单片机交流电动机转矩观测器

<正> 利用状态空间分析和电机双轴理论,推导出三相异步电动机的数学模型。该模型的特点是将原来描述的系统的非线性微分方程简化为线性矩阵微分方程,利用现代控制理论的方法设计状态观测器,来构     

基于Kripke结构的程序正确性证明

为了方便证明程序的正确性,引入了Kripke结构,提出基于Kripke结构的程序正确性证明。重新定义了适合证明的Kripke结构,并描述了将程序流程图转换为Kripke结构状态图的方法。给出了证明程序正确性的相关定理和基于Kripke结构的程序正确性证明方法。证明方法为:首先,把程序流程图转换为状态图;然后,根据状态之间的转移关系列出每个状态下的状态谓词;最后,证明每个状态谓词为真。根据状态谓词进行证明,能够反映出程序执行的状态。用该方法对一个实例进行了完整的证明。     

基于有限状态进程的事件约束定义

测试分布式程序需要定义事件约束来检测程序执行产生的事件序列.事件约束需要根据程序的规约来推导.FSP是一类描述并发程序形式化规约的进程代数记法.它将并发进程描述为动作序列,其中动作可对应到规约级事件.E-CSPE约束在给定状态谓词下定义前后运行事件间的顺序关系.根据FSP的操作符和并发控制机制可推导E-CSPE约束.推导出来的E-CSPE约束考虑到并发程序的安全和进展属性,可据以判断程序运行的正确性和测试的充分性.     

一个导弹飞行过程控制的Petri网模型

弹道式导弹是靠预先装订的弹道数据来控制飞行的.长期实践和理论研究表明,其飞行中各变量之间的关系可用一组常微分方程组来表达,而弹道数据的解算已有一套比较成熟的数值积分法.但飞行模型只能表达导弹的随时间变化而变化的状态,无法描述系统并发和异步的工作状态.提出一种基于petri网的描述系统动态性能的理论方法.它为导弹并行控制优化和控制系统性能评估提供了有效的方法.     

状态逻辑语言迭代程序的可计算性*

状态逻辑型程序设计语言是一种有坚实理论基础，既可描述递归又可描述迭代的高效、实用、新型的纯逻辑式程序设计语言．递归无疑地确保了其计算能力本文证明了仅用状态逻辑的迭代程序就可计算部分递归函数．这就等于证明了，任何图灵可计算的对象都可用纯逻辑迭代地定义和高效地计算．     

微分几何方法与非线性控制系统（2）

4 向量场与动态系统 众所周知,现代控制理论的研究是在状态空间上,使用状态方程,但有些动态系统,特别是非线性系统,其动态演变是在微分流形上进行的,演化结果是流形上的一条曲线,描述无穷小演化的微分方程是定义在流形上的向量场,因此,研究流形上的动态系统,就要分析流形上的向量场。流形上向量场的局部坐标表示是R~n中的微分方程组。在状态空间中,向量场就是状态方程的几何解释。应用向量场来研究动态系统的方法,就是几何方法。     

一类混杂系统的混杂时态Petri网模型

本语文为一类混杂系统的建模提出了混杂时态Ｐｅｔｒｉ网（ＨＴＰＮ）模型,在该模型下,系统的微观连续行为由混杂时态Ｐｅｔｉ网变迁对应的微分方程描述,宏观行为由变迁对应的离散事件描述,同时在该模型的基础上,讨论了混杂系统的宏观及微观运行问题,并提出了佥状态轨迹的概念来描述系统的动态行为。最后给出一实例来说明模型的合理性和应用。     

有限元分析软件平台FEPG

多数有限元软件一般只适用于某些特定领域和类型的问题,不能满足其他领域尤其是科研和教学领域工作者的需要,因此开发借助有限元语言等技术自动生成有限元程序的有限元分析软件平台FEPG.介绍用于描述有限元问题的有限元语言:该语言分为两部分,一部分用于描述偏微分方程表达式,另一部分用于描述求解微分方程的有限元算法;用户只需通过有...     

具有脉冲条件混合型一阶脉冲积分微分方程解的存在性

在现实世界里脉冲现象是普遍存在的．例如最优控制、化学技术、医疗等方面都会有脉冲现象。事实上,有脉冲的变化过程意味着在某一时刻的状态将发生急速的变化,脉冲微分方程是一种来描述有脉冲影响的系统的数学方法。运用上,下解法和单调迭代技术论证具有脉冲条件混合型一阶脉冲积分微分方程解的存在性。     

状态逻辑语言迭代程序的可计算性

状态逻辑型程序设计语言是一种有坚实理论基础，既可描述递归又可描述迭代的高效，实用、新型的纯逻辑式程序设计语言，递归无疑地确保了其计算能力，本文证明了仅用状态逻辑的迭工程序冰可计算部分递旭函数，这就等于证明了，任何图灵可计算的对象都可用纯逻辑代地定义和高效地计算。     

Domain of stability of synchronous generators by a cell mapping approach

In this paper, the theory of simple cell mapping is applied to the determination of domains of stability of synchronous generators. The generators are represented by two-dimensional differential dynamical systems including the effects of variable damping and saliency. First, the differential equation governing the behaviour of a generator is reduced to a cell-to-cell mapping. A scheme of compactification is introduced in order to obtain a complete cell state space which consists of a finite number of cells. The methodology of the simple cell mapping is then used to prepare a computer program. Using the program, all the singularities of the cell mapping and the domain of stability can be determined readily. The method is particularly attractive because it can easily take care of any non-linearity. Different systems can be treated by the same program by simply changing the form of the differential equation in the program and/or changing the system parameters. Three kinds of synchronous machine are studied in this paper to show the applicability of this approach. The results are compared with the best of those obtained by the Lyapunov method. It is seen that almost the complete domains of stability are obtained by the new approach, including those portions which are not discovered by the Lyapunov method.     

