Multiobjective controller synthesis via eigenstructure assignment with state feedback

A general parameter scheme for multiobjective controller synthesis via eigenstructure assignment with state feedback is proposed. The scheme provides total pole configurability, that is, pole assignment constraints, partial pole assignment constraints, generalised regional pole assignment constraints can be dealt with simultaneously without introducing essential conservatism. The scheme is derived from the pole assignment approach using Sylvester equations, and the parameter space is the Cartesian product of some subspaces characterising the free parameters. Under the scheme, the controller design problems are formulated as nonlinear optimisation problems with both objectives and constraints being differentiable and can be solved by derivative-based nonlinear programming technique. Numerical examples are given to illustrate the efficiency of the proposed method.     

Regional pole assignment for uncertain delta-operator systems

The pole assignment in a specified disk by state feedback for uncertain delta-operator systems is studied. By making use of algebra Riccati equations, a sufficient and necessary condition of pole assignment for a kind of parameter uncertain delta-operator system in a specified disk by state feedback is presented. And the design method of state feedback controller is also developed.The proposed method can unify some previous rehted results of continuous and discrete time systems into the delta framework. The efficiency of the design method is illustrated by a numerical example.     

不确定广义系统的圆形区域极点配置

考虑不确定连续或离散广义系统的圆形区域极点配置问题, 目的是设计状态反 馈控制律, 使得闭环系统正则, 无脉冲(连续广义系统情形)或因果(离散广义系统情形), 且 闭环极点位于一给定的圆形区域内. 给出了所期望的状态反馈控制律存在的充分条件及其解 析表达式.     

多变量系统固定状态反馈下的容错极点配置

本文研究了多变量系统对执行器故障的容错极点配置问题。基于n-线性特征系数系统理论及参数空间设计方法,提出了一种容错极点配置的方法。借助这一方法,对于给定的被控对象,可以设计出一个固定的状态反馈控制律,在执行器的各种故障模式下都将系统的闭环极点设置在预定的区域内。     

用输出反馈配置鲁棒极点*

本文讨论了线性定常多变量系统在时域上用输出反馈配置鲁棒极点的问题。用输出反馈配置极点时,有一些自由度,可以利用这些自由度指定特征向量。本文给出一种数值方法,它用于选择一组尽可能正交的特征向量,使闭环系统矩阵A+BKC尽可能接近正规,从而使闭环极点对于矩阵的系数变化是鲁棒的。     

The decoupling of generalized state-space systems via statefeedback

The input-output decoupling problem of generalized state-space systems (GSS) via proportional state feedback is studied. The following three major issues are resolved: the necessary and sufficient conditions for the problem to have a solution, the general analytical expressions of the controller matrices, and the general analytical expressions of the diagonal elements of the closed-loop system. It is concluded that the approach presented seems to be a quite powerful tool for solving several feedback design problems for GSS systems. Using this method, problems such as decoupling and simultaneous pole assignment and decoupling via output feedback are successfully studied     

On constraints in pole assignment by static feedback

A design method based on pole assignment considerations for an nth order linear time-invariant single-input p-output system by means of static (constant gain) feedback is presented for the case in which the rank p of an output matrix C is less than the number of system states n. The constraints in pole assignment are described in the form of linear relationships between the coefficients of the closed-loop characteristic polynomial and some open-loop system parameters. It has been shown that the problem of pole assignment is equivalent to the problem of solving a set of n linear equations with p unknowns in such a way that n – p equations are made linearly dependent by proper choice of coefficients of the closed-loop characteristic polynomial. As a result, all n system poles can be shifted to selected locations which satisfy the constraints. Of particular interest are the design methods for the cases when the number of arbitrarily assigned poles are equal to p and p – I.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

广义系统极点配置的一种代数几何方法

利用代数几何方法给出了可任意配置极点的条件,并证明了实数域上广义系统若存在复 反馈配置极点,则一定存在实反馈配置极点.     

