Eigenstructure assignment in a class of second-order descriptor linear systems: A complete parametric approach

1 Introduction Second-order linear systems capture the dynamic behaviour of many natural phenomena and have found wide applications[1～4] in robotics, vibration and structure analysis etc. Many results in second- order linear systems have focused on eigenstructure assignment[5～10] as an important design method. Most of the results relating to eigenstructure assignment are derived from conventional second-order linear systems. There have been few reported results produced from eigenstructure a…     

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n?dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.     

Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback . It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches.     

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of second-order dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.     

鲁棒比例与部分状态导数反馈控制系统设计

基于广义线性系统比例与部分状态导数反馈参数化特征结构配置结果和矩阵对广义特征值灵敏度结果, 得到了关于开环系统矩阵中摄动元素的闭环特征值灵敏度的参数表达式, 并在此基础上提出了广义线性系统比例与部分状态导数反馈最小灵敏度特征值配置的有效算法. 该算法不含有"返回"过程, 允许闭环特征值在希望的区域内方便地参与优化. 一个算例说明了算法的简单性和有效性.     

利用位置和加速度反馈的矩阵二阶系统特征结构配置

考虑一类利用位置和加速度反馈二阶线性系统的特征结构配置问题．在允许闭环系统的特征值是未知的前提下,结合矩阵多项式的右互质分解提出二阶线性系统特征结构配置的参数化方法,建立反馈增益阵和特征向量矩阵的显示参数化表达式．本文涉及的参数化方法直接将二阶系统模型转化为一阶状态空间形式,从而降低了系统设计中的计算工作量,并且提出的算法简单,无“返回”步骤．最后,数值算例表明了该算法的有效性．     

ESA in high‐order linear systems via output feedback

This paper considers eigenstructure assignment in high‐order linear systems via output feedback. Parametric expressions for the left and right closed‐loop eigenvectors associated with the finite closed‐loop eigenvalues and two simple and complete parametric solutions for the feedback gain matrices are obtained on the basis of the parametric solutions of the generalized high‐order Sylvester matrix equations. This approach does not impose any restrictions on the closed‐loop eigenvalues. An illustrative example shows the effect of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Eigenstructure assignment by decentralized output feedback-acomplete parametric approach

The problem of eigenstructure assignment in multivariable linear systems by decentralized output feedback is considered. By using a complete parametric solution of a generalized Sylvester matrix equation, parametric representations of both the left and right closed-loop eigenvectors and generalized eigenvectors as well as the feedback gains with respect to the closed-loop eigenvalues and two series of partially free parameter vectors are established. The obtained result does not require any conditions on the closed-loop eigenvalues, and generalizes some previous results in this area. An example shows the effect of the proposed approach     

矩阵方程AX-EXF=BY的通解及其应用

给出矩阵方程AX—EXY=BY的一个完全解析的、具有显式表达式和完全自由度的参数解(X,Y)．这里假设矩阵束(E,A B)为R-能控的,F为任意的方阵．相比于现有结论,求解算法不要求矩阵A和F具有特殊的形式,且对它们的特征值没有任何的限制,此外,本文给出的通解还具有结构简洁的特点,作为一个应用,给出了广义系统正常Luenberger函数观测器的一种参数化的设计方法,算例证明了方法的有效性．