离散随机模型降阶的最小条件信息损失方法

针对随机系统的模型降阶问题,从分析离散线性随机状态方程模型中的条件信息描述机制入手,讨论了模型状态集聚过程中系统的平均条件信息损失.运用在模式识别领域中获得成功应用的最小信息损失准则得出了一种新的模型降阶信息论方法———基于状态集聚的最小条件信息损失方法,并讨论了降阶模型阶次的选择.分析表明,当原系统是渐近稳定时,由该方法得出的降阶模型也是渐近稳定的.该方法运用简单,仿真研究也表明由该方法得出的降阶模型具有良好的近似性能.     

弹性飞机模型降阶软件设计

针对弹性飞机模型降阶问题,对几种适合弹性飞机模型降阶的方法进行了研究,采用Matlab的GUI技术开发了模型降阶软件.该软件以交互式界面实现Matlab环境下的模型自动降阶,可供不同的弹性飞机模型选择适用的降阶方法,并可以根据降阶效果修改降价阶次.以一个高阶弹性飞机模型为例,进行模型降阶软件的仿真应用与分析,演示了交互式界面软件使用方便、简单易学的特点,使得对弹性飞机模型降阶的设计与仿真更加方便、直观,大大缩短了设计周期,具有一定的工程意义.     

几种模型降阶方法的仿真对比研究

算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考.利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界.最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小.仿真算例证明了最小二乘法较前两者具有优越性.     

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.     

互连线高效时域梯形差分模型降阶算法

为了进一步提高现有互连电路模型降阶方法的精度和效率,提出一种基于时域梯形法差分的互连线模型降阶方法.首先将互连电路的时域方程用梯形法差分离散后获得一种关于状态变量的递推关系,形成了一个非齐次Krylov子空间;然后利用非齐次Arnoldi算法求得非齐次Krylov子空间的正交基,再通过正交基对原始系统进行投影得到降阶系统.该算法可以保证时域差分后降阶系统和原始系统的状态变量在离散时间点的匹配,保证时域降阶精度,同时也保证了降阶过程的数值稳定性及降阶系统的无源性.与现有的时域模型降阶方法相比,文中算法可降低计算复杂度;与频域降阶方法相比,由于避免了时频域转换误差,其在时域具有更高的精度.     

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.     

利用功率谱分解与系统辨识法对离散系统模型进行降阶处理

本文介绍一种离散系统模型降阶的混合方法.从能量影响的观点到系统的输出,系统中 处于主导地位的特征值会在系统输出产生优势的动态模态,从而确定降阶模型传函中分母的 参数估值,再用辨识技术求出分子参数.降阶模型与原系统相比,暂态响应与稳态响应中均有 很好的逼近.     

大规模系统集结降阶中的几个问题

本文讨论了线性定常系统集结法降阶的几个基本代数关系,论证了集结矩阵K应满足的 条件及其构造方法,指出精确集结降阶的可能性的限度,讨论了简化模型中系统系数矩阵F的 基本性质,并将所得结果用来对"保留主特征值方法"进行了具体的考察.     

面向产品级仿真的零部件模型降阶方法

为了提高复杂产品的产品级仿真速度,缩短产品开发周期,基于模态分析理论提出一种针对零部件结构的模型降阶方法,根据零部件几何模型网格划分结果,构建质量矩阵和刚度矩阵,计算结构的模态,根据合理的方法选取尽量少的模态构建零部件的降阶模型.最后通过对一个机翼模型进行降阶处理,对比分析降阶前后计算结果,证明了方法在保证精度的前提下,有效地降低了机翼模型的自由度,为产品级仿真提供了先决条件.     

参数优化配置的广义奇异摄动弹性飞机模型降阶研究

推导了广义奇异摄动法的降阶方法,介绍了其在飞机模型降阶应用中的优点,针对算法中出现的参数ξ进行了分析,以弹性飞机模型为平台提出了ξ的优化配置并进行了仿真。结果表明,采用该参数配置的广义奇异摄动模型降阶方法可以用于弹性飞机模型降阶。     

Singular perturbation approximation of balanced systems

This paper relates the singular perturbation approximation technique for model reduction to the direct truncation technique if the system model to be reduced is stable, minimal and internally balanced. It shows that these two methods constitute two fully compatible model-reduction techniques for a continuous-time system, and both methods yield a stable, minimal and internally balanced reduced-order system with the same L_∞-norm error bound on the reduction. Although the upper bound for both reductions is the same, the direct truncation method tends to have smaller errors at high frequencies and larger errors at low frequencies, while the singular perturbation approximation method will display the opposite character. It also shows that a certain bilinear mapping not only preserves the balanced structure between a continuous-time system and an associated discrete-time system, but also preserves the slow singular perturbation approximation structure. Hence the continuous-time results on the singular perturbation approximation of balanced systems are easily extended to the discrete-time case. Examples are used to show the compatibility and the differences in the two reduction techniques for a balanced system     

Robust reduced-order modeling via the optimal projection equationswith Peterson-Hollot bounds

