德拜媒质微波加热过程的H∞保性能温度跟踪控制

德拜媒质微波加热过程中，由于介电常数具有随温度变化的特性，导致电磁场的空间分布将会产生巨大的变化.若缺乏合理的功率调控策略，将导致燃烧、爆炸等一系列热失控现象.针对上述问题，本文提出一种滚动时域H_∞保性能温度跟踪控制策略，以实现对监测位置的最高温度进行控制.基于微波加热德拜媒质的机理模型，同时考虑跟踪系统稳定性、动态性能和输入约束，以H_∞增益和保性能函数作为性能指标，本文将温度跟踪问题转化为线性矩阵不等式（Linear matrix inequality，LMI）多目标优化问题，使得系统动态性能达到最优.最后以德拜媒质微波加热短波导模型为例，对所提出方法的有效性进行仿真验证.     

直拉硅单晶非均匀相变温度场最优控制

针对直拉硅单晶固液界面相变温度场的非均匀性导致晶体直径不均匀问题,提出一种基于偏微分方程(PDE)模型的温度场最优控制策略.考虑生长速率波动的影响,建立了一种改进的提拉动力学模型,确定了域边界演化动力学关系.研究基于抛物型PDE的时变空间域对流扩散过程的温度模型,描述了域运动在对流扩散系统上的单向耦合.针对无限维分布参数系统建模控制难问题,采用谱方法进行系统近似,选取整个空间域的全局和正交的空间基函数,通过Galerkin方法对无限维系统进行降维,获得了该系统的近似模型.采用线性二次型方法控制晶体生长温度,通过仿真实验对相变温度场模型进行验证.结果表明,优化后的模型能够获得较为平稳的晶体生长速率,减小了生长直径的波动,使得固液界面径向温度分布更加均匀,验证了该方法的有效性.     

基于一致性算法的多模式搅拌器微波加热系统温度均匀性优化

微波加热的内部传热方式及热点的随机分布特性导致采用常规测量方法难以获得温度的准确信息,在改进机械设计的研究中,螺旋辐射单模式搅拌器微波加热系统能够改善温度分布的均匀性.在单模式搅拌器的基础上,进一步探索具有多个模式搅拌器的微波加热系统的温度均匀性及其计算问题;同时,由于微波加热过程中多物理场的深度耦合及边界条件的时变特性,如何协同模式搅拌器的状态特征与有效计算温度场,开展温度均匀性的优化处理成为关注的重点.为此,应用一致性算法表达模式搅拌器的状态信息,对温度场分布的均匀性进行优化计算.一方面通过一致性算法将加热空间电磁场边界条件的时变性用编队队形表征,组合模式搅拌器的位置状态信息表达编队队形的变换;另一方面由整型变量与连续型变量混合的优化问题构建温度有限元模型,并对温度场的均匀分布优化解开展有效计算.数值计算结果验证了所提出一致性算法及其计算方法对微波加热温度均匀性的优化是可行和高效的.     

PDE与DAE耦合系统求解方法

针对目前Modelica语言只能解决由微分代数方程(DAE)描述的问题,而不能解决由偏微分方程(PDE)表达的问题,提出一种求解PDE与DAE耦合系统的方法.首先采用径向基函数构造近似函数,将未知量场函数的时空变量分开;然后运用配点法对空间变量进行离散,从而将PDE问题转化为DAE问题;最后采用成熟的DAE求解器进行求解,得到场函数在任意时空点的函数值.实例结果表明,该方法在不改变Modelica语法的前提下,能较好地实现PDE与DAE耦合系统的一致求解,且求解精度高、稳定性好、边界条件处理简单.     

基于动网格的微波加热温度均匀性数值计算方法

微波加热过程中物料内部温度的均匀性一直是研究的热点问题.针对“热失控”现象产生的机理,从微波传输线出发,根据广义传输线理论,利用传输线上电压和电流的分布关系推导出微波谐振腔内电磁场幅值与相位间的关系,在此基础上,提出一种微波加热运动状态物料的数值计算模型.该模型采用动网格技术跟踪求解域边界的变化量,分别针对求解域内部及其边界处网格移动变形给出控制函数,不仅可解决微波加热数值计算过程中由于求解域网格的移动导致的网格交叉缠绕问题,还可在满足计算精度的前提下,有效地减少网格节点移动的计算.数值计算结果表明,微波加热处于运动状态下物料的温度均匀性优于微波加热静止状态下物料的温度均匀性,且所提出的微波加热运动状态物料计算模型具有可行性和有效性.微波应用器装置加热活性炭球团的实验结果也表明,所提出的方法能有效抑制微波加热温度的突变.     

