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.     

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.     

Parametric state feedback design of linear distributed-parameter systems

The parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped-parameter systems. It yields an explicit parametric expression for the state feedback gain given the closed-loop eigenvalues and the set of corresponding parameter vectors. This contribution presents a parameterisation of state feedback controllers for linear distributed-parameter systems with scalar state and distributed control. By introducing the closed-loop eigenvalues and the parameter vectors as design parameters, an explicit expression for the state feedback is obtained. In contrast to the pure eigenvalue assignment, the parameterisation allows the assignment not only of the closed-loop eigenvalues but also of the closed-loop eigenfunctions. The usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a MIMO diffusion system with respect to its dominant modes.     

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．     

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 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     

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