无人机侧向系统LPV 模型降阶

无人机线性参变(LPV)模型能准确描述其非线性动态特性,但初始建立的LPV模型阶数较高,控制过程计算量较大.为此,提出一种基于平衡截断的LPV模型降阶方法.首先给出LPV系统的适定性、稳定性和平衡实现的定义;然后,提出LPV模型的平衡截断降阶方法.针对无人机侧向系统LTI模型,通过多项式拟合来建立LPV模型,并实现模型降阶.仿真结果表明,降阶模型的阶跃响应满足输出响应的精度要求.     

互连线分布电路阶跃响应上升时间的精确推算

采用MatLab软件对Wang[1]氏公式编程，对互连线1阶至2000阶RC梯形电路模型进行仿真，精确地推得其分布电路单位阶跃响应的上升时间，从而使低阶模型阶跃响应上升时间的误差估计有了科学依据。结果表明，16阶以下的低阶RC梯形电路模型误差大于5％，20阶误差为5％，100阶的误差约1％。结果对超大规模集成电路设计中互连线RC梯形电路低阶模型阶数的确定及其误差修正提供依据。     

尺度变换在互连线高阶模型仿真中的应用

Wang氏RC互连线模型的状态方程避免了矩阵求逆,传递函数采用巧妙的递归算法,使互连线的高阶仿真得以可行。但是在用MalLab做高阶仿真中,当在传递函数向状态方程转换以及用传递函数作阶跃响应和波特图时还是会发生困难。研究表明,困难来自互连线电容C值太小以及仿真阶数过高。对于高阶仿真,增大电容C值是解决发生困难的唯一途径。经过证明,增大电容C值等同于对频率进行尺度变换。电容C值扩大后,对阶跃响应图的时间轴进行同比例缩小或波特图的频率轴进行同比例扩大,即可得到原图。     

坦克瞄准线稳定系统的系统辨识方法研究

坦克瞄准线稳定系统复杂的内部结构导致机理建模的准确性大大降低,提出了利用经典阶跃响应法与遗传算法相结合的方法对某型坦克瞄准线稳定系统伺服控制回路进行系统辨识;通过DSP系统与三次样条插值数据处理测得了某种工况下的瞄准线稳定系统阶跃响应曲线;以先验知识为基础确定待辨识系统模型阶次,并利用改进遗传算法辨识模型参数,从而获取被控对象的模型;用阶跃响应性能指标误差评价法对系统辨识方法的效果进行了验证,结果表明,该方法能准确地实现瞄准线稳定系统的模型辨识.     

基于RLC模型的互连线时延估算

对VLSI电路中RLC互连线的时延进行了研究,使用改进的一阶模型来近似分布式均匀传输线的传输函数,计算出时域下的阶跃响应并得到简洁的时延计算公式.然后将其应用到具体的RLC互连树中计算源节点到漏节点的时延,其驱动器模型由电阻和电容组成,负载为容性负载.实验结果表明,该模型的计算结果与SPICE仿真结果的误差小于10%,计算量也比基于二阶传输函数的算法大为减少,在计算效率和精度两方面得到较好折衷,可以用于考虑时延效应的优化程序中.     

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.     

弹性飞机的建模与模型降阶方法研究

现代大型高速飞机的结构弹性变形日趋严重,而传统的刚性模型不能反映出飞机的结构变形特性,需要在建模时考虑飞机模型是弹性体.研究了基于Lagrange方程与"平均轴"坐标系的弹性飞机建模方法;说明了平衡截断降阶法及其改进方法平衡奇异摄动法的实现算法;以弹性飞机纵向方程为例,通过分析高、低弹性模型与刚性模型的频率响应,说明了弹性变形对飞机建模的影响,并应用平衡截断法和平衡奇异摄动法简化了高弹性飞机模型,得到了实用的低阶模型.最后分析了两种降阶方法的截断误差,指出了各自适用范围.     

