基于平衡截断法的离散时间线性时滞系统的低频域模型降阶

研究在系统工作频率范围为低频区间情形下的离散时间线性时滞系统模型降阶问题. 首先根据时滞系统在零频点处传递函数的性质, 构造了一类匹配其零频响应的带有可调参数的扩展线性时滞系统, 进而在其基础上结合已有的时滞系统平衡截断法给出了新的低频模型降阶算法. 通过调节其中的设计参数, 新方法所得降阶时滞系统模型能够以任意精度逼近原系统的零频响应特性, 进而可以用于改善低频范围内的模型逼近性能. 数值算例验证了所提方法的有效性和优越性.     

模型的快速降阶技术

为快速进行模型的降阶,结合平衡截断（Balanced Truncation,BT）方法和特征正交分解（Proper Orthogonal Decomposition,POD）方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解（Singular Value Decomposition,SVD）提取BT＋POD模态,对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶模型（Reduced Order Model,ROM）;该模型就成为全阶模型（Full Order Model,FOM）的ROM.通过对阶数n=406的LTI SISO系统和阶数n=9的2区间电力系统进行的验证表明,在保留BT方法输入输出平衡特性的基础上,该方法效率高于BT方法.     

平衡系统的降阶准则

本文讨论平衡系统的模型简化问题,给出了一个新的降阶准则,改进了Moore的结果,一个数值例子说明了所给方法的优越性。     

基于模型降阶的分数阶系统动态性能研究

由于大多数分数阶系统阶次过高,使得系统的控制器设计变得非常困难,会造成系统控制精度变差且动态性能降低等不利因素,而模型降阶技术是解决这一问题的有效工具.首先简要介绍了H2范数模型降阶的一般方法,并提出一种新的降阶模型结构,可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统.仿真结果证明,采用改进型H2范数模型降阶方法不仅保持了原有分数阶模型系统的动态性能而且还提升了原有整数阶模型系统的动态性能.     

大系统模型降阶的直接离散化方法

本文从频域最小二乘拟合出发,提出了高阶线性定常时间连续数学模型降阶为低阶线性定常时间离散模型的直接方法。本方法算法简单,便于编制计算机辅助设计程序,使降阶设计高度程序化;概念明确,在宽广的频带内具有较高的拟合精度,易为工程实际所应用。     

模型降阶方法研究

本文综合了模型降阶领域的现有方法,首先着重介绍了模型降阶的主要方法,并以图表的方式给出了各方法的分类及特性归纳。最后基于模型降阶的研究现状和存在的问题提出了一些看法,以便为实际工程应用提供参考。     

基于平衡截断方法的高超声速飞行器模型降阶

本文提出了一种适用于高超声速飞行器数学模型的模型降阶方法.该方法采用基于奇异值分解的投影技术,对高阶的高超声速飞行器数学模型进行平衡变换,进而通过截断获得低阶的微分方程,方便控制器的设计,达到模型降阶的目的.相比于传统的只适用于稳定系统的模型降阶方法,本文提出的模型降阶方法通过右互质分解可以应用于不稳定的系统的模型降阶.为了证明该模型降阶方法的准确性,本文通过平均灰色关联系数的计算,给出基于时域分析的定量验证结果.仿真部分成功应用该方法对美国空军实验室提出的弹性纵向模型实现了降阶,证明了该方法的有效性.     

离散时间系统Hankel最优模型降阶及其应用

针对离散时间系统Hankel最优模型降阶问题,对标量情况由最优Hankel范数近似给出了状态空间解。将这一理论应用于无限脉冲响应（IIR）滤波器的设计,进一步提出了一种基于最优Hankel范数近似的线性相位IIR滤波器设计方法。通过采用线性相位FIR滤波器和最优Hankel范数近似方法设计IIR滤波器,使其具有线性相位,减小了逆矩阵求解中的计算量。低通滤波器的仿真实例验证了该方法的有效性。     

关于模型降阶的一些试验结果

把几种具有较高逼近精度的频域降阶模型用于控制系统设计,给出设计后的仿真结果.说明不仅应研究如何提高逼近精度,而且应研究降阶设计方法.     

Coprime factors reduction methods for linear parameter varying and uncertain systems

We present a generalization of the coprime factors model reduction method of Meyer and propose a balanced truncation reduction algorithm for a class of systems containing linear parameter varying and uncertain system models. A complete derivation of coprime factorizations for this class of systems is also given. The reduction method proposed is thus applicable to linear parameter varying and uncertain system realizations that do not satisfy the structured ℓ₂-induced stability constraint required in the standard nonfactored case. Reduction error bounds in the ℓ₂-induced norm of the factorized mapping are given.     

On the balanced truncation and coprime factors reduction of Markovian jump linear systems

The paper deals with the balanced truncation and coprime factors reduction of Markovian jump linear (MJL) systems, which can have mode-varying state, input, and output dimensions. We develop machinery for balancing mean square stable MJL system realizations using generalized Gramians and strict Lyapunov inequalities, and provide an improved a priori upper bound on the error induced in the balanced truncation process. We also generalize the coprime factors reduction method and, in doing so, extend the applicability of the balanced truncation technique to the class of mean square stabilizable and detectable MJL systems. We provide tools to establish mean square stabilizability and detectability of the considered MJL systems. In addition, a notion of right-coprime factorization of MJL systems and methods to construct such factorizations are given. The error measure in the coprime factors reduction approach, while still norm-based, does not directly capture the mismatch between the nominal system and the reduced-order model, as is the case in the balanced truncation approach where mean square stable models are considered. Instead, the error measure is given in terms of the distance between the coprime factors realizations, and thus has an interpretation in terms of robust feedback stability. The paper concludes with an illustrative example which demonstrates how to apply the coprime factors model reduction approach.     

ℋ ∞ model reduction for linear parameter-varying systems with distributed delay

This paper is concerned with the ?_∞ model reduction for linear parameter-varying (LPV) systems with both discrete and distributed delays. For a given stable system, our attention is focused on the construction of reduced-order models, which approximate the original system well in an ?_∞ norm sense. First, a sufficient condition is proposed for the asymptotic stability with an ?_∞ performance of the error system by using the parameter-dependent Lyapunov functional method. Then, the decoupling technique is applied, such that there does not exist any product term between the Lyapunov matrices and the system matrices in the parametrised linear matrix inequality (PLMI) constraints; thus a new sufficient condition is obtained. Based on the new condition, two different approaches are developed to solve the model reduction problem. One is the convex linearisation approach and the other is the projection approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.     

WANG氏RC互连线模型平衡截断化简的分解算法

平衡截断（Balanced Truncation）是一种有效的模型简化（Model Reduction）方法,它的优点是简化模型有一个误差上限,使简化模型的性能得到保证.该文介绍一种平衡实现的分解算法,并应用Matlab对一4阶的Wang氏RC互连线模型的平衡实现及其模型截断简化进行编程仿真.单位阶跃响应和波特图显示原始模型与平衡模型曲线重合.给出了1阶、2阶、3阶平衡截断简化模型的阶跃响应和波特图,并对简化模型的理论误差上限与模型的实际最大误差进行了对比.方法可用于对IC互连线等模型的简化.     

Disturbance decoupling of switched linear systems

In this paper, we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version, the exogenous input is considered as the disturbance, in the second, the switching signal and in the third both of them are considered as disturbances. All three versions of disturbance decoupling have direct counterparts for linear parameter-varying (LPV) systems, while the latter instance of the problem is relevant for disturbance decoupling of piecewise linear systems, as we will show. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.