An optimal reduced-order modeling problem with parametric plant uncertainty is considered. A model-reduction bound, suggested by recent work of I.R. Petersen and C.V. Hollot, is utilized for guaranteeing robust reduced-order modeling over a specified range of uncertain parameters. Necessary conditions which generalize the optimal projection equations for model reduction are used to characterize the reduced-order model which minimizes the model-reduction bound. The optimality equations thus effectively serve as sufficient conditions for characterizing robust reduced-order models     

Robust, reduced-order modeling for state-space systems viaparameter-dependent bounding functions

One of the most important problems in dynamic systems theory is to approximate a higher-order system model with a low-order, relatively simpler model. However, the nominal high-order model is never an exact representation of the true physical system. In this paper the problem of approximating an uncertain high-order system with constant real parameter uncertainty by a robust reduced-order model is considered. A parameter-dependent quadratic bounding function is developed that bounds the effect of uncertain real parameters on the model-reduction error. An auxiliary minimization problem is formulated that minimizes an upper bound for the model-reduction error. The principal result is a necessary condition for solving the auxiliary minimization problem which effectively provides sufficient conditions for characterizing robust reduced-order models     

Generalization of optimal Hankel-norm and balanced model reduction by bilinear mapping

In this paper the standard optimal Hankel-norm model reduction and balanced model reduction are generalized to optimal Hankel-norm model reduction and balanced model reduction over a disc in the complex plane. Important properties of the new model-reduction concept such as the monotone property of the generalized Hankel norm with respect to the domain, and the L _∞ error bound over a disc D are given. Applications like the approximation of unstable systems and model reduction for specific working signals are discussed.     

Model reduction via balanced realizations: an extension andfrequency weighting techniques

Two model-reduction methods for discrete systems related to balanced realizations are described. The first is a technique which utilizes the least controllable and observable subsystem in deriving a balanced discrete reduced-order model. For this technique as L ^∞ norm bound on the reduction error is given. The second method is a frequency-weighting technique for discrete- and continuous-time systems where the input-normal or output-normal realizations are modified to include a simple frequency weighting. For this technique, L^∞ norm bounds on the weighted reduction errors are obtained     

Model reduction using the output equation error

A model-reduction method based on the minimization of the output equation error for suitable inputs is presented. The method is characterized by remarkable computational simplicity and flexibility compared with other reduction methods based on equation errors. The practicability of the proposed procedure is discussed and some examples are given.     

Combined L2/H∞ model reduction

A model-reduction problem is considered which involves both L ₂ (quadratic) and H _∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L ₂ model-reduction criterion subject to a prespecified H _∞ constraint on the model-reduction error. The principal result is a sufficient condition for characterizing reduced-order models with bounded L ₂ and H _∞ approximation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e. idempotent matrix. When the H _∞ constraint is absent, the sufficient condition specializes to the L ₂ model-reduction result given by Hyland and Bernstein (1985).     

Management of demand-driven production systems

Control-synthesis techniques are developed for demand-driven production systems. The resulting policies are time-optimal for a deterministic model, and approximately time-optimal for a stochastic model. Moreover, they are easily adapted to take into account a range of issues that arise in a realistic, dynamic environment. In particular, control synthesis techniques are developed for models in which resources are temporarily unavailable. This may be due to failure, maintenance, or an unanticipated change in demand. These conclusions are based upon the following development. i) Workload models are investigated for demand-driven systems, and an associated workload-relaxation is introduced as an approach to model-reduction. ii) The impact of hard constraints on performance, and on optimal control solutions is addressed via Lagrange multiplier techniques. These include deadlines and buffer constraints. iii) Rules for choosing appropriate safety-stocks as well as hedging-points are described to ensure robustness of control solutions with respect to persistent disturbances, such as variability in demand and yield.     

An approximate approach to H2 optimal model reduction

Deals with the problem of computing an H₂ optimal reduced-order model for a given stable multivariable linear system. By way of orthogonal projection, the problem is formulated as that of minimizing the H₂ model-reduction cost over the Stiefel manifold so that the stability constraint on reduced-order models is automatically satisfied and thus totally avoided in the new problem formulation. The closed form expression for the gradient of the cost over the manifold is derived, from which a gradient flow results as an ordinary differential equation (ODE). A number of nice properties about such a flow are established. Furthermore, two explicit iterative convergent algorithms are developed from the flow; one has a constant step-size and the other has a varying step-size and is much more efficient. Both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates. A procedure for closing the gap between the original and modified problem is proposed. In the symmetric case, the two problems are shown to be equivalent. Numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence     

Digital decoupling controller design for multiple time-delay continuous-time transfer function matrices

This paper presents an extended adjoint decoupling method to conduct the digital decoupling controller design for the continuous-time transfer function matrices with multiple (integer/fractional) time delays in both the denominator and the numerator matrix. First, based on the sampled unit-step response data of the afore-mentioned multiple time-delay system, the conventional balanced model-reduction method is utilised to construct an approximated discrete-time model of the original (known/unknown) multiple time-delay continuous-time transfer function matrix. Then, a digital decoupling controller is designed by utilising the extended adjoint decoupling method together with the conventional discrete-time root-locus method. An illustrative example is given to demonstrate the effectiveness of the proposed method.