基于阶跃响应曲线特征的线性系统辨识方法研究

针对阶跃响应法建模的局限性,提出一种基于阶跃响应曲线特征的线性系统辨识方法。高阶线性系统可由多个一阶与二阶典型环节并联而成,分析典型环节各参数对曲线形状影响的规律,并依据其调整各参数值,以典型环节并联模型的拟合曲线逼近实际的阶跃响应曲线,从而得到系统的传递函数。另外,借助Matlab图形用户界面（GUI）平台,开发了辨识软件以验证该算法的正确性与可行性,实验结果表明,该方法辨识精度高,对于复杂控制系统建模具有一定的参考性。     

IMNMSSPC算法在盾构机土压平衡控制中的应用

针对盾构掘进过程中密封舱内土压平衡控制的精确度低、效果差的问题,提出了一种改进的多变量非最小相位状态空间模型预测控制（IMNMSSPC）应用于密封舱多点土压平衡控制。该方法利用阶跃响应数据建立传递函数模型,将模型转换成状态空间的形式,在目标函数中引入了可调因子,反馈校正中对预测误差补偿进行校正,有效减小了模型失配时产生的误差;建立了以密封舱多监测点土压力为输出,以盾构机推进速度、螺旋输送机转速为输入的盾构土压平衡过程模型,通过多步预测直接递推出过程预测输出,并对控制量进行优化求解,从而实现土压平衡的自动控制。应用结果表明该算法具有较高的控制精度、良好的跟踪性能和强鲁棒性。     

基于随机行走电容提取且保证准确度的线网时延计算方法

从随机统计原理出发,考虑基于随机行走电容提取的多端线网时延计算,提出保证准确度的多端线网自适应互连时延计算方法.首先推导了互连时延的随机误差与随机行走电容提取结果误差的依赖关系,给出了时延误差的理论上限;然后提出了基于误差上限估计和基于误差微调的2种自适应互连时延计算策略,它们根据用户指定的时延误差阈值自动调整执行随机行走电容提取的精度设置与次数,并通过"断点续算"提取技术缩短整体计算时间.对实际电路版图中互连线网结构进行计算的实验结果表明,该方法能够保证时延结果的准确度,而基于误差微调的自适应策略比基于误差上限估计的策略效率更高,在确保时延误差可控的同时使包含电容提取的总计算时间最短.     

Parameterization theory of balanced truncation method for any evenly distributed RC interconnect circuits and transmission lines

This paper presents a parameterization theory of balanced truncation method (BTM) for any evenly distributed RC interconnect and transmission lines and their BTM reduction models. The parameterization theory shows that any evenly distributed RC line circuits of the same order have the same balanced gramian, BTM error upper bound, and BTM approximation error, which are independent of their RC parameters. Thus, the prototype model is proposed for research to dramatically reduce the computations for various RC parameters. Under normalized (scaled) time axis and frequency axis, any time responses and the Bode plots of their BTM reduction models are also the same as the ones of the prototype BTM reduction models, respectively. The simulations demonstrate the theory. The reduction model order can be identified by the prototype model. The new results can be applied to not only the model reduction of interconnects or transmission lines, but also control systems with transmission lines, networks, or time delay units.     

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.     

Identification/reduction to a balanced realization via the extendedimpulse response gramian

A new identification/reduction algorithm for linear, discrete time-invariant (LDTI) systems is proposed which is based on the extended impulse response gramian first defined here for LDTI systems. The reduction algorithm employs singular value decomposition to retain states corresponding to dominant singular values of these gramians. The proven properties of the reduced order models include convergence to a balanced realization with conditional controllability, observability, and asymptotic stability. A suboptimal property of the model (in minimizing an impulse response error norm) is also demonstrated. The proposed technique can handle impulse response data of deterministic or stochastic nature for system identification application     

