基于阻抗特性多项式拟合的直驱风电机组次同步振荡稳定判据

近年来,阻抗分析法已成为分析新能源发电并网系统稳定性问题的一种主要研究方法。以直驱风电机组并网系统为例,分析了现有的奈奎斯特（Nyquist）稳定判据的特点和适用范围。为了弥补现有阻抗稳定判据的不足,提出了一种基于阻抗特性分式多项式函数拟合的量化稳定判据,采用分式多项式函数等效拟合理论推导或实测的风电机组端口阻抗特性,在拟合频段内分式多项式与原阻抗特性等价。通过求取拟合多项式零点获得了系统振荡频率和阻尼水平,量化分析了系统稳定特性,拓展了阻抗稳定判据的适用范围。最后,通过理论分析和时域仿真验证了分式多项式拟合判据的正确性和有效性。     

具有时滞和阶段结构的L-V竞争系统的稳定性分析

具有阶段结构的L-V时滞竞争系统是一类重要的反映种群竞争关系的生态系统,它考虑了时滞效应以及不同阶段幼体和成体竞争能力差异.本文讨论了一类具有两个时滞和阶段结构的L-V竞争系统平衡点的局部稳定性以及正平衡点的全局稳定性.根据Hurwitz判据,我们得到了该系统平衡点局部稳定的条件;依据单调系统的相关理论以及迭代法,我们...     

中立型灰色随机分布时滞系统的指数鲁棒稳定性

为了得到一类中立型灰色随机分布时滞系统的指数鲁棒稳定性,本文利用Lyapunov-Krasovskii泛函法、灰矩阵的连续矩阵覆盖的分解技术和Ito公式,分别得到了以非线性矩阵不等式和线性矩阵不等式(LMI)表示的该系统指数鲁棒稳定的时滞依赖性判据。对非线性矩阵不等式判据,我们给出了一般性算法,解决了非线性矩阵不等式判据不便于实际应用的问题。数值例子表明,本文所给判据是有效的,且系统的指数稳定性和时滞,随着绝对灰度矩阵的谱范数的增大而减小。     

基于频域的多变量广义预测控制（MIMO-GPC）稳定性分析

提出了基于频域的多变量广义预测控制（MIMO-GPC）稳定性分析方法，推导了MIMO-GPC的闭环反馈结构，给出了基于闭环特征多项式的MIMO-GPC的稳定性判据和奈奎斯特稳定性判据。这些判据可作为MIMO-GPC控制器参数设计的重要依据。     

一类不连续系统的Φ-变差稳定性

本文借助Φ-有界变差函数理论,讨论了一类不连续系统的Φ-有界变差解的稳定性,给出了该类不连续系统的Φ-变差稳定、Φ-变差吸引以及渐近Φ-变差稳定的定义,建立了Φ-有界变差解Φ-变差稳定性和渐近Φ-变差稳定性的Lyapunov型定理。该结果是对一类不连续系统变差稳定性定理的本质推广。     

一类固定时刻脉冲微分系统的Φ-变差稳定性

本文借助Φ-有界变差函数理论,以及一类不连续系统的Φ-有界变差解的稳定性理论,讨论了一类固定时刻脉冲微分系统的Φ-变差稳定性,给出了该类脉冲微分系统的Φ-变差稳定、Φ-变差吸引以及渐近变差稳定的定义,建立了该类脉冲微分系统Φ-有界变差解的Φ-变差稳定性和渐近Φ-变差稳定性的Lyapunov型定理.     

钨带灯的稳定性判据试验

我们通过对国产ＢＷ—１４００型真空钨带灯的稳定性判据进行研究，发现通过钨带灯的电流达到稳定的时间很短（小于５分钟），而钨带灯的灯电阻需要经过２０分钟后才能达到稳定，因此，用电流稳定性作为钨带灯的热平衡判据是不够的，更可靠的判据还应看灯电阻是否达到平衡。     

直流分布式电源系统稳定性判据研究综述

在实际工程应用中,需要利用稳定性判据判断直流分布式电源系统（direct current distributed power system,DCDPS）的稳定性,以便采取合适的控制策略。因此,DCDPS稳定性判据成为国内外学者研究的热点。对基于等效源变换器（子系统）和负载变换器（子系统）的稳定性判据、基于母线电压控制变换器和母线电流控制变换器的稳定性判据、基于无源性的稳定性判据、大扰动信号情况下稳定性判据的基本思想、特点进行分析。指出这些稳定性判据的优点与不足,给出了DCDPS稳定性判据研究的趋势,提出了基于无源性的稳定性判据和其他判据相结合的稳定性判断新方法。     

