基于混合集成建模的硅单晶直径自适应非线性预测控制

大尺寸、电子级直拉硅单晶生长过程中物理变化复杂、多场多相耦合、模型不确定且存在大滞后和非线性等特性, 因此如何实现硅单晶直径控制是一个具有理论意义和实际价值的问题. 本文结合工程实际提出一种基于混合集成建模的晶体直径自适应非线性预测控制方法. 首先, 为了准确辨识晶体直径模型, 提出基于互相关函数的时滞优化估计方法和基于Lipschitz商准则与模型拟合优度的模型阶次辨识方法; 其次, 基于“分而治之”原理构建晶体直径混合集成模型. 其中, 采用小波包分解(Wavelet packet decomposition, WPD)方法将原始数据分解成若干个子序列, 以减少其非平稳性和随机噪声. 极限学习机(Extreme learning machine, ELM)和长短时记忆网络(Long-short-term memory networks, LSTM)分别建立近似(低频)子序列和细节(高频)子序列的预测模型, 最终晶体直径预测输出由各子序列的预测结果汇总而成; 然后, 针对晶体直径混合集成模型失配问题以及目标函数难以求解问题, 提出一种基于蚁狮优化(Ant lion optimizer, ALO)的自适应非线性预测控制策略. 最后, 基于工程实验数据仿真分析, 验证了所提建模及控制方法的有效性.     

基于速度模型的改进内模控制算法

对非线性动态系统采用速度线性化方法建立全局的线性模型,速度模型的线性参变(LPV)系统由输入和输出的信息来描述,而稳态信息由偏差来表示.针对速度模型的内模控制(IMC)不能有效消除线性参变模型稳态误差的问题,提出了一种改进结构的内模控制器,以实现零稳态误差.此方法可应用于具有强非线性pH值的中和过程,仿真结果表明该方法的有效性.     

无模型容积卡尔曼滤波及其应用

提出一种融合高斯过程回归(GPR)的无模型容积卡尔曼滤波(MF-CKF)方法.容积卡尔曼滤波(CKF)是一种新的非线性高斯滤波方法,比无迹卡尔曼滤波(UKF)更具优势.为了克服建模不准确时容积卡尔曼滤波精度下降问题,通过将高斯过程回归引入到容积卡尔曼滤波之中,对训练数据学习建立系统非线性模型,从而有效地避免模型不准确造成的滤波性能下降.仿真结果验证了无模型容积卡尔曼滤波在系统模型不准确情况下的优越性.     

污水处理过程的集合型监测方法研究

针对具有非线性、多变量特性的污水处理过程监测准确性有待提高问题,提出一种集合型EMD-IFCM-KPCA过程监测方法.该方法首先利用经验模态分解方法对数据进行预处理,然后用改进的模糊C均值聚类对数据进行聚类,最后采用核主成分分析方法对污水处理过程中的异常状态进行监测.水处理基准模型(BSM1)过程监测实验结果表明,将EMD-IFCM-KPCA集合型方法应用于污水处理过程,监测准确性优于传统KPCA,IFCM-KPCA等方法.     

基于改进核主元分析的TE故障诊断

PCA、KPCA作为常用的多变量统计监控算法,一般适用于定常过程。针对实际工业过程的时变、非线性特性,提出一种基于分块的改进KPCA算法。该方法通过采用随时间更新的核矩阵代替固定核矩阵用于主元模型的建立,使非线性监控模型能够在线更新,从而提高KPCA的检测正确率。与KPCA方法相比,该方法的运算复杂度明显降低。将该方法应用于TE(Tennessee Eastman)过程,仿真结果显示,该方法具有较好的监测性能,且所需时间大大减小,说明了本算法的有效性。     

基于国际评价基准的溶解氧控制方法研究

针对活性污泥污水处理过程溶解氧浓度(DO)控制的非线性特性，以DO为控制对象、国际评价基准（benchmark）为平台，将PID控制、增益调度控制和一般模型控制(GMC)方法应用于DO控制中，并进行了控制器性能的比较．仿真结果表明，所提一般模型非线性控制方法的性能优于其他两种控制方法，体现出该方法的有效性和优越性．     

基于最优保留遗传算法的非线性模糊预测控制

针对传统的模型预测控制不能很好解决具有严重非线性、不确定性的对象或过程的控制问题，提出将模糊模型用于描述对象的非线性动态特性，通过将模糊模型的输出反馈作为模型输入，从而构成了模糊多步预测器。采用一种收敛精度高、速度快的具有最优保留特性遗传算法(EGA)，依据模型预测输出在线滚动求解控制律的非线性预测控制算法。仿真结果表明该算法对一类非线性系统具有较快的响应速度和较强的抗干扰能力。     

