A parametric approach for eigenvalue assignment by static output feedback

A well-known method of eigenvalue assignment by static output feedback is improved. The main result is a parametric expression for the output feedback controller gain matrix explicitly characterized by the set of non-linear system of equations obtained for the state feedback design and the set of linear equations resulting from static output feedback consideration. In practice, it is shown that all the possible controllers can be generated for exactly assigning the prescribed eigenvalues of the nominal plant by appropriate software for solving the set of non-linear system of equations thus obtained. This in turn makes it possible to select the output feedback matrix with minimum norm or other constraints. Some numerical examples are presented to illustrate the design technique.     

Complementary formulations in vibrations: bond graph structures and modal transformations

Lumped parameter, undamped vibratory system models are studied starting from a vector bond graph representation which yields a symmetric set of equations of motion in terms of momenta and displacements. Four additional formulations are obtained depending upon the choices of displacement or impulse-momentum degrees of freedom including the classical formulation in terms of mass displacements. Differences in terms of forcing and response variables are found among the alternative formulations and differences in system order are explained. A new form of normal mode equations is developed using first order symmetric variables and a bond graph representation is given. Advantages in the use of the new model analysis for subsystem coupling are discussed.     

贵州大树茶的核型变异与进化

本文对贵州大树茶7种1变种11类型的核型进行了分析。结果表明，这些种类均为二倍体2n＝30。五室茶Camellia quinquelocularis 2n＝30＝24m+6sm；四球茶C．tetracocca 2n＝30=22m+8sm；大理茶C．taliensis 2n=30＝22m+8sm；秃房茶C．gymnogyna 2n＝30＝22m+6sm+2st与2n=30＝20m+8sm+2st；假秃房茶C. gymnogynoides 2n＝30=22m+6sm+2st与2n＝30=20m+8sm+2st；榕江茶C. jungkiangensis 2n＝30+20m+8sm+2st；茶C．sinensis 2n=30＝20m+8sm+2st以及变种淡红花茶C．sinensis var．ruolla 2n＝30=20m+8sm+2st；均属2A核型。染色体结构变异在茶组植物演化中起了重要作用。所划分的两大类核型，即m和sm类与m，sm，和st类是与其子房室数，即5室和3室相一致的。根据核型的不对称性程度、外部形态及生化分析，探讨了各种类的亲缘关系与系统演化途径，论证了茶组植物的原产地是位于滇、桂、黔毗邻交汇处的云贵高原，探讨了茶组植物的分类学问题。     

A nonlinear inverse problem in estimating simultaneously the external forces for a vibration system with displacement-dependent parameters

The conjugate gradient method (CGM), or the iterative regularization method, is applied to a generalized inverse nonlinear force vibration problem, (i.e. system parameters are function of displacement), to simultaneously estimate the unknown time-dependent external forces for a multiple-degree-of-freedom damped system by using the measured displacements. The system parameters of the present study are considered function of displacement, thus it is classified as a genuine nonlinear inverse vibration problem. The numerical experiments are performed to test the validity of CGM by using different types of system parameters, external forces and measurement errors in this study.     

基于增长态归因矩阵法的中国产业动态关联分析

分别利用Leontief逆矩阵和Ghosh逆矩阵构建增长态归因矩阵,提出完全需求拉动作用和完全供给推动作用的评价模型。实证分析表明:增长态归因矩阵法可有效地辨识产业动态关联,有助于选择产业关键部门;拉动作用增强的产业主要依赖间接拉动作用,而其他产业则主要依赖直接拉动作用;就推动作用而言也能得到相同结论。提出我国产业结构调整应立足于需求拉动,优先发展拉动作用与推动作用均增强的产业。     

Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations

A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations. This method transforms the IDE system and the given conditions into the matrix equations via Chebyshev collocation points. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Chebyshev coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the systems of differential and integral equations.     

