基于输出反馈的鲁棒容错D-稳定性分析

研究线性不确定系统基于输出反馈的鲁棒容错控制问题.基于连续型执行器故障模式,利用线性矩阵不等式LMI,给出了系统基于输出反馈的鲁棒容错D-稳定的充分条件,并把控制器的设计方法归结为求解一族线性矩阵不等式组.与常规的方法相比,给出的控制器不仅保证闭环系统对执行器故障具有完整性,并且使闭环系统的极点配置在指定区域D中.通过仿真示例表明,无论执行器发生故障与否,得到的基于输出反馈的鲁棒容错控制器均保证闭环系统是D-稳定的,从而验证了所提出设计方法的有效性.     

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.     

基于IGHS算法的分段系统鲁棒极点配置优化

针对分段线性控制系统鲁棒极点配置问题,利用IGHS算法对特征向量矩阵条件数优化具有较好的收敛性,限制了特征向量选择的自由度.优化后的控制器使闭环系统矩阵允许有更大的摄动或不确定性.与已有方法相比,本文方法对条件数优化计算既不需要考虑梯度和二次可微信息,也不需要对条件数进行凸转化处理.最后,仿真实验结果验证了本方法的有效性.     

基于在线优化的线性系统状态反馈鲁棒镇定

建立关于Sylvester方程的鲁棒极点配置梯度流优化算法模型,在线求解相应的二次优化问题,并在线计算状态反馈增益矩阵.使得闭环系统矩阵的伞部特征值位于给定的区域中.对于一切满足条件的扰动,具有最小灵敏度,闭环系统人范围一致渐近稳定.仿真结果验证了该方法适用十非线性系统的鲁棒镇定问题和在线鲁棒极点配置问题.     

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.     

二次型最优控制系统鲁棒特征结构配置的计算机辅助设计

本文根据系统极点的鲁棒性与特征向量的关系,构造了一个以配置鲁棒特征结构为目标,并具有线性二次型最优控制为约束条件的最优化问题。解此最优化问题,即可得到具有鲁棒特征结构的二次型最优状态反馈。本算法无需首先确定二次型性能指标中的加权阵Q、R。由此算法确定的状态反馈阵所构成的闭环系统的极点,将位于设计者所指定的希望极点附近,并具有较强的鲁棒性。根据本文提出的算法,用 FORTRAN-80 语言建立了 CSCAD程序,并在 IMS-8000 微机上调试通过。     

Delta算子不确定系统的多目标鲁棒 H∞控制

研究Delta算子描述的线性不确定离散系统在区域极点配置约束下的鲁棒H∞控制问题。目的是设计状态反馈控制器，使得闭环极点位于预先指定的圆形区域，且闭环系统传递函数的H∞范数小于给定的正常数。基于Delta算子系统具有H∞范数界二次D可镇定的概念，导出状态矩阵和输入矩阵均存在不确定性时，Delta算子系统具有H∞范数界的鲁棒区域极点配置的充要条件及其状态反馈设计。研究结果表明，可将现有结果推广到更为一般的情形，并可统一处理连续与离散系统的相关问题。     

圆盘区域极点约束鲁棒非脆弱控制

针对一类参数不确定线性系统,研究了具有圆盘区域极点约束的状态反馈鲁棒非脆弱控制器设计问题.系统中的参数不确定性满足范数有界条件,设计的非脆弱控制器具有加性和乘性不确定项.基于线性矩阵不等式(LMI),提出了将闭环系统极点配置到指定圆盘区域的状态反馈鲁棒非脆弱控制器存在的充分条件.然后利用G辅助变量替换技术拓展了圆盘极点配置的线性矩阵不等式(LMI)条件,提出保守度较低的状态反馈非脆弱控制器设计方法.数值仿真例子验证了给出的控制器设计方法的可行性.     