带测量误差的非线性退化过程建模与剩余寿命估计

剩余寿命(Remaining useful lifetime, RUL)估计是设备视情维护和预测与健康管理(Prognostics and health management, PHM)中的一项关键问题. 采用退化过程建模进行剩余寿命估计的研究中,现有方法仅考虑了具有线性或可以线性化的退化轨迹的问题.本 文提出了一种基于扩散过程的非线性退化过程建模方法,在首达时间的意义下,推导出了剩余寿命的分布.该方法可以描述一般的非线性退化轨迹, 现有的线性退化建模方法是其特例.在参数的推断中,考虑到真实的退化过程受到测量误差的影响,难以直接测量得到, 因此,在退化建模的过程中引入了测量误差对退化观测数据的影响,通过观测数据,提出了一种退化模型未知参数的极大似然估计方法. 最后,通过激光发生器和陀螺仪的退化测量数据验证了本文方法明显优于线性建模方法,具有潜在的工程应用价值.     

基于最优保留遗传算法的非线性模糊预测控制

针对传统的模型预测控制不能很好解决具有严重非线性、不确定性的对象或过程的控制问题。提出将模糊模型用于描述对象的非线性动态特性。通过将模糊模型的输出反馈回来作为模型输入，从而构成了模糊多步预测器，采用一种收敛精度高、速度快的具有最优保留特性遗传算法(EGA)依据模型预测输出在线滚动求解控制律的非线性预测控制算法。仿真结果表明该算法对一类非线性系统具有较快的响应速度和较强的抗干扰能力。     

基于神经网络的多变量发酵过程自适应控制

运用非线性系统的线性化方法与神经网络在线辨识技术，提出了一种基于神经网络 的多变量自适应控制策略．提出的控制策略，当过程模型缺乏足够的先验知识时，对多变量 非线性连续发酵过程取得了良好的控制性能．仿真结果表明，提出的自适应控制方法能够适 应过程模型的不确定性和参数的时变性，具有较强的鲁棒性．并且通过对比分析得出，基于 微分几何理论的输入输出线性化解耦控制方案，由于控制器的设计依赖于过程模型，对模型 参数的变化很敏感，应用在发酵过程的非线性控制中，控制精度较低，鲁棒性较差．     

Hybrid modelling of a sugar boiling process

The first and maybe the most important step in designing a model-based predictive controller is to develop a model that is as accurate as possible and that is valid under a wide range of operating conditions. The sugar boiling process is a strongly nonlinear and nonstationary process. The main process nonlinearities are represented by the crystal growth rate. This paper addresses the development of the crystal growth rate model according to two approaches. The first approach is classical and consists of determining the parameters of the empirical expressions of the growth rate through the use of a nonlinear programming optimization technique. The second is a novel modeling strategy that combines an artificial neural network (ANN) as an approximator of the growth rate with prior knowledge represented by the mass balance of sucrose crystals. The first results show that the first type of model performs local fitting while the second offers a greater flexibility. The two models were developed with industrial data collected from a 60 m³ batch evaporative crystallizer.     

Nonlinear predictive control of irregularly sampled multirate systems using blackbox observers

This work aims the development of an inferential nonlinear model predictive control (NMPC) scheme based on a nonlinear fast rate model that is identified from irregularly sampled multirate data, which is corrupted with unmeasured disturbances and measurement noise. The model identification is carried out in two steps. In the first step, a MISO fast rate nonlinear output error (NOE) model is identified from the irregularly sampled output data. In the second step, a time varying nonlinear auto-regressive (NAR) type model is developed using the residuals generated in the first step. The deterministic and stochastic components of the observer are parameterized using generalized ortho-normal basis filters (GOBF). The identified NOE and NAR models are combined to form MISO state observers. We then proceed to use these identified observers to formulate a nonlinear MPC strategy for controlling irregularly sampled multirate systems. The identified observers are used to generate inter-sample estimates of the irregularly sampled outputs and for performing future trajectory predictions. The efficacy of the proposed modeling and control scheme is demonstrated using simulations on a benchmark continuous fermentation process. This process exhibits input multiplicity and change in the sign of steady state gain in the operating region. The validity of the proposed modeling and control scheme is also established by conducting identification and control experiments on a laboratory scale heater-mixer setup. The proposed NMPC gives satisfactory regulatory as well as servo performance over a wide operating range in the irregularly sampled multirate scenario.     