广义系统极点配置的一种代数几何方法

利用代数几何方法给出了可任意配置极点的条件，并证明了实数域上广义系统若存在复反馈配置极点，则一定存在实反馈配置极点．     

广义系统的反馈控制

本文介绍了广义系统的状态（输出）反馈的一种方便计算方法及反馈作用。讨论了系统的能控性结构指数并指出它是广义系统的不变量。最后研究了广义系统的极点结构配置和静态输出反馈下的极点配置。     

鲁棒极点配置控制器设计

采用多变量控制系统极点配置方法设计控制器时,往往有许多剩余的自由度.本文在极点配置方法的基础上,利用剩余自由度来优化一鲁棒性指标,提出了一种鲁棒极点配置控制器设计方法,推导了参数阵为鲁棒最优的必要条件,并给出了易于在计算机上实现的设计算法的计算步骤.     

用输出反馈配置鲁棒极点的李雅普诺夫直接法*

本文讨论了输出反馈配置线性多变量定常系统鲁棒极点的问题,提出了一种设计方法和有关定理,并用实例说明了该法的应用。     

线性状态变量反馈控制系统的应用研究

本文提出用二阶标准系统作为设计线性状态变量反馈控制系统的理想模型,探讨了闭环 极点配置和实现输出调节的一些方法,介绍了在工程应用中需要解决的有关问题.     

Robust eigenstructure assignment with minimum subspace separation

A computation method for delivering a state feedback controller that assigns closed‐loop eigenstructure with a minimum subspace separation and is robust towards unstructured perturbations is presented. The subspace separation is measured via the difference between two subspace projections, while the eigenstructure robustness is achieved by maximizing an upper bound on the allowable perturbation size such that the closed‐loop system remains stable. By exploiting the Sylvester equation parametrization, the constraint of pole assignment can be satisfied intrinsically and the robust eigenstructure assignment design essentially becomes an unconstrained optimization task. Analytical gradient formulas of the objective functions to be handled are developed. The design approach is demonstrated through numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.     

线性多变量系统设计自由度利用的探讨

本文提出一种参数最优化的方法,对状态反馈阵最小范数问题和最优极点配置问题进行了探讨。前者归结为平方和形式函数无约束极小化问题,后者归结为多元多项式函数无约束极小化问题。     

输入多采样率数字控制系统的同时极点配置

在利用提升(lifting)技术所构造出来的多采样率数字控制系统的线性时不变状态空间模型的基础上, 讨论l个被控对象通过输入多采样率数字控制系统的同时极点配置问题. 分别引入了解决这一问题的状态空间方法和多项式矩阵插值方法. 通过适当的变换, 将同时极点配置问题归结为一系列线性方程组的求解问题. 指出, 当系统的输入采样率满足一定条件时, 可以利用输入多采样率的输出静态反馈控制系统, 实现对l个被控对象的同时极点配置.     

状态反馈极点配置问题

本文研究了线性时不变多变量系统引进状态反馈任意配置闭路极点问题,首先导出了系统的一种新的标准型,然后给出了计算状态反馈矩阵的一种新方法,其主要的运算是解一组含有n-p+1个未知数的线性代数方程,算法简单,然后举例说明了这种方法的应用。文中同时还证明了状态反馈闭路系统特征方程可以分解为二个多项式之积,其阶数分别为n-p+1和p-1,而其系数为反馈矩阵元素的线性函数。     

混沌范德玻—杜芬系统的T—S模糊控制

针对混沌ADVP（范德玻—杜芬）系统,进行了T-S模糊建模和模糊控制器设计,实现了系统的稳定。在用T-S模糊模型精确重构系统结构的基础上,利用反馈同步思想和极点配置方法,基于并行分布补偿（PDC）技术,进行了控制器设计。整个设计过程只需在模糊模型基础上作极点配置,简化了计算,得到了简单且易实现的控制器。仿真表明,受控系统能够快速达到收敛,验证了方法的有效性。