函数作为存贮函数,使系统在满足无源性的条件下达到了要求的性能,具有明确的物理意义.仿真结果表明,设计的闭环控制系统能够快速响应负载阻力的变化,具有良好的鲁棒性.     

高维力学系统的能量方程

在低维系统中,能量方程因其明晰的物理意义而得到广泛的应用,而研究高维力学系统的能量方程也同样具有理论价值和实际意义,如位移对时间的导数是速度,速度对时间的导数是加速度,这些具有明显的物理意义,而加速度的导数其物理意义就不是很清晰了,但具有理论上的意义.本文应用广义经典力学中关于广义拉格朗日函数、广义动量和广义哈密顿函数等概念,推导了高维系统的能量方程,文中举了实例具体说明新方程的应用,为力学数学系统能量方程的推广提供了一种途经.     

离散哈密顿系统的几个结论

给出了离散哈密顿系统的几个结论和Ｐｉｃｏｎｅ恒等式，其结果是连续哈密顿系统相应结果的离散化。     

三相PWM整流器的状态误差PCH控制与仿真研究

采用一种新的状态误差端口受控哈密顿(PCH)和能量成形控制方法,实现三相电压型PWM整流器的单位功率因数和输出直流电压恒定控制。在d-q旋转坐标系下给出三相电压型PWM整流器的PCH模型,构建了期望的闭环状态误差PCH系统。根据系统的设计目标和引入比例积分控制确定期望的平衡点。基于能量成形原理选取了期望的闭环哈密顿函数,通过互联和阻尼配置设计了控制器。利用SVPWM信号变换控制整流桥。仿真结果表明,系统达到了控制目标且具有良好的负载扰动抑制能力。     

一类广义Hamilton系统的有限时间稳定性及其在仿射非线性系统控制设计中的应用

研究了一类广义Hamilton系统的有限时间稳定性及其在仿射非线性系统控制设计中的应用,并给出几个新结果。利用Hamilton系统的结构特性和已有的关于局部有限时间稳定的结果,给出该类Hamilton系统有限时间稳定的几个判定准则。把得到的新结果应用于仿射非线性系统的有限时间控制设计中。通过选取恰当的Hamilton函数,并利用正交分解Hamilton实现及阻尼注入技术,为一类仿射非线性系统设计了一类有限时间控制器。给出两个例子以验证本文结论的有效性。     

Geometric structure of generalized controlled Hamiltonian systems and its application

The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the co-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, called N-group, and its Lie algebra, called N-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.     

Poisson流形上广义Hamilton系统的保结构算法

Poisson流形是研究广义Hamilton系统的恰当几何结构。本在Poisson流形上讨论广义Hamilton系统的保结构的数值解法，为广义Hamilton系统的数值计算提供了理论基础。中通过算例证明了算法的保结构性和稳定性，同时说明了该算法可以推广到广义Hamilton控制系统。     

Hamiltonian realization of power system dynamic models and its applications

Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely researched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Hamiltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hamiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no linearization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized. Supported in part by the National Natural Science Foundation of China (Grant Nos. 50707009 and 50525721), in part by Program for Changjiang Scholars and Innovative Research Team in University under IRT0515 and in part by Ministry of Education of China (Grant No. 20070079014)     

Uncountable Infinity of Periodic Solutions of Some Nonlinear Autonomous Differential－Difference Equations

ＵｎｃｏｕｎｔａｂｌｅＩｎｆｉｎｉｔｙｏｆＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｏｆＳｏｍｅＮｏｎｌｉｎｅａｒＡｕｔｏｎｏｍｏｕｓＤｉｆｆｅｒｅｎｔｉａｌ－ＤｉｆｆｅｒｅｎｃｅＥｑｕａｔｉｏｎｓＬｉＪｉｂｉｎ，ＺｈａｏＸｉａｏｈｕａ，ＬｉｎＹｉｐｉｎｇ（...     

三角网格的统一单分辨率与多分辨率表示方法

通过三角形之间的拓扑相邻关系,将最高分辨率的三角网格划分为广义三角形带的集合,然后利用Hamiltonian三角剖分的性质对广义三角形带进行简化,从而构造三角网格的多分辨率表示.该方法统一了单分辨率网格和多分辨率网格的表示方法,当模型有c个不同分辨率的表示时,其编码效率与c的对数成正比.     

P(n,2)的Hamilton圈的计数

本文给出了广义 Petersen图 P(n,2)的Hamilton圈的个数的计算公式.     

铁摩辛柯梁弯曲问题的对偶求解体系

从能量变分原理出发,由勒让德变换引入对偶变量,导出了Timoshenko梁弯曲问题的哈密顿对偶求解体系,将梁的控制微分方程转化为哈密顿对偶方程,为借鉴现代控制理论的方法求解Timoshenko梁弯曲问题建立了理论基础。     

Qualitative analysis of the CCEBC/EEAC method

The CCEBC/EEAC method is an effective method in the quantitative analysis of power system transient stability. This paper provides a qualitative analysis of the CCEBC/EEAC method and shows that from a geometrical point of view, the CCCOI-RM transformation used in the CCEBC/EEAC method can be regarded as a projection of the variables of the system model on a weighted vector space, from which a generalized P-δ trajectory is obtained. Since a transient process of power systems can be approximately regarded as a time-piecewise simple Hamiltonian system, in order to qualitatively analyse the CCEBC/EEAC method, this paper compares the potential energy of a two-machine infinite bus system with its CCEBC/EEAC energy. Numerical result indicates their similarity. Clarifying the qualitative relation between these two kinds of energies is significant in verifying mathematically the CCEBC/EEAC method for judging the criterion of power system transient stability. Moreover, the qualitative analysis of the CCEBC/EEAC