低阶实时最优Runge-Kutta算法

在控制系统实时Runge-Kutta算法中,为了满足实时仿真快速性需求,希望尽可能地采用大的计算步长.如果采用大步长,那么数值计算就会引起数值不稳定或者计算误差太大的问题.在现有低阶实时龙格-库塔公式基础上,首先利用RK公式的稳定性方程求解出最大稳定域,然后根据截断误差与相关系数的关系,将其化为一个约束求极小最优问题,并最终推导出实时最优三级二阶RK公式和四级三阶RK公式.仿真结果表明,该算法具有一定的优越性.     

弹道仿真中的数值计算方法研究

在弹道仿真计算中,为了既达到要求的仿真精度又能满足实时仿真,分析了仿真步长的选择方法,然后在龙格－库塔转阿当姆斯法中引入变步长积分方法,推导了阿当姆斯变步长积分公式,同时对弹道仿真中的间断非线性系统提出条件函数求零的方法来解算弹道。仿真结果表明,方法可以获得较高的仿真精度和较快的运行速度。     

延迟实时系统数字仿真的一种方法

在延迟实时系统的数字仿真中,既要求仿真具有快速性,又要求仿真结果具有足够的精度。在前人的工作基础上,将具有大稳定域的四阶连续实时RK公式对应用于延迟实时系统的数字仿真。在每步积分步距中,将延迟实时系统后续仿真所需的相关输出节点处状态向量的值计算并存储,可以有效地解决所需输出节点与计算节点不相吻合的问题。由于不增加微分方程的右端函数值的计算次数,因而不会对实时仿真的快速性产生本质上的影响。仿真结果表明,该方法满足实时仿真的精度需求,具有一定的实用价值。     

一种自适应变步长RKF方法及其在卫星轨道预报中的应用

为提高常规的变步长RKF方法的运算效率,提出了一种基于范数控制的自适应变步长RKF法。该方法给出局部截断误差范数值、误差限与步长的定量函数关系,根据这种函数关系自动调整步长,并对局部误差范数值为0或极小值的情况进行了讨论。卫星轨道动力学系统的描述可以归结为一阶向量常微分方程初值问题的求解,将自适应变步长RKF方法应用在该问题上,实现了考虑地球非球形和日月等三体摄动下的卫星轨道积分。仿真结果表明,该算法能满足高精度的轨道预报要求,提高了计算速度,在轨道预报中具有很好的使用价值。     

改进变步长算法在实时飞行仿真中的应用

飞行模拟机是民航训练飞行员的重要装备,飞行仿真系统是飞行模拟机的重要系统之一.飞行仿真要建立飞机的全量运动方程,利用数值算法解算运动方程达到仿真飞机飞行状况的目的.采用四元数法表示的飞机欧拉方程能够克服普通欧拉方程奇异性,但用定步长方法解算会产生较大累积误差,所以必须采用变步长方法.实时飞行仿真要求较高的实时性与逼真度,通过仿真试验分析,确定了采用一种改进变步长2阶Runge-Kutta法,该方法具有迭代次数少,解算精度高,实时性强的优点.利用该改进变步长算法,编写了实时飞行系统仿真软件,软件中使用相应算法解决了变步长算法选择步长与系统迭代定时时间不匹配的矛盾,实现了精确的实时仿真.     

实时仿真Runge-Kutta算法的误差分析

进行实时仿真时必须采用相应的实时仿真算法,而实时Runge-Kutta算法在实时仿真中得到了广泛的应用.在使用Runge-Kutta算法进行实时数字仿真时,一方面对实时Runge-Kutta算法的截断误差进行计算,构造出实用的实时Runge-Kutta算法;另一方面还要对其误差进行估计,对误差的大小进行分析,以便对实时RK算法定步长进行合适的选择,使此时定步长仿真下的误差能满足精度要求和稳定性要求,而且能够达到实时仿真计算速度的要求.仿真结果表明,该误差分析方法简单方便有效.     