Finite element approximation of nonlinear transient magnetic problems involving periodic potential drop excitations

This paper deals with the computation of nonlinear 2D transient magnetic fields when the data concerning the electric current sources involve potential drop excitations. In the first part, a mathematical model is stated, which is solved by an implicit time discretization scheme combined with a finite element method for space approximation. The second part focuses on developing a numerical method to compute periodic solutions by determining a suitable initial current which avoids large simulations to reach the steady state. This numerical method leads to solve a nonlinear system of equations which requires to approximate several nonlinear and linear magnetostatic problems. The proposed methods are first validated with an axisymmetric example and sinusoidal source having an analytical solution. Then, we show the saving in computational effort that this methodology offers to approximate practical problems specially with pulse-width modulation (PWM) voltage supply.     

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.     

Neural network modelling of continuous microbial cultivation accounting for the memory effects

Three approaches to the problem of Neural Network (NN) modelling of chemostat microbial culture accounting for the memory effects are considered and, based on the results they are compared. The first approach uses feedforward NNs with time delay feedback connections from and to the output neurons, for the entire process modelling. The second and third approach relay on Hybrid NN modelling. The second one applies feedforward NNs with time delayed inputs for the specific growth rate approximation within the framework of the classical unstructured model. In this case the specific consumption rate is assumed to be proportional to the specific growth rate. The yield factor is assumed to be constant or polynomial function of the substrate concentration. The third approach is also based on a classical unstructured model, but different feedforward NNs with delay elements for both specific growth rate and specific consumption rate approximation are adopted. On the example of the growth of a strain Saccharomyces cerevisiae on a glucose limited medium different NN topologies are studied and a suitable model is figured out.     

Pumping with electroosmosis of the second kind in mesoporous skeletons

This paper presents the use of mesoporous silica skeletons as substrates for electroosmotic (EO) micropumps. Mesoporous silica skeletons have bimodal pore size distributions consisting of macropores and cation-permselective mesopores. These materials have the potential for high flow rate per power because the cation-permselective mesopores can generate an induced charge layer (ICL) and electroosmosis of the second kind (EO-2) under high applied electric fields. The diffuse charge layers induced by the electric field result in an EO-2 flow rate that increases quadratically with increasing electric field. In contrast, the flow rate of the more common electroosmosis of the first kind (EO-1) is linearly proportional to electric field. Here, we investigate the impact of finite pressure loads on the EO-2 flow rate with experiments and an engineering model to evaluate the potential of mesoporous skeletons for micropumping applications. Our results include analyses of maximum flow rate, maximum pressure, and flow rate with intermediate pressure loads. The results indicate the existence of a critical pressure load at which reverse pressure-driven flow significantly diminishes the EO-2 flow. We also investigate the scaling of flow rate per power with respect to substrate thickness and area, demonstrating significant increases in flow rate per power with thinner substrates and favorable scaling for miniaturization of EO-2 pumps.     

磁悬浮系统的两种线性化控制方法

本文首先利用动力学和电磁学方法建立了磁悬浮系统的模型 ,然后给出了直接反馈线性化方法的控制器设计 ,接着给出了基于平衡点展开的控制器设计 ,最后将两种控制方法的性能做了仿真比较 ,得出了两种方法的优劣结论。     

PF-MPC: Particle filter-model predictive control

In this article, a new model predictive control approach to nonlinear stochastic systems will be presented. The new approach is based on particle filters, which are usually used for estimating states or parameters. Here, two particle filters will be combined, the first one giving an estimate for the actual state based on the actual output of the system; the second one gives an estimate of a control input for the system. This is basically done by adopting the basic model predictive control strategies for the second particle filter. Later in this paper, this new approach is applied to a CSTR (continuous stirred-tank reactor) example and to the inverted pendulum. These two examples show that our approach is also real-time-capable.     

Optimal control of convection–diffusion process with time-varying spatial domain: Czochralski crystal growth

This paper considers the optimal control of convection–diffusion systems modeled by parabolic partial differential equations (PDEs) with time-dependent spatial domains for application to the crystal temperature regulation problem in the Czochralski (CZ) crystal growth process. The parabolic PDE model describing the temperature dynamics in the crystal region arising from the first principles continuum mechanics is defined on the time-varying spatial domain. The dynamics of the domain boundary evolution, which is determined by the mechanical subsystem pulling the crystal from the melt, are described by an ordinary differential equation for rigid body mechanics and unidirectionally coupled to the convection–diffusion process described by the PDE system. The representation of the PDE as an evolution system on an appropriate infinite-dimensional space is developed and the analytic expression and properties of the associated two-parameter semigroup generated by the nonautonomous operator are provided. The LQR control synthesis in terms of the two-parameter semigroup is considered. The optimal control problem setup for the PDE coupled with the finite-dimensional subsystem is presented and numerical results demonstrate the regulation of the two-dimensional crystal temperature distribution in the time-varying spatial domain.     

Convergence in economic model predictive control with average constraints

In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples.