任意平面区域的变尺寸有限元网格划分

利用任意平面域边界表述中的拓年要素定义网格的控制信息,通过引入节点间距函数来控制区域内网格尺寸变化,并将结合前沿生成法和Ｄｅｌａｕｎａｙ三角化方法的优点,优先处理前沿的最长边,尽可能在局部生成边长逐渐减小的Ｄｅｌａｕｎａｙ三角形,最终实验区域内网格的疏密过渡。     

压电复合材料层合板自适应结构的振动控制

本文针对板壳型自适应结构,研究了压电材料作为作动器的自适应结构的振动控制。利用四节点压电复合材料层合板单元进行自适应结构的有限元动力分析;采用模态控制方法,将结构的各阶模态的阻尼比作为控制目标,并以此计算出各压电片的控制电压,达到控制结构振动的目的。算例给出了数值计算的结果。     

论基础数学工具的创新运用

在建立叶轮机三元流面理论时,吴仲华巧妙地、创造性地提出了全导数型的沿流面方向偏导数的概念和表达式,导出了两类流面气动力学数学模型,不但数学形式简洁,而且具有明晰的物理意义,有利于分析和求解。在吴氏流面理论的启示下,作者不断致力于基础数学工具和概念的推广和创新运用,挖掘并发挥其潜在功能。本文将通过流体力学、传热学以及最优控制论方面的一些实例来综合介绍个人的心得和体会。     

作动器/传感器优化配置的研究进展

给出了作动器／传感器优化配置问题的数学描述,综述了作动器／传感器优化配置方法的发展现状．阐述了振动控制和模态试验中作动器／传感器优化配置的关系．并给出需要进一步研究的几个问题      

密频系统振动控制的状态估计

首先在研究了重频系统中状态可观察的必要条件基础上,给出了设计重频系统状态估计器的方法,使得状态估计的误差能以事先指定的速率衰减。随后给出两种方法将上述重频系统的估计器用到密频系统上去：一种是直接用重频系统估计器来估计密频系统状态,另一种是用按重频系统设计得到的估计矩阵构造密频系统的观察器,并分析由此引起的误差。分析表明,第一种方法简单易行,并且在频率分散度比较小时可以得到理想的结果;第二方法的精度较高,其误差与状态变量本身无直接关系。数值例子表明,用提出的状态估计器,并按相应的状态控制器,可以使密频系统的振动按事先给定的衰减程度趋向于零。     

The invariant manifold method and the controllability of nonlinear control system

The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A.M.Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics of rigid body to nonlinear control system for the first time and obtained a series of efficient results. Based on Kovalev’s oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition was discussed. At last, the motion of a rigid body with two rotors was investigated and the necessary condition which is satisfied by this system was proved.     

A reduced‐order approach for optimal control of fluids using proper orthogonal decomposition

In this article, a reduced‐order modeling approach, suitable for active control of fluid dynamical systems, based on proper orthogonal decomposition (POD) is presented. The rationale behind the reduced‐order modeling is that numerical simulation of Navier–Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. The possibility of obtaining reduced‐order models that reduce the computational complexity associated with the Navier–Stokes equations is examined while capturing the essential dynamics by using the POD. The POD allows the extraction of a reduced set of basis functions, perhaps just a few, from a computational or experimental database through an eigenvalue analysis. The solution is then obtained as a linear combination of this reduced set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations (PDEs). It is used here in active control of fluid flows governed by the Navier–Stokes equations. In particular, flow over a backward‐facing step is considered. Reduced‐order models/low‐dimensional dynamical models for this system are obtained using POD basis functions (global) from the finite element discretizations of the Navier–Stokes equations. Their effectiveness in flow control applications is shown on a recirculation control problem using blowing on the channel boundary. Implementational issues are discussed and numerical experiments are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture

In this paper, we consider an optimal control problem of microbial fermentation process in which glycerol is converted to 1,3-propanediol by Klebsiella pneumoniae in fed-batch culture. During the period of reaction, the variation of pH value is monitored to determine glycerol replenishment quantity, guaranteeing that microorganism can always keep growing fast under enough nutrition. Every time pH value is lower than seven, the quantity of glycerol added is such that pH value returns seven again. Glycerol is poured into reactor at discrete time instant and the quantity is controllable. The problem is to determine for each discrete time instant the glycerol quantity to add and maximize the final concentration of 1,3-propanediol. We present a controlled explicit nonlinear impulsive dynamical system of fed-batch culture with state independent vector measures as controls and study the existence, uniqueness, boundedness, continuous dependence and Gâteaux differentiability of its solution with respect to controls. We then propose a multiple objective programming model and demonstrate the regularity of cost functionals and weak compactness of admissible control set. Finally we discuss the existence of optimal control and implement a hybrid particle swarm optimization algorithm to solve the model optimally. Computational results are presented on a numerical example.     

Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem

In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.     

高阶控制增稳系统等效拟配参数时域在线辨识方法

现代控制增稳飞机是高达几十阶的复杂系统,将其降阶为特定形式的低阶等效系统才能与已有飞行品质规范进行比较,进而预测和评价飞机飞行品质.从时域角度出发,提出了一种高阶控制增稳系统等效拟配参数在线辨识方法.分析了时域等效系统拟配的基本方法,提出了等效系统实时在线拟配的系统框架思路,基于Tustin变换法推导了由高阶系统时域响应获取四阶等效系统参数的数学公式,应用最小二乘法在MATLAB中实现了算法编程,并用试飞数据验证了所提方法的可行性.计算结果表明,所提方法可以快速准确地实现高阶控制增稳系统的等效系统参数辨识.