Solving inverse laplace transform,linear and nonlinear state equations using block-pulse functions

A recursive algorithm is developed for solving the inverse Laplace transform, linear and nonlinear state equations using block-pulse functions. The relationships between the solution of the continuous-time state equation using block-pulse functions and that of the equivalent discrete-time state equation using trapezoidal rule are investigated. A complete computer program is presented for solving the differential equations of linear and nonlinear state equations using block-pulse functions.     

一种热风炉燃烧数据分析与控制的方法

热风炉燃烧控制不够理想,经过提取生产过程数据信息,建立热风炉的状态方程模型,构建预见控制在非线性过程控制中的误差状态方程;用偏微分方法推导预见时刻控制系数,确定最优控制目标的时间序列值;编写最优预见控制程序进行仿真,仿真结果表明最优预见控制效果理想.     

Applying data redundancy to differential equation solvers

Data redundancy methods evaluate the output of a program on a given input by examining the outputs produced by the same program on additional inputs. This papers explores the use of data redundancy to detect and/or tolerate failures in differential equation solvers. Our first goal is to show that data redundancy techniques are applicable to a wide class of differential equations. Our second task is to identify circumstances in which an independence model of the sort used in program checking can be exploited to build highly reliable solvers from moderately reliable components. We conclude with illustrative examples of applying various data redundancy techniques to a standard differential equation solver. The method has potential for critical systems in which the application’s control laws are specified as sets of differential equations.     

Control bifurcations

A parametrized nonlinear differential equation can have multiple equilibria as the parameter is varied. A local bifurcation of a parametrized differential equation occurs at an equilibrium where there is a change in the topological character of the nearby solution curves. This typically happens because some eigenvalues of the parametrized linear approximating differential equation cross the imaginary axis and there is a change in stability of the equilibrium. The topological nature of the solutions is unchanged by smooth changes of state coordinates so these may be used to bring the differential equation into Poincare/spl acute/ normal form. From this normal form, the type of the bifurcation can be determined. For differential equations depending on a single parameter, the typical ways that the system can bifurcate are fully understood, e.g., the fold (or saddle node), the transcritical and the Hopf bifurcation. A nonlinear control system has multiple equilibria typically parametrized by the set value of the control. A control bifurcation of a nonlinear system typically occurs when its linear approximation loses stabilizability. The ways in which this can happen are understood through the appropriate normal forms. We present the quadratic and cubic normal forms of a scalar input nonlinear control system around an equilibrium point. These are the normal forms under quadratic and cubic change of state coordinates and invertible state feedback. The system need not be linearly controllable. We study some important control bifurcations, the analogues of the classical fold, transcritical and Hopf bifurcations.     

不确定拟哈密顿系统的随机最优控制

本文提出了不确定拟哈密顿系统、基于随机平均法、随机极大值原理和随机微分对策理论的一种随机极大极小最优控制策略.首先,运用拟哈密顿系统的随机平均法,将系统状态从速度和位移的快变量形式转化为能量的慢变量形式,得到部分平均的It随机微分方程;其次,给定控制性能指标,对于不确定拟哈密顿系统的随机最优控制,根据随机微分对策理论,将其转化为一个极小极大控制问题;再根据随机极大值原理,建立关于系统与伴随过程的前向-后向随机微分方程,随机最优控制表达为哈密顿控制函数的极大极小条件,由此得到最坏情形下的扰动参数与极大极小最优控制;然后,将最坏扰动参数与最优控制代入部分平均的It随机微分方程并完成平均,求解与完全平均的It随机微分方程相应的Fokker-Planck-Kolmogorov(FPK)方程,可得受控系统的响应量并计算控制效果;最后,将上述不确定拟哈密顿系统的随机最优控制策略应用于一个两自由度非线性系统,通过数值结果说明该随机极大极小控制策略的控制效果.     

On a new procedure for finding nonclassical symmetries

A new technique for deriving the determining equations of nonclassical symmetries associated with a partial differential equation system is introduced. The problem is reduced to computing the determining equations of the classical symmetries associated with a related equation with coefficients which depend on the nonclassical symmetry operator. As a consequence, all the symbolic manipulation programs designed for the latter task can also be used to find the determining equations of the nonclassical symmetries, without any adaptation of the program. The algorithm was implemented as the MAPLE routine GENDEFNC and uses the MAPLE package DESOLV (authors Carminati and Vu). As an example, we consider the Huxley partial differential equation.     

Stabilisation of time-varying linear systems via Lyapunov differential equations

This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches.     

基于神经网络的非线性系统的输出调节

非线性系统输出调节问题可解的充要条件是存在一个中心流形满足某个非线性偏微分方程。本文用多层前向神经网络求解该非线性偏微分方程，从而逼近非线性系统的中心流形。在此基础上，构造状态反馈控制律，实现非线性系统的输出调节。     

PASHEMOS: a versatile program written in Pascal to simulate patterns on the shells of molluscs, according to the Meinhardt model

In this paper we describe PASHEMOS, a user-friendly program written in Pascal to solve the Meinhardt-Klingler model numerically. This model studies the shell pattern pigmentation of molluscs. Moreover, PASHEMOS enables theoretical analysis to be performed on the different steady states. The program takes into account the four differential equation systems established in the model. It numerically solves these systems. This program is developed in such a way that both the equation system type and the parameter values can be chosen. The pattern is displayed in each case, and other output possibilities are available (i.e. three-dimensional concentration plotting, phase plane, phase space, stability analysis). The implementation of the program for the case of a three-variable system is shown as an example of PASHEMOS handling. Program applications for other models are also discussed.