一种基于可观测标准型的模型降阶算法

模型降阶方法在大规模集成电路的仿真中有着广泛的应用.由于对互联网络提取寄生参数后电路的规模巨大,使用传统的电路仿真方法将会消耗大量的资源,而模型降阶使得仿真计算量显著减小的同时精度并没有多少损失.文章针对互连线网络的MNA(Modified Nodal Analysis)矩阵通常可观测性较弱的特点,提出了一种基于可观测标准型的模型降阶算法:MOROC.文中推导证明了该算法能够匹配原系统的前q个矩,且具有形式简单和容易检验稳定性的特点.并给出了应用该算法对耦合互连线的降阶建模和仿真结果.     

A frequency weighted model order reduction technique and error bounds

A new frequency weighted technique for balanced model reduction is proposed. The proposed technique not only provides stable reduced order models for the case when both input and output weightings are included but also yields frequency response error bounds. The method is illustrated using numerical examples and the results are compared with other frequency weighted model reduction techniques.     

Reduced bases for model updating in structural dynamics based on constitutive relation error

This paper deals with the application of a model reduction method to the updating of models of industrial structures with many degrees of freedom. The updating method is based on the concept of constitutive relation error. This is an iterative method in which each iteration consists of a first step in which the most important errors in the model are localized and a second step in which these errors are corrected. The reduction method follows a classical approach in which we introduce a truncated modal basis to which the static responses associated with different excitations are added. The efficiency of the method is illustrated on one example of a finite element model containing 10,000 degrees of freedom. In the first part, we update the mass and stiffness properties of the model based on eigenmodes and eigenfrequencies. In the second part, the damping properties are updated based on the frequency response functions of the structure.     

Identification and model reduction from impulse response data

Two new algorithms for identification and model reduction of stable linear continuous systems are proposed, based on the weighted impulse response gramians (Agathoklis and Sreeram 1988 b). In identification, the model parameters are obtained from the solution of a linear system of equations with coefficients obtained from the numerical evaluation of the weighted impulse response gramians. The reduction technique is based on retaining part of the original weighted impulse response gramians obtained as the solutions to the Lyapunov equation for the original system in controllability canonical form. This yields different stable models for different values of the weighting factor. The model corresponding to zero weighting factor matches the impulse response norm of the original system and its derivatives exactly. Finally, the method is illustrated by a numerical example and is compared with well-known balanced realization techniques.     

基于保角变换的片内互连线电容二维解析模型

通过保角变换严格推导了计入交叠电场贡献的有用电容元的解析表达式,在此基础上提出的互连线二维解析模型能够在一定的连线截面几何参数范围内取得精确的提取结果.实验证明,对于双线系统和多线系统,文中推导的解析模型的提取误差的均方值分别小于2%和7%,均优于对比文献的提取精度.作为一种有竞争力的电容提取方法,该解析模型能够应用于互连线分析设计工具软件之中.     

Model order reduction of nonlinear models based on decoupled multi-model via trajectory piecewise linearization

In this paper a novel model order reduction method for nonlinear models, based on decoupled multi-model, via trajectory piecewise-linearization is proposed. Through different strategies in trajectory piecewise-linear model reduction, model order reduction of a trajectory piecewise-linear model based on output weighting (TPWLOW), has been developed by authors of current work. The structure of mentioned work was founded based on Krylov subspace method, which is appropriate for high order models. Indeed the size of the Krylov subspaces may increase with the number of inputs of the system. As a result, the use of Krylov subspace method may become deficient the case for multi-input systems of order few decades. This paper aims to generalize the idea of model reduction of TPWLOW model by concentrating on balanced truncation technique which is appropriate for medium size systems. In addition, the proposed method either guarantees or provides guaranteed stability in some mentioned conditions. Finally, applicability of the reduced model, instead of high-order decoupled multi-model in weighting multi-model controllers, is investigated through the control of a nonlinear Alstom gasifier benchmark.