导弹翼面结构摄动矩阵法可靠性设计研究

给出了导弹翼面结构可靠性预测与可靠性设计的随机有限元摄动矩阵法的基本原理与算式；提出对翼面壁板厚度作可靠性设计的思路，并用ＦＯＲＴＲＡＮ语言编制了可在微机上运行的计算机程序。试算表明：由本文方法得到的结果与试验数据的统计分析结果十分一致。本文的方法可以应用于常用的战术导弹翼面结构的可靠性预测与可靠性设计。

基于摄动传递矩阵法的随机参数系统振动分析

随机参数对多刚柔体结构动态特性具有一定影响,含随机参数系统的振动特性分析是现代多刚柔体结构研制与动态性能设计的重要环节之一。基于多体系统传递矩阵法和摄动方法,推导了含随机参数系统零阶、一阶和二阶摄动总传递方程,建立了含随机参数的多体系统特征值问题的分析方法,实现了含随机参数柔性结构振动特性快速分析。分别应用文中方法与Monte Carlo方法对某含随机参数的柔性结构和平面振动多刚柔体系统特征值问题进行了分析,两种方法的计算结果吻合较好,证明了文中方法的有效性和高效性。

对流-弥散方程的小噪声方法与应用

通过小噪声摄动理论,建立了小噪声随机微分方程.并借助于摄动矩的理论,求出了随机微分方程质点位移的均值与方差,之后将对流-弥散方程进行正态近似,得到了方程的近似解.最后将小噪声摄动理论应用到求解实际的高对流-弥散方程中,并与广义差分迎风格式的方法作比较,得到了满意结果.

简支梁随机特征值的探讨

根据具有不定参数的结构特征值Taylor展开式,推导出特征值随机变化的统计特性(均值、方差)计算公式.以具有随机参数的简支梁为例,运用摄动Riccati传递矩阵法,计算了简支梁在结构质量密度发生随机变化时结构特征值的统计特性,通过数值解和理论解的比较,验证该方法的适用性,利用该方法还计算了当简支梁截面抗弯刚度和长度分别发生随机变化时随机特征值的均值及方差,定量描述了具有随机参数的简支梁结构特征值的统计特性.

Robust Non-fragile PID Controller Design for the Stroke Regulation of Metering Pumps

This job focuses on the stroke regulation of a class of high-precision metering pumps.A parametertuning method of robust non-fragile PID（proportional-integral-derivative）controllers is proposed with the assumption that a PID controller has additive gain perturbations.An H-infinite robust PID controller can be obtained by solving a linear matrix inequality.This approach can guarantee that the closed-loop control systems is asymptotically stable and the H-infinite norm of the transfer function from the disturbance to the output of a controlled system is less than a given constant to attenuate disturbances.The simulation case shows that the control performance of the proposed strategy is significantly better than the traditional PID approach in the situation with perturbations of controller parameters.

A direct-variance-analysis method for generalized stochastic eigenvalue problem based on matrix perturbation theory

It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty effects are indispensable during the process of product development.Besides,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best design.Taking uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational costs.Owing to the situations above,matrix perturbation method has been investigated by researchers worldwide recently.However,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational process.This has become the bottleneck of application for matrix perturbation method.In this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation method.In the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have changed.Combining the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure directly.Hence the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being involved.The feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing structure of MA700 commercial aircraft),in which the DVA method also shows superiority in computational efficiency when compared to the Monte-Carlo method.

Matrix perturbation based approach for sensitivity analysis of eigen-solutions in a microgrid

Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.

A generalized trajectory tracking controller for robot manipulators with bounded inputs

A generalized controller based on stability theory of singularly perturbed systems is proposed,to deal with the problem of bounded actuator inputs in robot trajectory tracking control.The saturation function with error-gain matrix is applied in the torque control law,which ensures the upper bound of torque inputs in any given limited range.Through appropriately setting the entries of the error-gain matrix,the tracking performance can be improved.Moreover,a pseudo signal is generated from a linear filter to substitute for the actual velocity error,eliminating the need for velocity measurements.Finally,to verify the ef-fectiveness of the generalized controller,a new saturated controller with error-gain-contained arc tangent function is designed.Comparison experiments show that the proposed controller can strictly guarantee the bound of the torque inputs in situations with non-zero initial tracking errors,and gives a better tracking result than other controllers.

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem

We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H（div）- conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H（div）-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.

Weighted Polar Decomposition

In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.

Unified calculation of eigen-solutions in power systems based on matrix perturbation theory

Calculation of eigen-solutions plays an important role in the small signal stability analysis of power systems.In this paper,a novel approach based on matrix perturbation theory is proposed for the calculation of eigen-solutions in a perturbed system.Rigorous theoretical analysis is conducted on the solution of distinct,multiple,and close eigen-solutions,respectively,under perturbations of parameters.The computational flowchart of the unified solution of eigen-solutions is then proposed,aimed toward obtaining eigen-solutions of a perturbed system directly with algebraic formulas without solving an eigenvalue problem repeatedly.Finally,the effectiveness of the matrix perturbation based approach for eigen-solutions’calculation in power systems is verified by numerical examples on a two-area four-machine system.