基于二阶矩阵微分方程的机械振动系统线性二次型调节器设计

本文讨论机械振动系统线性二次型状态调节器（LQR）问题，直接针对系统二阶运动微分方程，性能指标为一个依赖于二阶导数的泛函。由欧拉-拉格朗日方程得出一个系统矩阵增广的二阶线性微分方程，指出该方程稳定的特征对就是最优控制振动系统闭环特征对，并给出求解最优控制状态反馈矩阵的方法，另外，由本文方法还可得出基于速度和加速度反馈的最优控制反馈矩阵。这里不涉及求解代数矩阵Riccati方程。     

土—结构系统随机地震响应的频—时域影响函数法

提出了分析土－结构系统随机地震响应的频－时域影响函数法。假定地震激励为具有演变谱的非平稳Ｇａｕｓｓ过程，土－结构系统为具有滞后型材料阻尼的线性时不变系统。采用频域的有限元复反应分析方法，首先确定土－结构系统的频率影响函数，然后通过快速富氏逆变换求得单位脉冲影响函数，根据线性时不变系统对随机激励的传递关系，确定系统非平稳均方响应及其谱参数，由此确定系统响应的概率分布特征和统计参数以及系统的动力可靠度     

一种改善测量系统动态特性的数字补偿方法

本文研究了提高和改善工程测试系统动态特性的原理和方法，并针对线性时不变系统提出了一种实用的数字补偿方法以及相应的计算机控制系统，由于在补偿方法中采用子数字滤波和样条插值技术，使得所建立的控制系统对任意的输入作用都具有良好的稳定性和补偿效果。     

论常数变异法解一阶线性常微分方程

常数变异法式求解微分方程的一种重要方法，本文主要介绍了如何利用常数变异法求解一阶线性常微分方程。     

谐波理论在机车控制中的应用

机车系统的稳定性在很大程度上依赖于变频控制的优劣。变频器自身具有随时间变化的特点，使线性时不变系统的相关理论无法直接被运用。文章将谐波函数理论应用到线性周期系统中，它有助于使系统稳定性和鲁棒性分析以及控制器设计更加系统化。     

含有有色噪声的自适应Kalman滤波

通过时一类时不变线性有色噪声系统的卡尔曼滤波理论的分析．提出了一种在滤波过程中不断估计并修正未知参数的算法，最后给出了有关这种估值的渐近无偏性证明以及实时应用的例子．     

连续梁瞬态振动离散时间精细传递矩阵法

针对连续梁振动问题,将通常诸如中心差分法、Hewmark-β法等结构动力学差分方法和矩阵指数精细积分法相结合,提出了一种高效求解连续梁瞬态振动的方法,离散时间精细传递矩阵法.该方法基于连续梁振动偏微分方程,将惯性项中加速度通过差分法线性化为位移的线性函数,于是原系统的连续偏微分方程就转化为线性非齐次常微分方程组.通过精细积分法求解该系统从一端到系统另一端的传递矩阵,非齐次项可选用梯形积分、高斯积分等方法得到,结合边界条件既可进行系统动力学分析.系统固有振动分析可视为读方法的特例.通过数值算例证明提出的方法精度高、有效.     

两种模态理论时域解的数学关系

当阻尼满足一定条件时,一个有阻尼的n个自由度的线性振动系统在其主空间的运动仍可解耦。解决以上系统的振动问题的理论和方法被称之为实模态理论。若振动系统的阻尼不满足解耦条件,则研究此类问题的理论和方法被称之为复模态理论。在讨论这两种理论的兼容性的时候,则多是在频域内从传递函数出发去认识它。事实上,我们也可以在时域内,从具有一般阻尼的n个自由度的线性振动系统的状态方程出发,借助于一阶线性微分方程组的exp(At)形式解和矩阵函数理论来进一步认识两种模态理论的     

变系数线性微分方程的求解

【摘要】本文针对变线性微分方程的求解进行集中讨论，通过变量代换或将其转化为常系数线性微分方程，或者把高阶方程化为较低阶的方程．举例说明运用变动任意常数法、幂级数法求解变系数线性微分方程．‘     