基于球摆模型的离散变分积分子算法研究

在动力学系统长时间的仿真计算中,力学系统固有的结构将影响到计算精度及稳定性.离散变分积分子能够保持力学系统的能量,动量及辛结构的守恒.结合离散变分原理,通过对系统的拉格朗日函数进行离散化以及求变分和积分的过程,可以得到力学系统的离散变分积分子算法.该算法是一种递归算法,给定初始条件便可得到系统的动力学参数的时间历程.使用该原理可以构造具有完整约束的拉格朗日系统的辛-动量积分子方法.与连续算法相比,离散变分积分子算法能够直接在离散拉格朗日函数的基础上得到姿态与角速度的递推公式,而不需要复杂的迭代计算.本文研究是基于第一类拉格朗日函数的离散变分积分子算法.球摆模型是一个具有完整约束的拉格朗日系统.仿真结果表明,系统的能量值在长时间的仿真中得到保持,且计算的精度与步长的数量级呈现二次方的关系,系统角速度和姿态的仿真结果都符合球摆的运动规律.     

电力电子电路的传输线计算机仿真模型研究

准确、稳定的电力电子电路计算机仿真模型是进行电路分析和研究的基础,传输线模型(TLM)是一种基于数值求解微分方程的电力电子电路计算机仿真模型,通过研究电路元件传输线模型的数值计算局部截断误差和整体截断误差,证明了电力电子电路传输线模型数值计算的收敛性和稳定性.与原有的分析电力电子电路暂态过程的离散分析方法相比,这种方法使用简单,物理概念明确,在小步长情况下同样有较好的稳定性,通过Matlab的M文件对模型的仿真结果与经典RK4计算结果的比对,表明了该方法的有效性.     

一种基于改进双曲正切函数的变步长自适应滤波算法

摘 要：为了改进现有变步长LMS（least mean square）算法性能方面存在的缺陷,提出一种改进的变步长谐波检测算法。该算法在原有双曲正切函数的基础上引入包含输入信号的因子 ,跟踪输入信号变化,以便分析算法性能,提高其抗干扰能力;并采用增加补偿项来确保算法的收敛速度;同时将步长迭公式中固定约束范围转变为动态范围,使步长变化相对平滑,稳态失调相对较小;最后利用归一化的处理方法改进权值公式,增大输入信号的动态范围。仿真结果表明,新算法在收敛速度、跟踪能力、抗干扰能力、稳态误差等方面较现有的变步长谐波检测算法有较大提高,是一种可行、有效、具有一定工程应用价值的算法。     

基于串音误差与分离度的变步长EASI盲源分离算法

当源信号各分量差异较大或全局矩阵为非行元素优势矩阵时,基于串音误差的变步长等变自适应分离(EASI)算法难以正确评价分离效果,导致步长选取错误。针对该问题,提出一种改进的变步长EASI算法。通过计算基于串音误差的步长平方根适当增大步长,同时定义信号分离度对步长做进一步调整,减小因串音误差分离结果评价不准确而导致步长错误变小的影响。仿真结果表明,该算法具有较好的步长调节能力,相对传统EASI算法和基于串音误差、基于串音误差步长平方根、基于分离度的变步长EASI算法分离效果更佳。     

A contribution to the real-time simulation of coupled finite element models of machine tools – A numerical comparison

In this paper the real-time simulation of finite element (FE) models of machine tools on a multi-processor architecture is presented. The simulation model is based on several FE component models that are connected by non-linear couplings. These couplings allow relative motions of the components in a wide range. The coupled linear FE models are decomposed at the non-linear coupling nodes and each component is solved locally. The linear structure of the components can be used for efficient simulation methods and the components can be distributed to several processors for a parallel computation. Methods that differ in numerical accuracy and stability, computational effort and real-time capacity will be presented. By means of a complex example, it will be illustrated that a parallel, stable computation can be realized time-deterministically.     

Flexible multibody simulation using hybrid integration scheme

One issue in the dynamic simulation of flexible multibody system is poor computation efficiency, which is due to high frequency components in the solution associated with a deformable body. Standard explicit numerical methods should take very small time steps in order to satisfy the absolute stability condition for the high frequency components and, in turn, the computational efficiency deteriorates. In this study, a hybrid integration scheme is applied to solve the equations of motion of a flexible multibody system for achieving better computational efficiency. The computation times and simulation results are compared between the hybrid scheme and conventional methods. The results demonstrate that the efficiency of a flexible multibody simulation can be improved by using the hybrid scheme.     