一种抗参数变化的最优控制器设计方法

本文描述了一种抗参数扰动的最优控制器设计方法。它从解 Sylvester 矩阵方程入手,求取状态反馈增益 F,来配置期望的闭环极点。另一方面,又充分利用了多输入状态反馈配置闭环极点以外的自由度,使控制系统设计达到多目标最优。实例及仿真结果表明:由最优控制器构成的闭环系统,既能获得满意的瞬态响应,又具有较强的抗参数变化的能力。     

圆形区域内鲁棒极点配置优化

本文基于和声搜索算法将精确极点配置的思想推广到圆形区域极点配置,通过对圆域内极点全局优化的方法,实现圆域内鲁棒极点配置问题.首先,基于几何原理描述极点在圆形区域内的位置信息,确定了在圆形区域内动态选择极点的规则,可以保证算法在圆形区域内动态选取极点.然后,对圆形区域内的极点,基于精确鲁棒极点配置的思想,利用和声搜索算法优化摄动或不确定性的谱范数上界,从而得到一组允许闭环系统具有更大摄动或不确定性的极点及相应的状态反馈控制器.最后,通过实例进行仿真,仿真结果表明本文采用和声搜索算法全局优化动态选择极点方法得到的闭环系统具有更好的鲁棒性.     

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.     

A new tool for the analysis of modal control laws: the `poleattractors'

In the design of modal control laws, the choice of the closed-loop eigenvalues is emphasized. In the output feedback case, this choice becomes more and more crucial as the degrees of freedom appearing in the control design are decreasing. Then, the assignment of right eigenvectors often induces weakly observable poles. The reluctance of the feedback to move these poles away can be represented by some attracting zones of the complex plane called pole attractors. The pole attractors are presently geometrically defined and their attraction is quantified. The usefulness of such a concept for synthesizing modal control laws is illustrated on a realistic aircraft autopilot design     

Insensitive and robust control design via output feedback eigenstructure assignment

Insensitive and robust control design using output‐feedback eigenstructure assignment for linear multivariable systems is considered in this paper. A parametric expression of closed‐loop eigenvectors and generalized eigenvectors is developed. It can cope with the case where the closed‐loop eigenvalues are multiple and/or the same as the open‐loop ones so that the system to be designed can be uncontrollable and/or unobservable. The controller designed via output‐feedback eigenstructure assignment is expressed by proposed parameter vectors. The freedom provided by output‐feedback eigenstructure assignment is used to optimize some performance functions which are used to measure the sensitivity of the closed‐loop matrix and the robustness of the closed‐loop system. Copyright © 2000 John Wiley & Sons, Ltd.     

A note on pole assignment in uncertain systems

A new method for full-rank state-feedback pole assignment is introduced. A particular advantage of this method is that no freedom in the design parameters is lost. Hence, further design problems such as robust pole assignment in uncertain systems are alleviated. An application of this feature is shown for a particular linear model of the F16 aircraft. The connections between state feedback and several concepts in the literature such as incomplete input feedback, incomplete state feedback, output feedback and incomplete pole assignment are also given.     

Some necessary and sufficient conditions for eigenstructure assignment

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.     

一类连续区间系统的鲁棒圆盘极点配置

针对一类连续线性区间系统,基于线性矩阵不等式,介绍一类能够将给出的连续区间系统的闭环系统的极点配置到指定圆盘中的状态反馈和输出反馈增益矩阵的设计方法.这类设计方法也包括分别基于执行器故障和传感器故障的可靠控制器的设计方法,基于矩阵的谱半径不大于自身的最大奇异值的理论以及矩阵的Schur补引理,将矩阵的最大奇异值限定后就...     

A robust periodic pole assignment algorithm

In this note a robust periodic pole assignment algorithm is proposed for linear, time-invariant, discrete-time systems. The condition numbers of the eigenvector matrices of the closed-loop system are assumed as a robustness measure and a periodic state-feedback law is deduced by the minimization of the condition numbers associated to the eigenvectors of the monodromy matrix of the closed-loop system. The proposed periodic pole assignment algorithm has been tested on a number of examples, giving satisfactory results     

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.     

线性离散周期系统输出反馈参数化极点配置

采用周期输出反馈的途径, 考虑了线性离散时间周期系统的极点配置问题. 通过将闭环单值性矩阵进行一系列转化, 周期输出反馈律的求解问题可以转化为一类Sylvester矩阵方程的求解问题. 利用Sylvester矩阵方程的最新结果, 可以将输出反馈增益表示为参数化形式, 从而得到了能够实现极点配置的所有输出反馈控制器. 数值算例验证了方法的有效性.