不同规模数据集下的人脸识别方法

系统研究了类内变化和类数目增加所引起的人脸识别中的非线性识别问题，并比较了线性识别方法和非线性识别方法在不同用户集规模下的适用性．采用CAS-PEAL大型人脸数据库中的表情集（330人）和姿势集（1000人）进行了3组实验．实验结果表明：当训练集的人数在300人（表情集）以内时，增加类内的变化不会对线性识别方法造成影响，并可以提高识别的准确率；但是，当保持类内图片数不变而增加类的数目时，类数（人数）增加对线性方法和非线性方法产生了不同的影响．随着人数增加，线性识别方法的识别准确率逐渐降低，而基于核方法的非线性方法却能够一直保持识别准确率的稳定．因此，应该根据类的总数合理地选择识别方法，并合理地设计类内的图片数，这样有助于提高人脸识别系统的识别率．同时，实验也验证了基于核方法（kernel）的非线性人脸识别方法更适宜于人数规模较大的情况．     

Robust controllability of linear time-invariant interval systems

The robust controllability problem for linear time-invariant interval systems is studied in this article. The rank preservation problem is converted to a non-singularity analysis problem of the minors of the matrix in discussion. Based on some essential properties of matrix measures, a new, sufficient, algebraically elegant criterion for the robust controllability of linear time-invariant interval systems is established. A numerical example is given to illustrate the application of the proposed sufficient algebraic criterion, and to show that the proposed sufficient condition can obtain less conservative results than the existing ones reported recently in the literature.     

Adaptive optics: wave-front correction by use of adaptive filtering and control

A class of adaptive-optics problems is described in which phase distortions caused by atmospheric turbulence are corrected by adaptive wave-front reconstruction with a deformable mirror, i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, as opposed to the linear time-invariant control loops used in conventional adaptive optics. The basic problem is posed as an adaptive disturbance-rejection problem with many channels. The solution given is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. Simulation results are presented for a 1-m telescope with both one-layer and two-layer atmospheric turbulence profiles. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared with a classical linear time-invariant control loop.     

Minimum sensitivity pole placer

A method is presented for designing a constant-gain state feedback controller for assigning the closed-loop poles of a linear time-invariant multivariable system to desired locations which at the same time minimizes the sensitivity of these poles to variation in the parameters of the plant. The design procedure is illustrated by examples.     

Minimum sensitivity pole placer

A method is presented for designing a constant-gain state feedback controller for assigning the closed-loop poles of a linear time-invariant multivariable system to desired locations which at the same time minimizes the sensitivity of these poles to variation in the parameters of the plant. The design procedure is illustrated by examples.     

Estimation and Validation of Semiparametric Dynamic Nonlinear Models

An approach for measurement-based modeling of nonlinear devices is proposed. The method that is commonly used for linear time-invariant systems, namely, parametric modeling and nonparametric verification, is hereby extended to a class of nonlinear systems. The applicability of the method is illustrated on the baseband modeling of a radio-frequency amplifier over a wide power and frequency range.     

On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations

In this note we describe the maximal and the minimal values of Lyapunov exponents for second-order discrete time-invariant linear system perturbed by time-varying bounded perturbations. An interpretation of the results in terms of generalized spectral radius is given. An application of obtained formulas to the robust stability problem is demonstrated on a numerical example.     

Stabilization of linear time-varying reduced-order models: A feedback controller approach

Many of the commonly used methods in model-order reduction do not guarantee stability of the reduced-order model. This article extends the eigenvalue reassignment method of stabilization of linear time-invariant ROMs, to the more general case of linear time-varying systems. Through a postprocessing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained nonlinear lease-square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The choice provides a control on the upper bound of the growth of the energy of the reduced system. The optimization problem is applied to several time-invariant, time-periodic, and time-varying problems, and the reproductive and predictive capabilities of the proposed method, with respect to novel inputs and the system parameters, are evaluated.     

共轭复指数随机激励及有关响应分析

本文首先介绍共轭复指数随机函数。作为一种典型的随机激励模型,列举了它的工程应用背景。然后系统地叙述在这一激励下常参数线性系统响应(包括位移、速度、加速度响应)相关特性的解析公式。     

Biaxial dynamic bending of elastoplastic beams

Summary An elastic-inelastic analogy is presented for dynamic biaxial bending of beams. Inelastic effects are treated as fictitious additional sources of self-stresses in the adjoint linear elastic structure of time-invariant stiffness. Thus, superposition applies and linear methods such as Green's functions and Duhamel's integral may be used in a convenient manner. Fictitious loadings themselves are determined from the inelastic material's law in a time-stepping procedure. As an example problem, a preloaded elastoplastic beam under harmonic excitation of support motion type is considered.With 4 Figures