无结构网格上解油藏数值模拟方程的区域并行差分格式

1.导 论 我们知道,结构网格有很多优点,对简单几何区域网格生成是直接的,可利用其顶点间的连结特点发展解算法,算法易于向量化.对复杂的计算区域,特别是油藏数值模拟所要计算的区域,产生适当的(有)结构网格是困难的,因此对网格放弃内在的结构要求,采取了完全无结构网格.由于无结构网格结构复杂,如何在它们上离散油藏数值模拟方程(组)一直是     

An Entropy Stable <Emphasis Type="Italic">h</Emphasis> / <Emphasis Type="Italic">p</Emphasis> Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property

This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre–Gauss–Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between non-conforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h / p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.     

A scheduling algorithm for applications in a cloud computing system with communication changes

This paper proposes a scheduling algorithm to solve the problem of task scheduling in a cloud computing system with time‐varying communication conditions. This algorithm converts the scheduling problem with communication changes into a directed acyclic graph (DAG) scheduling problem for existing fuzzy communication task nodes, that is, the scheduling problem for a communication‐change DAG (CC‐DAG). The CC‐DAG contains both computation task nodes and communication task nodes. First, this paper proposes a weighted time‐series network bandwidth model to solve the indefinite processing time (cost) problem for a fuzzy communication task node. This model can accurately predict the processing time of a fuzzy communication task node. Second, to address the scheduling order problem for the computation task nodes, a dynamic pre‐scheduling search strategy (DPSS) is proposed. This strategy computes the essential paths for the pre‐scheduling of the computation task nodes based on the actual computation costs (times) of the computation task nodes and the predicted processing costs (times) of the fuzzy communication task nodes during the scheduling process. The computation task node with the longest essential path is scheduled first because its completion time directly influences the completion time of the task graph. Finally, we demonstrate the proposed algorithm via simulation experiments. The experimental results show that the proposed DPSS produced remarkable performance improvement rate on the total execution time that ranges between 11.5% and 21.2%. In view of the experimental results, the proposed algorithm provides better quality scheduling solution that is suitable for scientific application task execution in the cloud computing environment than HEFT, PEFT, and CEFT algorithms.     

基于功率控制的多节点协同目标跟踪算法

为适应资源有限的无线传感器网络节点的目标跟踪需求,并在保证跟踪性能的同时降低算法复杂度,提出一种功率控制和多节点协调(PC&MC)目标跟踪算法.借鉴Rao-Blackwellized技术,实现多节点协同作业以保证对动态目标的跟踪精度,采用基于连续/离散混合模型的准高斯粒子滤波器完成对目标的跟踪,在跟踪过程中使用功率控制...     

A new methodology to compute stabilizing control laws for continuous‐time LTV systems

This paper is devoted to the problem of computing control laws for the stabilization of continuous‐time linear time‐varying systems. First, a necessary and sufficient condition to assess the stability of a linear time‐varying system based on the norm of the transition matrix computed over a sequence of successive finite‐time intervals is proposed. A link with a stability condition for an equivalent discrete‐time model is also established. Then, 3 approaches for the computation of stabilizing state‐feedback gains are proposed: a continuous‐time technique, ie, directly derived from the stability condition, not suitable for numerical implementation; a method based on the stabilization of the discrete‐time equivalent model along with a transformation to generate the desired continuous‐time gain; and the computation of stabilizing gains for a set of periodic discrete‐time systems. Finally, by adapting one of the existing methods for the stabilization of periodic discrete‐time systems, an algorithm for the computation of a stabilizing state‐feedback continuous‐time gain is proposed. A numerical example illustrates the validity of the technique.     

Investigation of the dynamics of a double pendulum with following and conservative forces

For a double pendulum loaded by following and conservative forces, in the nonlinear statement, the problem of stability of its zero equilibrium position is solved for the following critical stability cases: a single zero root, a pair of purely imaginary roots, a single zero root and a pair of purely imaginary roots of the characteristic equation. All results of the analytical computations are illustrated by numerical simulation.     

Stability Analysis,Chaos Control of Fractional Order Vallis and El-Nino Systems and Their Synchronization

In this article the authors have studied the stability analysis and chaos control of the fractional order Vallis and El-Nino systems. The chaos control of these systems is studied using nonlinear control method with the help of a new lemma for Caputo derivative and Lyapunov stability theory. The synchronization between the systems for different fractional order cases and numerical simulation through graphical plots for different particular cases clearly exhibit that the method is easy to implement and reliable for synchronization of fractional order chaotic systems. The comparison of time of synchronization when the systems pair approaches from standard order to fractional order is the key feature of the article.