控制级数

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

Kinetic parameters calculated by Freeman-Carroll method show that the dehydration of ammonium carnallite is not an elementary reaction, but controlled by a series of elementary reactions in different temperature ranges.

用Freeman-Carroll法计算的动力学参数表明，铵光卤石在各温度范围内的脱水反应均不是基元反应，而是由多个不同级数的基元反应所控制。

The result verifies that the discrete model with power series direct discretization method requires 100 memory length to obtain the better approximation, while one with continued fraction direct discretization method requires only 10 order. Thus the continued fraction direct discretization method is preferable to digital realization of fractional order control algorithms in engineering applications.

研究结果表明，幂级数直接离散法得到近似离散模型需要记忆长度为100方可获得较好的近似，而连分式直接离散法近似离散模型为10阶时就可以获得较好的近似，因此连分式直接离散法比较适合于分数阶控制算法的实际工程应用。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

Keywords: Multiscales analysis,Marr edge detection operator,Wavelet decomposition,Edge detection,Degree of the details selection

小波分解的级数控制观察距离"调焦"，改变 Marr算子中的标准差σ、可实现在同一分辨率级上所要求检测边缘的细节程度。

Based on Reddy higher-order shear deformation plate theory and general von Kármán-type equations, the analytical solutions for free vibration and dynamic response of simply supported functionally graded plates with piezoelectric layers in thermal environments are described with double Fourier series, where temperature-dependent material properties are taken into account.

基于Reddy高阶剪切变形理论和广义Kármán 型方程，用双重Fourier级数展开法求得了热环境下带压电层的功能梯度复合材料混合层合板的自由振动及动力响应的解析解，分析中考虑了材料热物参数对温度变化的依赖性，讨论了环境温度和控制电压对固有频率及动力响应的影响。

This method is based on the time-varying Fourier coefficients series of the system variables,and focuses on the dynamics behavior of the Fourier coefficients.

为适应电力系统快速精确仿真和分析控制的需要，采用了一种新的建模方法—基于时变傅立叶级数的动态相量法，对电压源型直流输电进行建模和仿真。

It's much easier to implement the scalable FFT processor based on multilevel pipeline processing architecture.

特别是流水线结构使得FFT处理器在进行不同点数的FFT计算时可以通过对模块级数的控制很容易的实现。

Based on this, this paper develops the modal series method, expounds its mathematic foundation and theory system, and compares it with the linear modal analysis and the method of norm form of vector fields.

开发了基于模态级数法的HVDC/AC互联电力系统分析软件包，通过此软件可以得到系统的非线性响应，获得非线性系统零输入响应的近似闭式解，进行系统模态分析、非线性模态交互作用分析，并为控制系统设计提供有价值的特征信息。

The orthogonal expansion of the solution of the rotating disk motion equation is analyzed, and the stability of the system that includes the controller and the dynamics of sensor and actuator are analyzed.

本文通过对旋转圆盘运动方程解的正交级数展开的分析，由此在考虑控制器、作动器和传感器的动态特性情况下，分析了旋转圆盘振动主动控制系统的稳定性，指出了系统失稳的条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。