基于广义逆的桁架结构非线性homologous设计方法

运用M-P广义逆理论,研究了桁架结构的非线性homologous设计问题。将homologous变形约束条件引入结构基本方程,运用M-P广义逆矩阵的性质,将基本方程解的存在条件表示为含可变节点坐标变量的非线性方程组,通过求解该非线性方程组找到了满足homologous变形约束要求的解,并为此推导了AA (A为任意矩阵,A 为A的M-P广义逆矩阵)求偏导数的显式表达。最后的算例验证了本方法的正确性和有效性。     

Observer design and stability analysis for a class of PDE chaotic systems

This paper deals with observer design and stability for a class of partial differential equation (PDE) systems governed by one-dimensional wave equations with mixed derivative terms and superlinear boundary conditions, whose dynamics exhibits chaos when the system parameters change within certain ranges. Firstly, a sufficient and necessary condition that guarantees the stability of this class of systems is obtained. Secondly, based on the method of characteristics, an observer is designed by injecting the measurement output estimation error on the boundary, and the observation error dynamics is proved to be stable with a necessary and sufficient criterion, which can identity the range of the feedback gain for the observer. Finally, two numerical examples are provided to illustrate the validity of the theoretical conclusions.     

二阶线性单面非完整系统的Lie对称性与守恒量

研究二阶线性单面非完整系统的Ｌｉｅ对称性与守恒量。利用运动微分方程在无限小变换下的不变性,建立Ｌｉｅ对称性所满足的确定方程和限制方程,给出了结构方程和守恒量,讨论了二阶线性单非完整系统的Ｌｉｅ对称性逆问题,并举例说明结果的应用。     

Event-triggered backstepping control for attitude stabilization of spacecraft

To decrease the communication frequency between the controller and the actuator, this paper addresses the spacecraft attitude control problem by adopting the event-triggered strategy. First of all, a backstepping-based inverse optimal attitude control law is proposed, where both the virtual control law and the actual control law are respectively optimal with respect to certain cost functionals. Then, an event-triggered scheme is proposed to realize the obtained inverse optimal attitude control law. By designing the event triggering mechanism elaborately, it is guaranteed that the trivial solution of the closed-loop system is globally exponentially stable and there is no Zeno phenomenon in the closed-loop system. Further, the obtained event-triggered attitude control law is modified and extended to the more general case when the disturbance torque cannot be ignored. It is proved that all states of the closed-loop system are bounded, the attitude error can be made arbitrarily small ultimately by choosing appropriate design parameters and the Zeno phenomenon is excluded in the closed-loop system. In the proposed event-triggered attitude control approaches, the control signal transmitted from the controller to the actuator is only updated at the triggered time instant when the accumulated error exceeds the threshold defined elaborately. Simulation results show that by using the proposed event-triggered attitude control approach, the communication burden can be significantly reduced compared with the traditional spacecraft control schemes realized in the time-triggered way.     

谈火力发电厂烟气连续监测系统

针对目前已安装的烟气在线监测系统的组成、安装、故障处理及运行维护等问题进行简略性阐述。烟气污染物在线监测系统是实时、连续监测污染物参数的系统,主要监测烟气中的颗粒物浓度(或浊度)、气态污染物浓度(SO2、NOx、)、辅助参数(烟气温度、流速、氧量、湿度、压力)等【1】。颗粒物浓度监测方法有激光透射法、激光反散射法及电荷感应法,气态污染物浓度监测方法主要有完全抽取法、稀释法、电化学法3种。在电力行业中,颗粒物监测主要采用激光反散射法,气态污染物浓度监测主要采用完全抽取法。     

线性方程组求解的新方法

利用向量组的线性组合来讨论线性方程组的相容性,给出一种新的解法,即将方程组所确定的矩阵进行初等行变换以后,可以直接写出齐次线性方程组的基础解系和非齐次线性方程组的通解.它比通常所用的消元法简单明了,使用方便,容易掌握.     

