【作者】 刘皞；

【导师】 戴华；

【作者基本信息】 南京航空航天大学 ， 一般力学与力学基础， 2007， 博士

【摘要】 本文运用代数特征值反问题的理论与方法,研究了一阶线性系统、无阻尼结构系统与阻尼结构系统的特征结构配置问题,全文主要包括以下内容。研究了一阶线性系统指定区域的特征结构配置问题。本文根据孙继广给出的系统鲁棒性的度量,把问题转化为一个无约束的优化问题,分析了问题的性质,给出了目标函数梯度向量的计算公式,提出了求解此问题的一个新算法,该方法计算公式简单,大大提高了计算效率。数值算例表明,这一算法具有良好的数值性态。研究了无阻尼结构系统的特征结构配置问题。对于给定了全部特征结构的情形,分析了问题有解的条件,给出了解的表达式,并根据矩阵扰动理论给出了无阻尼结构系统鲁棒性的度量,由此提出了求解此问题的数值方法;研究了无阻尼结构系统保持对称性的特征结构配置问题,给出了此问题有解的条件与解的表达式,并考虑了在控制矩阵不给定的情况下,如何根据给定的特征结构求控制矩阵与反馈矩阵的方法;研究了无阻尼结构系统部分特征结构配置问题,即只改变系统的一部分特征值与相应的特征向量,而保持其余的特征结构不变,给出了此问题有解的条件与解的表达式,并给出了系统的鲁棒性度量,提出了求解此问题的两个算法:正交化向量方法与正交基方法;为了保持系统的对称性,利用输出反馈,给出了保持对称性的部分特征结构配置问题的一个特解;研究了一类结构动力模型修正问题,利用振动测量数据修正质量矩阵,使得修正后的动力学分析结果与相应的试验结果相一致。研究了阻尼结构系统的特征结构配置问题。对于给定了全部特征结构的情形,利用阻尼结构系统鲁棒性的度量,提出了求解此问题的两个数值解法,新方法具有较好的数值稳定性。对于阻尼结构系统部分特征结构配置问题,利用矩阵扰动理论与特征值的灵敏度分析,给出了在测量的特征结构不完备时,如何选择要配置的若干个特征值与特征向量,并设计了一个数值算法来有效地求解此问题。对一般的特征结构配置问题,研究了对任意给定的特征值与特征向量,在控制矩阵不给定的情况下,如何设计控制矩阵与反馈矩阵的问题,提出了同时确定控制矩阵与反馈矩阵的方法。更多还原

【Abstract】 According to the theory and methods of the algebraic inverse eigenvalue problems, in this dissertation, we study the eigenstructure assignment problems on linear systems, undamped structural systems and damped structural systems. The main contribution is as follows.The robust eigenstructure assignment problem of linear system in a specified region is studied. The problem is formulated as an optimization problem. According to a Sun’s measure of robustness, we analyze the properties of this problem, and suggest the formula of the gradient vector of the objective function. Then a new algorithm for solving this problem is presented. Numerical examples show that the problem of robust pole assignment in a specified region can be solved effectively.The eigenstructure assignment problems of undamped structural systems are considered. For the case that all the poles are prescribed, we give the conditions and the expressions of the solutions, and give a new measure of robustness according to the theory of matrix perturbation. Thus, we propose a numerical method for solving this problem. we study the preserve symmetric eigenstructure assignment problem, and give the conditions and the expressions of the solutions. We study the partial eigenstructure assignment problem of undamped structural systems, that is a few eigenvalues and eigenvectors of system are undesirable, and the rest of the eigenstructure invariant, and we give the conditions and the expressions of the solutions. According to a new measure of robustness, we give an algorithm for solving this problem. Moreover, in order to preserve the symmetry of the system, we consider the partial eigenstructure assignment problem using output feedback, and give a special solution of this problem. Lastly, we consider a structural dynamics model updating problem.The eigenstructure assignment problems of damping structural systems are investigated. For the case that all the poles are prescribed, we give two algorithms for solving this problem. The procedure of this method is easy to realize, and have a good numerical stability. For the partial eigenstructure assignment problems of damping structural systems, according to the perturbation theory of matrices, we give a method for choosing the assigned eigenstructure, and propose an algorithm for solving this problem. For general eigenstructure assignment problem, in the case of the assigned eigenvectors are given arbitrarily, we give a method for getting the control matrix and the feedback matrices in the condition of the control matrix is unknown.更多还原