复变函数中极点阶数判断的两种特别方法

复变函数中,极点阶数的判断是计算留数的前提.常见的孤立奇点有可去奇点、极点和本性奇点.而可去奇点处的留数为0,本性奇点出的留数只能用展开式来判断.最常见的莫过于极点处的留数计算了,而这个前提就是极点处阶数的判断,下面用两种特别方法来例证.     

求解网格奇点的曲率传输方法

为了降低网格在参数化过程中产生的扭曲,提出一种基于曲率传输求解网格奇点个数和位置的方法.首先,通过求解Yamabe方程获得网格顶点的共形缩放因子,利用共形缩放因子的持续性确定第1部分的奇点,并计算基于该奇点集合的参数化扭曲;然后,根据参数化扭曲确定第2部分的奇点,并优化奇点的位置;最后,顶点曲率集中到奇点上计算出最优传输代价,通过不断地更新奇点位置,使上述最优传输代价达到最小,得到最终奇点分布.经过计算大量的网格,实验结果表明,与其他曲率方法以及近几年的方法相比,利用该方法确定的奇点可以有效地降低网格参数化带来的扭曲.     

二阶自治广义Birkhoff系统的奇点分析

建立二阶自治广义Birkhoff系统的微分方程.给出该系统的线性化方程,得到该线性方程转化为梯度系统的条件,利用梯度系统的性质对线性系统的奇点进行了分析,然后再利用Perron定理探讨了相应的非线性系统的奇点类型.结果表明,如果线性系统能成为梯度系统,那么相应的非线性系统的奇点可能是结点或者鞍点.     

水平集演化中的奇点与改进的窄带算法

对保持距离函数约束的水平集演化过程作了系统的分析,提出了奇点的概念,并给出了奇点的重要性质及其证明,详细分析了奇点在水平集演化过程中的数值影响.在此基础上对窄带算法作了改进,以避免奇点的不良影响,同时窄带宽度具有自适应性.实验结果表明,改进的窄带算法具有较好的鲁棒性.     

一种提高姿态测量精度的新途径——冗余量测法

关于单轴姿态确定的一般方法和精度分析,国外已有不少文献论及[1]，但无论哪种姿态确 定方法都有不可避免的奇点存在.在这些奇点附近确定姿态精度差,没有实用价值.为了获 得较好的姿测效果,人们只得精心选择发射卫星的日期和时刻;使得姿测期间避开这些奇点. 为了克服这一困难,本文提出了冗余量测的概念.使用冗余量测信息模型确定姿态,改善了通 常方法的奇点分布,提高了姿测精度,扩大了发射窗口.     

分布参数系统边界控制的Haar小波算法

由于分布参数系统通常由偏微分方程描述,采用解析法求解分布参数系统最优边界控制问题,是非常难以解决的.正交函数逼近的方法在分布参数系统控制方面,已经取得了较好的效果.Haar小波作为正交基函数,利用小波的一些运算及变换矩阵,将分布参数系统转化为集总参数系统,再求其逼近解.仿真示例验证了所提出的算法是非常有效的.该方法为分布参数系统的控制算法提出了一条新的解决方案.     

弱非线性耦合二维各向异性谐振子的动力学行为

研究了弱非线性耦合二维各向异性谐振子的奇点稳定性及其在相空间中的轨迹.首先,求得弱非线性耦合二维各向异性谐振子的奇点;其次,分别利用Lyapunov间接法和梯度系统方法讨论该系统的平衡点稳定性;最后,用Matlab方法对系统进行数值模拟,并运用庞加赖截面观察系统在相空间的运动轨迹,发现随着能量的增加系统经历规则运动、规则运动与混沌并存等阶段,最后出现了混沌现象.     