带前馈输入观测——状态反馈控制系统的CAD

带前馈输入观测——状态反馈控制系统的设计过程,涉及带符号变量的矩阵方程组求解,其通解一般难于求出,国内外大多数文献只能用递推法求其前几个采样值。借助MATLAB符号数学工具箱的有关函数,直接进行带符号变量矩阵运算和方程组求解,得到其准确的通解,系统设计全过程由编制的M文件自动完成。仿真结果表明,提出的设计方法和求解过程是正确的。     

二阶系统数值解耦方法的研究

数值代数领域通过保持Lancaster结构来研究二阶系统的解耦问题,但寻找解耦变换涉及到了非线性方程组求解问题,难以实现. 提出了一种二阶系统数值解耦的新方法. 根据系统解耦前后的同谱信息确定解耦后的系统,将寻找解耦变换的非线性问题转化为齐次Sylvester方程求解问题; 并利用矩阵的Kronecker积理论求解二阶系统的解耦变换. 数值试验证明了该方法的可行性,为二阶系统的数值解耦找到了更便易的实现途径.     

Some New Convergence Conditions for Jacobi's Method

Let Aχ = b be a linear system or equations in which A is an n × n matrix and both χ and b are n dimensional column vectors. If in addition A is row diagonally predominant (i.e. for any i, ¦:a_ii¦>¦:a_ij¦: for all 1?j?n,i≠j), then criteria are developed to show how to ascertain when such matrix problems may be successfully solved using Jacobi's iterative method.     

A robust unscented transformation for uncertain moments

This paper proposes a robust version of the unscented transform (UT) for one-dimensional random variables. It is assumed that the moments are not exactly known, but are known to lie in intervals. In this scenario, the moment matching equations are reformulated as a system of polynomial equations and inequalities, and it is proposed to use the Chebychev center of the solution set as a robust UT. This method yields a parametrized polynomial optimization problem, which in spite of being NP-Hard, can be relaxed by some algorithms that are proposed in this paper.     

Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems

We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used to model second-order linear systems in a very dense manner. These linear bimatrix equations include generalized Sylvester bimatrix equations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunov bimatrix equations. Complete and explicit solutions are provided in terms of the bimatrices that are coefficients of the equations/systems. The obtained solutions are then used to solve the full state feedback pole assignment problem for complex-valued linear system. For a special case of complex-valued linear systems, the so-called antilinear system, the solutions are also used to solve the so-called anti-preserving (the closed-loop system is still an antilinear system) and normalization (the closed-loop system is a normal linear system) problems. Second-order linear systems, particularly, the spacecraft rendezvous control system, are used to demonstrate the obtained theoretical results.     

小子样条件下反坦克导弹的命中精度评估方法研究

针对反坦克导弹定型试验发数少,验前试验信息源多的特点,提出小子样条件下,通过可信性检验分别得到每个验前信息源的可信度,在导弹落点偏差分布为正态一逆伽马分布的假设下,获得评估的验前分布参数,选择基于可信度的加权方法对多源验前信息进行融合,采用估计方法得到命中精度：最后结合实例说明了该方法较传统的方法更稳健,很适合反坦克导弹命中精度的评估。     

Robust observer design for multi-motor web-winding system

This paper develops a novel observer design method for multi-motor web-winding system. Firstly, the multi-motor web-winding system is regarded as a synthetic system with several subsystems, where the dynamic model for each subsystem is given. Then, the nonlinear diffeomorphism transformation is introduced to obtain a transformed system with block triangular structure and the interconnections among the subsystems are allowed. Next, a decentralized high-gain observer with sliding mode is designed for the transformed system, based on which the estimation error dynamics can be got. Sufficient condition of asymptotic stability for estimation error dynamics is derived by the Lyapunov stability theory and the observer gain is obtained. After that, the observer for original multi-motor web-winding system is achieved via inverse transformation. Finally, the simulation and analysis are performed in the three-motor web-winding system to verify the effectiveness of the proposed observer.     

Maple在弹性力学教学中的应用

弹性力学具有很强的理论性、抽象性和高度概括性的特点,而且它的求解过程对数学运算依赖性大,所以加大了学生的学习难度。Maple是一个具有强大符号运算能力、数值计算能力和图形处理能力的交互式计算机代数系统,可以利用它解决各种方程、方程组、微分方程、线性代数等数学问题。因此,可以利用maple来求解弹性力学中的一些具体问题,具体实例表明,将Maple软件应用到弹性力学的教学中可以减轻学生对数学运算的依赖性,减小学习难度,使弹性力学从抽象变得直观。从而为弹性力学教学提供了一种方便、快捷地实现直观性教学的方法。