不等距网格上求解ODE特征值问题若干高精度格式的计算与分析

本文针对不等距网格,从Raylei曲商(Raylei曲quotient)角度出发,构造了若干求解ODE特征值问题的高阶格式,并进行误差分析.文中高阶格式的构造是基于线性有限元及其对应的差分格式进行的.单纯的线性有限元及其对应的差分格式求解PDE特征值问题都只有二阶精度,我们利用质量集中和加权组合的思想通过将二者结合得到四阶精度的算法.本文从理论和实验的角度构造高阶格式并进行了相应的误差分析.通过在五种网格上计算四阶精度格式的误差阶系数,将四阶格式加权组合的新格式甚至可以达到六阶精度.最后用数值实验验证了构造的高阶格式的误差阶.同时,本文构造的两种四阶格式相对于传统的线性有限元方法,在同等量级误差的要求下,需要的网格数有量级的减少.     

基于网格划分策略的微波功率的实时控制

根据媒质在微波加热中的介电特性、温度、吸收功率随时间而变化的特点,使用基于网格划分策略对温度和吸收功率建立目标函数,从而对微波功率进行多目标优化控制。对目标函数中不同参数取值下的微波功率进行了分析与对比。对于微波加热过程中的热失控现象,通过设定单温度阈值来进行检测,然后进行功率调整,使媒质温度最终稳定在预期的稳态温度。经过网格划分策略优化后,有助于提高微波加热效率和控制热失控现象。     

基于正交函数的立式淬火炉控制系统参数辨识

大型立式淬火炉体积庞大,工况复杂,炉内温度分布呈本征非均匀性.为了获得温度控制高精度和高均匀性提出参数辨识算法,包括求解正交函数正、反向积分运算矩阵,以块脉冲函数为基函数利用正交函数变换将由偏微分方程描述的分布参数系统模型转化为最小二乘形式的代数方程.辨识过程中考虑了大型立式淬火炉温度分布参数系统模型边界条件和初始条件的影响,提高了参数辨识精度,算法计算量小且保持了系统的空间分布特性.     

原子力显微镜中微悬臂梁分布参数系统的Hammerstein模型

为提高原子力显微镜(atomic force microscope,AFM)中微悬臂梁分布参数模型的精度,本文提出了包含非线性时空特性的改进模型,在此基础上简化控制器的结构.首先加入非线性补偿项修正传统分布参数模型;然后采用Karhunen-Loève(K–L)方法提取系统主导空间基函数,实现系统输出的时空变量分离.利用求解得到的时间系数和系统激励,建立系统时域Hammerstein模型,使系统无限维偏微分方程模型转化为时域有限维常微分方程形式,控制器的设计无需考虑空间耦合的影响;最后,利用最小二乘支持向量机结合奇异值分解法辨识模型中的参数.与传统分布参数模型进行仿真和实验结果比较,验证了方法的有效性.     

基于一致性理论的多源微波加热温度均匀性优化

在使用多微波源阵列进行空间功率合成的微波应用装置时,如何协同多微波源馈入功率的状态信息以利用温度分布的自组织特性优化温度均匀性是研究的重点.为此,一方面,提出微波源构成智能体的必要要素,并构建技术方案.在此基础上,引入基于代数图论的二阶非全连接通信拓扑一致性算法协同多微波源的功率馈入状态信息,保证在利用自组织特性优化温度分布的过程中不会有新的热点产生;另一方面,使用有限元方法,构建解决整型变量和连续型变量混合优化的数值计算模型,开展优化温度场分布均匀性的有效计算.最后通过仿真实验验证微波源智能体化方案的有效性,数值计算结果表明:所提模型较通用加热模型在各水平和铅垂截面能够分别提升24.3%～55.5%和20.4%～82.9%的均匀性;同时能提升10.0%～43.7%的热能转化效率.以上结果验证了所提基于一致性理论的多源微波加热温度均匀性优化方法是可行且高效的.     

Discrete artificial boundary conditions for transient scalar wave propagation in a 2D unbounded layered media

This paper presents an efficient numerical method for direct time-domain solution of the transient scalar wave propagation in a two-dimensional unbounded multi-layer soil. The unbounded domain is truncated by an artificial boundary which demands the corresponding boundary conditions. In the new approach, only the artificial boundary is discretized into one-dimensional finite elements, yielding a new time-dependent partial differential equation (PDE) for displacements with respect to only one spatial coordinate. Factorization of the PDE and introduction of the residual radiation functions, there results a linear first-order ordinary differential equation (ODE). Its stability is ensured. The time-dependent discrete artificial boundary conditions are determined by the solution of the ODE. In general, it is local in time, but it is non-local in space. Several numerical examples are given to verify the superiority of the proposed method.     

