线性系统的分散输出反馈特性结构配置

本文考虑了利用分散输出反馈配置多通道线性系统特征结构的问题;建立了闭环特征向量矩阵容许集及分散反馈增益集合关于闭环特征值和四组参向量的两种参量表示。     

线性系统的干扰解耦与抑制——基于特征结构配置的设计

本文利用线性系统的输出反馈特征结构配置结果,给出了利用输出反馈实现线性系统的干扰——输出解耦问题的充要条件和求解线性系统干扰抑制问题的一个有效算法,进一步推广了文中的结果。本文给出的方法即可把握闭环系统的特征结构,又可使闭环极点在一定的希望区域内参于优化,从而既较大程度地抑制了干扰的影响,又顾及了系统性能,且还适用于单输入或单输出系统。仿真算例证明了本文方法的有效性。     

线性系统的模型匹配问题

本文考虑利用实现线性系统的模型匹配问题。基于若当分解将线性系统的模型匹配问题归结为线性系统的特征向量匹配问题,并利用线性系统的特征结构配置结果给出了问题的最小二乘解。一个数值算例说明了方法的应用过程及有效性。     

二维线性系统特征结构配置的两种新算法

本文提出了二维线性系统特征结构配置的两种新算法,并给出了状态反馈矩阵存在的充分条件。     

线性系统状态反馈规范型设计及可视化仿真

本文针对线性系统的状态反馈设计问题．给出了能控规范Ⅰ型的设计方法，该方法通过对系统进行能控规范Ⅰ型线性变换，在能控规范Ⅰ型坐标系中确定反馈增益矩阵来实现的。采用此方法可根据用户要求的任意的配置极点对系统进行设计。本文根据此算法编写了便于仿真实现的MATLAB通用程序，且给出了此程序的解算流程图。最后对实例进行仿真．仿真结果说明了该方法的使用性和方便性。     

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．     

利用动态补偿器配置线性系统特征结构的参数方法

本文在文[5,6]的基础上建立了带有动态补偿器的线性多变量控制系统的特征结构配置问题所有解的统一参量表示,并在此基础上给出了使得闭环系统具有希望特征结构的最小阶动态补偿器设计算法。     

基于特征结构配置的二阶线性系统鲁棒容错控制设计

研究基于特征结构配置的二阶线性系统鲁棒容错控制设计问题,目的是重新设计状态反馈控制律,使得故障闭环系统和正常闭环系统具有相同的特征值.两闭环系统的特征向量依最小二乘法接近,而且能通过极小化灵敏度指标提高系统的鲁棒性.基于状态反馈特征结构配置的参数化结果,将系统灵敏度指标优化问题转化为含有约束条件的优化问题,并提出了鲁棒容错控制设计方法.数值算例及其仿真结果验证了所提出设计方法的有效性.     

线性系统的鲁棒状态反馈控制器

本文基于线性系统的状态反馈特征结构配置结果和矩阵特征值灵敏度分析理论,提出了线性系统的一种鲁棒状态反馈控制器,它在满足闭环系统特性要求的前提下,使得闭环极点关于系统参数摄动具有最小的灵敏度.     

An eigenspace and residual approach to transfer function matrix synthesis

Based on results from eigenspace and residual assignment a closed-form parameterization of all transfer function matrices obtainable by state feedback is given.     

矩阵二阶系统的鲁棒极点配置

直接在矩阵二阶框架下,利用特征结构配置参数化方法,研究矩阵二阶线性系统的鲁棒极点配置问题.将两种测量闭环特征值灵敏度方法有机地结合起来,给出一个新的优化性能指标,此指标的优化过程完全依赖于特征结构配置中的设计自由度.为进一步提高闭环系统的鲁棒稳定性,闭环极点也作为设计自由度的一部分参与优化.数值例子分析结果表明了该方法的有效性.     

On pole structure assignment in linear systems

The problem of pole structure assignment (PSA) by state feedback in implicit, linear and uncontrollable systems is discussed in the article. It is shown that the problem is solvable if the system is regularisable. Then necessary and sufficient conditions for characteristic polynomial assignment are established. In the case of PSA (invariant polynomials assignment) just necessary conditions have been obtained. But it turns out that these conditions are also sufficient in some special cases. This happens, for example, when the system does not possess any non-proper controllability indexes. A possible application of the achieved results to modelling a constrained movement of a robot arm is outlined, too.     

Robust microscale grasping through a multimodel design: synthesis and real time implementation

This paper deals with robust force control at the microscale for safe manipulation of deformable soft materials. Since mechanical properties of micrometer sized objects are highly uncertain, instability often occurs during a gripping task. This leads to object damage or destruction due to excessive gripping force. In this paper we propose the design of a robust dynamic output feedback controller that is able to insure desired performances for a set of 65 soft and resilient microspheres whose diameter ranges from 40 μm to 80 μm and stiffness varies from 2.8 N/m to 15.7 N/m. The degrees of freedom of the controller are managed by the use of a set of elementary observers. Robustness with respect to parametric uncertainties is satisfied thanks to an iterative procedure alternating between multimodel closed loop eigenstructure assignment and worst case analysis. The developed controller is of low order and can be implemented in real time. Robust gripping force control is for the first time demonstrated experimentally when dealing with the manipulation of a large number of variable deformable soft materials at the microscale. Both simulations and experimental results validate the interest of such control design 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.     

输出反馈任置极点的精确解与粗壮性

本文研究m+r-1≥n的完全系统.n、1、m分别是系统的状态、输入、输出变量个数.以前对任置极点只证明了ε-近似解的存在性,本文则证明了精确解的存在性,并进而给出了几乎全部精确解集的全部自由参数.本文指出,利用文[1]的指标,可对这些参数进行两级递阶优选,从而使所配置的闭路特征结构对系统参数中可能出现的各种扰动不敏感,全方位调节特性较优且保持相对稳定.     

An eigenstructure assignment approach for constrained linear continuous-time singular systems

This paper establishes necessary and sufficient algebraic conditions for positive invariance of convex polyhedra with respect to some linear continuous-time singular systems. They can be considered as an extension for linear singular systems of the classical positive invariance relations for regular linear systems. For a stabilizable and impulse controllable singular system with constrained inputs, a stabilizing state feedback control guaranteeing the closed-loop positive invariance of some polyhedral sets determined from the feedback matrix is studied. An analysis of the closed-loop positive invariance relations is thus presented in terms of eigenstructure and stability properties. An eigenstructure assignment technique is proposed depending on the number of stable finite poles of the singular system.