下肢外骨骼系统稳定性分析和步态控制研究

本文在传统ZMP稳定性判据的基础上对ZMP稳定性判据进行了改进,建立了人的外界干扰因素对系统稳定性的影响的数学模型,然后对下肢外骨骼人机系统的运动过程稳定性进行研究,按最大稳定裕量原则对步态进行优化。为了在不同情况下保持平衡,提出了步幅、调整新的控制措施。通过仿真实例验证了所提出方法的正确可行性。     

带有食饵保护的Holling-Ⅲ型扩散捕食系统的稳定性分析

本文研究了一类具食饵保护的Holling-Ⅲ型扩散捕食系统,带有齐次Neumann边界条件.首先,讨论了系统的全局吸引性;其次,给出了系统正常数平衡态局部/全局渐近稳定的充分条件,这些条件依赖于食饵保护参数;特别地,获得了扩散对系统常数平衡态稳定性的影响,即当扩散系数较大时可使得常数平衡态不稳定.     

Stability of schur polynomials under coefficient perturbation

Abstract

In this paper, we are concerned with the stability robustness of characteristic polynomials with perturbed coefficients for linear discrete‐time systems. An upper bound on the allowable coefficient perturbation of a Schur polynomial with retaining stability is obtained. The proposed upper bound is directly formulated in terms of the polynomial under consideration and its value can be determined by numerical computation. We also provide a sufficient condition for the stability of interval polynomials.     

Global asymptotic stability in a model of networks

Global asymptotic stability is of importance from a theoretical as well as an application point of view in several fields. We study a system of cubic polynomials that models biological networks. We classify the equilibria and show that the property that the interconnection matrix is Lyapunov diagonally stable is a key feature that determines convergence to a single equilibrium. The results are applied to chains of negative edges, cycles, and to interconnected graphs. We give numerical examples and study network graphs obtained from a model of the Drosophila circadian clock.     

Analytical solutions of coupled-mode equations for multiwaveguide systems, obtained by use of Chebyshev and generalized Chebyshev polynomials

A novel approach is proposed for obtaining the analytical solutions of the coupled-mode equations (CMEs); the method is applicable for an arbitrary number of coupled waveguides. The mathematical aspects of the CMEs and their solution by use of Chebyshev polynomials are discussed. When mode coupling between only adjacent waveguides is considered (denoted weak coupling), the first and second kinds of the usual Chebyshev polynomials are appropriate for evaluating the CMEs for linearly distributed and circularly distributed multiwaveguide systems, respectively. However, when one is considering the coupling effects between nonadjacent waveguides also (denoted strong coupling), it is necessary to use redefined generalized Chebyshev polynomials to express general solutions in a form similar to those for the weak-coupling case. As concrete examples, analytical solutions for 2 x 2, 3 x 3, and 4 x 4 linearly distributed directional couplers are obtained by the proposed approach, which treats the calculation as a nondegenerate eigenvalue problem. In addition, for the 3 x 3 circularly distributed directional coupler, which gives rise to a degenerate eigenvalue problem, an analytical solution is obtained in an improved way. Also, for comparison and without loss of generality, to clarify the difference between the two coupling cases, analytical solutions for a 5 x 5 circularly distributed directional coupler are obtained by use of the usual and the redefined generalized Chebyshev polynomials.     

Stability of linear time‐periodic delay‐differential equations via Chebyshev polynomials

This paper presents a new technique for studying the stability properties of dynamic systems modeled by delay‐differential equations (DDEs) with time‐periodic parameters. By employing a shifted Chebyshev polynomial approximation in each time interval with length equal to the delay and parametric excitation period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. This defines a linear map which is the ‘infinite‐dimensional Floquet transition matrix U’. Two different formulas for the computation of the approximate U, whose size is determined by the number of polynomials employed, are given. The first one uses the direct integral form of the original system in state space form while the second uses a convolution integral (variation of parameters) formulation. Additionally, a variation on the former method for direct application to second‐order systems is also shown. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. An extension of the method to the case where the delay and parametric periods are commensurate is also shown. Stability charts are produced for several examples of time‐periodic DDEs, including the delayed Mathieu equation and a model for regenerative chatter in impedance‐modulated turning. The results indicate that this method is an effective way to study the stability of time‐periodic DDEs. Copyright © 2004 John Wiley & Sons, Ltd.     