基于Chebyshev小波的分布参数系统辨识

工程实际和社会系统中广泛存在着分布参数系统,因而研究分布参数系统的辨识与控制具有重要意义.但由于其复杂性,对分布参数系统的辨识研究十分困难.借助于Chebyshev多项式的逼近性质,以及小波的时频特性,构造了Chebyshev小波,并利用其积分运算矩阵,运用于分布参数系统的辨识,从而将一类分布参数系统的辨识问题转化为一般代数问题.并且考虑了初始条件和边界条件对辨识结果的影响,因此具有较好的适用性,仿真结果证实了该方法的有效性.     

基于小波变换的二阶线性分布参数系统预测控制

分布参数系统由于其复杂性,控制系统设计一直是控制理论的难点.寻求解决分布参数系统控制的新思路,本文提出了基于正交小波变换的线性离散时间分布参数系统预测控制概念,应用正交小波变换将二阶线性分布参数系统预测控制命题变换为集总参数系统预测控制问题,并设计预测控制器,将控制律进行反演获得原系统的具有分布特性的控制律.仿真研究表明,本文提出的分布参数系统预测控制算法取得了理想的控制效果,对系统模型失配和扰动具有较好的鲁棒性,验证了算法的有效性.     

发动机功率故障诊断系统的设计与实现

论文利用Labview软件模拟设计了发动机功率故障诊断系统,系统提供用户自由设定需要监测的参数并且利用发动机的特性曲线进行诊断,图形化的输入输出,完成对各个系统是否出现故障进行诊断,通过系统的实验证明本性对发动机故障诊断快速,直观,准确,从而达到快速排除故障点的作用.     

Stability of differential-difference equations representing heat exchanger and certain other systems†

Conditions for the stability of certain typos of first-order nonlinear difTerential-difforonce equations are derived. Some of the results are applicable to a simplified model of certain distributed parameter systems, such as heat exchanger.     

Comment on “Stability of systems with rhp pole-zero cancellations”

Through the heat exchanger example of.Koppel et at. (1968) u rapid sub-optimal control algorithm is developed for optimal regulator problems in linear distributed parameter systems. The Galerkin approximation is first applied to obtain a lumped ODE model for the distributed parameter system. Then, a sub-optimal open-loop control for the resulting linear ODE optimal regulator problem is obtained through the Ritz-Trefftz algorithm of Bosarge and Johnson (1970). One-dimensional polynomial basis functions (modes) are employed to approximate both time and spatial behaviour throughout. To facilitate mode selection, emphasis is placed upon sequential ono-dimensional approximations rather than upon a single multidimensional approximation.

Applications of the resulting algorithm are characterized by low storage and on-line computational requirements. Numerical results for the heat exchanger example are presented and compared with those currently available in the literature. Performance of the algorithm with a small number of polynomial modes is assessed and experimental user-oriented guidelines are provided.     

Weighted residual methods and the suboptimal control of distributed parameter systems†

A suboptimal control algorithm for distributed parameter systems is developed in a framework which synthesizes weighted residual methods and mathematical programming. The heat exchanger example of Koppel et al. (1968) is employed for introducing the algorithm. First, the Galerkin procedure with polynomial modes is applied to obtain a lumped ODE model for the distributed parameter system. Then the state and control variables of the lumped control problem are approximated by cubic splines on a uniform mesh. Through collocation at the knots, the ODE model is reduced to a sot of linear algebraic equations and the suboptimal control is determined from the solution of a quadratic programming problem with sparse matrices.

Numerical results for the heat exchanger example are presented and compared with those obtained by the authors (Neuman and Sen 1972) using the Ritz-Trefftz algorithm (Bosarge and Johnson 1970) for the lumped control problem. For this example, the two algorithms yield essentially identical results with comparable computational requirements. Application of the Ritz-Trefftz algorithm, however, is limited to lumped, linear-quadratic control problems without constraints on the state or control. The approach advocated in this paper, therefore, offers a viable approach to control problems in distributed parameter systems.     