Nonlinear Galerkin methods for a system of PDEs with Turing instabilities

We address and discuss the application of nonlinear Galerkin methods for the model reduction and numerical solution of partial differential equations (PDE) with Turing instabilities in comparison with standard (linear) Galerkin methods. The model considered is a system of PDEs modelling the pattern formation in vegetation dynamics. In particular, by constructing the approximate inertial manifold on the basis of the spectral decomposition of the solution, we implement the so-called Euler–Galerkin method and we compare its efficiency and accuracy versus the linear Galerkin methods. We compare the efficiency of the methods by (a) the accuracy of the computed bifurcation points, and, (b) by the computation of the Hausdorff distance between the limit sets obtained by the Galerkin methods and the ones obtained with a reference finite difference scheme. The efficiency with respect to the required CPU time is also accessed. For our illustrations we used three different ODE time integrators, from the Matlab ODE suite. Our results indicate that the performance of the Euler–Galerkin method is superior compared to the linear Galerkin method when either explicit or linearly implicit time integration scheme are adopted. For the particular problem considered, we found that the dimension of approximate inertial manifold is strongly affected by the lenght of the spatial domain. Indeeed, we show that the number of modes required to accurately describe the long time Turing pattern forming solutions increases as the domain increases.     

L1 adaptive control for general partial differential equation (PDE) systems

This paper addresses the L₁ adaptive control problem for general Partial Differential Equation (PDE) systems. Since direct computation and analysis on PDE systems are difficult and time-consuming, it is preferred to transform the PDE systems into Ordinary Differential Equation (ODE) systems. In this paper, a polynomial interpolation approximation method is utilized to formulate the infinite dimensional PDE as a high-order ODE first. To further reduce its dimension, an eigenvalue-based technique is employed to derive a system of low-order ODEs, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE system is augmented with nonlinear time-varying uncertainties. On the basis of the reduced-order ODE system, a dynamic state predictor consisting of a linear system plus adaptive estimated parameters is developed. An adaptive law will update uncertainty estimates such that the estimation error between predicted state and real state is driven to zero at each time-step. And a control law is designed for uncertainty handling and good tracking delivery. Simulation results demonstrate the effectiveness of the proposed modeling and control framework.     

A finite volume scheme for cardiac propagation in media with isotropic conductivities

A finite volume method for solving the monodomain and bidomain models for the electrical activity of myocardial tissue is presented. These models consist of a parabolic PDE and a system of a parabolic and an elliptic PDE, respectively, for certain electric potentials, coupled to an ODE for the gating variable. The existence and uniqueness of the approximate solution is proved, and it is also shown that the scheme converges to the corresponding weak solutions for the monodomain model, and for the bidomain model when considering diagonal conductivity tensors. Numerical examples in two and three space dimensions are provided, indicating experimental rates of convergence slightly above first order for both models.     

2450‐MHz microwave ablation temperature simulation using temperature‐dependence feedback of characteristic parameters

Temperature predictions of microwave ablation (MWA) are currently restricted by the specific temperature‐dependent data of tissue characteristic parameters. To address this issue, a new parameter feedback method based on temperature simulations and single‐thermometry measurements was presented. Experimental data of 2450‐MHz microwave antenna was obtained from ex vivo porcine livers. A temperature distribution model was constructed, and the contributions of characteristic parameters were acquired by the sensitivity analysis method. Subsequently, parameter feedbacks were conducted based on a minimization of the errors between numerical data and single‐thermometry measurements. The temperature distribution model was then optimized using the feedback parameters. Finally, temperature measurements were compared with simulation data to validate the accuracy of the model. According to the temperature distribution model with parameter feedback, the averages of maximum error, average error, as well as SD between the simulation temperatures and the measurements were 2.952, 1.323, and 0.852°C, respectively. The simulated and measured temperature changes were generally in good agreement. The proposed method can be useful in MWA temperature simulations to improve temperature prediction accuracy.     

A galerkin/neural-network-based design of guaranteed cost control for nonlinear distributed parameter systems.

This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.     

基于有限元的衰荡光腔内温度分布仿真

衰荡光腔受温度影响长度变化使腔内光斑模式改变,影响测量精度,为达到衰荡光腔内温度均匀分布,利用仿真平台,对控温箱体内加热片发热功率进行仿真计算。首先设计控温箱体几何模型,确定热传导模型和边界条件,通过有限元分析初步确定控温箱体内温度分布;然后通过参数化扫描和迭代运算,优化控温箱体温度场分布,得到均匀化温度分布所需的各加热片最佳工作功率。通过测试,控温箱体内最大温差小于0.06℃,沿衰荡光腔方向,温差小于0.002℃,达到±0.0005℃的控温精度,满足衰荡光腔内温度变化小于±0.003℃的精度要求。