锤击桩的定向稳定性问题

为了讨论锤击桩在打入时的定向稳定性,本文发展了一种分析方法。由假定桩顶的作用力呈周期变化从而导得Mathieu方程。对于不同类型的土,桩的临界长度可以以Mathieu方程的稳定界限得到。恒定作用力的情况可以作为本文的一个特例。     

某大跨度网壳结构的稳定性分析

稳定性分析是网壳结构,特别是单层网壳结构设计中的关键问题。该文以某大跨度球类馆为工程实例,采用非线性有限元法针对承载力计算时的11种工况进行整体稳定计算,考虑了材料和几何非线性,对实际工程进行了第一类和第二类稳定分析,其中,第二类稳定分析采用截面边缘纤维屈服准则,该文给出了两种典型工况的第一类稳定屈曲模态和两类稳定系数。结果表明:该网壳结构的第一类稳定符合相关规范的要求;其第二类稳定性较差。因此,第二类稳定分析应该受到重视。     

利用Zernike多项式对湍流波前进行波前重构

分析了利用Ｚｅｒｎｉｋｅ多项式进行波前重构时模式耦合与混淆产生的原因，以及模式耦合与混淆对受大气湍流影响的光学波前进行波前重构的精度和稳定性的影响。取除去平移的前６５项Ｚｅｒｎｉｋｅ多项式构造湍流波前。针对６１单元自适应光学系统的波前传感器子孔径布局进行仿真，通过比较Ｎｓ不同取值时的湍流波前重构精度和稳定性，得出了该条件下Ｎｓ的最佳取值。     

悬挂建筑框架结构弹性稳定性估算方法

悬挂建筑框架结构是获得建筑大空间的可选方案。结构的稳定性是设计中的重要问题。本文先介绍悬挂建筑框架结构稳定性的计算模型。然后采用力矩分配法推出临界荷载的估算公式，并给出实用曲线。最后针对典型的悬持建筑结构，讨论弹性稳定性。所提出的方法对悬挂建筑结构的设计有重要作用     

The stability of stars of triangular equilibrium plate elements

Equilibrium models for finite element analyses are becoming increasingly important in complementary roles to those from conventional conforming models, but when formulating equilibrium models questions of stability, or admissibility of loads, are of major concern. This paper addresses these questions in the context of flat plates modelled with triangular hybrid elements involving membrane and/or flexural actions. Patches of elements that share a common vertex are considered, and such patches are termed stars. Stars may be used in global analyses as assemblies of elements forming macro‐elements, or in local analyses. The conditions for stability, or the existence and number of spurious kinematic modes, are determined in a general algebraic procedure for any degree of the interpolation polynomials and for any geometric configuration. The procedure involves the determination of the rank of a compatibility matrix by its transformation to row echelon form. Examples are presented to illustrate some of the characteristics of spurious kinematic modes when they exist in stars with open or closed links. Copyright © 2008 John Wiley & Sons, Ltd.     

Rays and fields in general astigmatic resonators

General astigmatic (GA) resonators are discussed in detail. Eigenrays, eigenmodes and eigenvalues (Gouy-factors) of this resonator are evaluated. A stability diagram for such resonators is introduced, which clearly depicts the stable and unstable regions for rays as well as for fields. Eigenrays and their stability regions are evaluated using the ABCD-law. For the beam propagation Collins' integral and the second moment method are applied. The eigenfunctions for rectangular symmetry are the generalized Hermite polynomials multiplied by the Gaussian exponential factor. It is shown that for general astigmatic resonators these polynomials are the product of normal Hermite polynomials. The generating function of the eigenfunctions depends on the special resonator. It is a useful tool for all calculations and it is determined. Furthermore it is shown that the second moment characterization of the modes is a useful and easy to handle procedure to evaluate beam width, beam divergence, radius of curvature and twist of the generalized Gauss–Hermite functions.