Optimal operation of thermal regenerators

The thermally most efficient operation of a thermal regenerator, a particular type of heat exchanger, is analyzed through the minimum principle for distributed parameter systems and Laplace transform techniques. It is found that for optimal operation the gas inlet temperature during the heating phase should equal its maximal allowable value, and that the optimal gas flow rate during the heating phase is constant.     

抛物型分布参数系统的变结构控制

本文研究抛物型分布参数控制系统的变结构控制问题,在较文[4]更一般的条件下,首先证明了等效控制法对于研究无限维变结构系统的有效性,得到了系统的滑动方程式,并讨论了滑动模的稳定性条件;然后研究了热加工等实际问题中出现的抛物型分布参数系统的滑动模设计,解决了文[4]中提出的问题。     

Identification of non-linear rational systems using a prediction-error estimation algorithm

Identification of discrete–time non–linear stochastic systems which can be represented by a rational input–output model is considered. A prediction–error parameter estimation algorithm is developed and a criterion is derived using results from the theory of hypothesis testing to determine the correct model structure. The identification of a simulated system, and a heat exchanger are included to illustrate the algorithms.     

Principle of equipartition of entransy dissipation for heat exchanger design

In the present work,a principle of equipartition of entransy dissipation(EoED) for heat exchanger design is established,which says that for a heat exchanger design with given heat duty and heat transfer area,the total entransy dissipation rate reaches the minimum when the local entransy dissipation rate is uniformly distributed along the heat exchanger.When the heat transfer coefficient is unfixed,the total entransy dissipation obtained by the EoED principle is less than that obtained by the principle of eq...     

Online policy iteration algorithm for optimal control of linear hyperbolic PDE systems

In this paper, the linear quadratic (LQ) optimal control problem is considered for a class of linear distributed parameter systems described by first-order hyperbolic partial differential equations (PDEs). Reinforcement learning (RL) technique is introduced for adaptive optimal control design from the design-then-reduce (DTR) framework. Initially, a policy iteration (PI) algorithm is proposed, which learns the solution of the space-dependent Riccati differential equation (SDRDE) online without requiring the internal system dynamics of the PDE system. To prove its convergence, the PI algorithm is shown to be equivalent to an iterative procedure of a sequence of space-dependent Lyapunov differential equations (SDLDEs). Then, the convergence is established by showing that the solutions of SDLDEs are a monotone non-increasing sequence that converges to the solution of the SDRDE. For implementation purpose, an online least-square method is developed for the approximation of the solutions of the SDLDEs. Finally, the proposed design method is applied to the distributed control of a steam-jacketed tubular heat exchanger to illustrate its effectiveness.     

Irreversible thermodynamics of phase change heat transfer: Basic principles and applications to latent heat storage

This paper reviews some recent results concerning the irreversible thermodynamics of phase-change processes. A general scheme, of which the classical Stefan problem is a special case, is developed. The limits of validity of the Stefan formulation are established and several possible extensions are reviewed. The properties of entropy generation as an evolution characteristic of phase-change processes are studied. The Second Law analysis of latent heat storage systems for power generation applications is presented. The general formalism is applied to a typical distributed system based on a tube-and-shell heat exchanger. Optimal conditions for the operation of the system are derived.     

Feedforward—feedback control of distributed parameter systems†

Regulatory control of distributed systems subjected to load disturbances is considered by using feedforward and state measure control configurations. Dynamic compensation of the feedforward signal is accomplished with a lead-lag function, the time constants of which are determined by means of a numerical search technique. Compensation of the state measure signal is provided by the distributed nature of the process itself. Exit temperature regulation of a tubular heat exchanger acted upon by velocity and inlet temperature disturbances is considered as an application for feedforward control. Considerably better performance is obtained with the addition of dynamic compensation to the feedforward signal. State measure control is applied to the exchanger for a feed temperature upset and the effects of sensor location on outlet performance are investigated. An optimal sensor location is determined which minimizes the integral-square error at the outlet.