基于Taylor Series-LQR复合策略的双关节机械臂时滞补偿控制

为解决时滞导致的颤振问题,提出了一种基于Taylor Series-LQR(Linear Quadratic Regulator)复合策略的双关节机械臂时滞补偿控制方法。首先,利用两个一阶泰勒级数分别构建基于两机械臂当前理想控制力预测下一时滞时刻的理想控制力的预测方程;然后,利用这两个预测方程对描述双关节机械臂运动的状态方程进行扩展;最后,根据LQR控制策略设计时滞补偿预测控制器求取预测控制力。应用结果显示,随着时滞的变大,使用无补偿措施的LQR控制器的双关节机械臂的颤振逐渐增大,并最终走向运动发散,而使用Taylor Series-LQR时滞补偿预测控制器的双关节机械臂在较大时滞范围内均能稳定跟踪期望轨迹而不产生颤振,说明Taylor Series-LQR复合策略具有良好的双关节机械臂时滞补偿效果。

TAYLOR SERIES AND ORTHOGONALITY OF THE OCTONION ANALYTIC FUNCTIONS

The Taylor series of the Octonion analytic function is given. And the orthogonal formula for the Octonion analytic functions is also obtained.

SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES

Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN C^n

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.

THE DISTRIBUTION OF VALUES OF TAYLOR SERIES

Clarify some classical results and their proofs on the distribution of values of simple Taylor series and extend them to multiple Taylor series.

On Random Taylor Series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.

A Strong Stability Preserving Analysis for Explicit Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions

High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for the solution of hyperbolic PDEs.Multi-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs,and the strong stability properties of these methods are of interest.In our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative formulation.However,many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation,but rather with a more natural Taylor series formulation.In this work we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series formulation.We call these strong stability preserving Taylor series(SSP-TS)methods.We also prove that the maximal order of SSP-TS methods is p=6,and define an optimization procedure that allows us to find such SSP methods.Several types of these methods are presented and their efficiency compared.Finally,these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods,the need for the SSP property,and the sharpness of the SSP time-step in many cases.

Solution of Delay Differential Equations Using a Modified Power Series Method

This paper presents a Modified Power Series Method (MPSM) for the solution of delay differential equations. Unlike the traditional power series method which is applied to solve only linear differential equations, this new approach is applicable to both linear and nonlinear problems. The method produces a system of algebraic equations which is solved to determine the coefficients in the trial solution. The method provides the solution in form of a rapid convergent series. The obtained results for numerical examples demonstrate the reliability and efficiency of the method.

Application of Synthetic Meteorological Time Series in BROOK90:A Case Study for the Tharandt Forest in Saxony,Germany

This study presents an extended version of a single site daily weather generator after Richardson. The model is driven by daily precipitation series derived by a first-order two-state Markov chain and considers the annual cycle of each meteorological variable. The evaluation of its performance was done by deploying its synthetic time series into the physical based hydrological model BROOK90. The weather generator was applied and tested for data from the Anchor Station at the Tharandt Forest, Germany. Additionally its results were compared to the output of another weather generator with spell-length approach for the precipitation series (LARS-WG). The comparison was distinguished into a meteoro-logical and a hydrological part in terms of extremes, monthly and annual sums and averages. Extreme events could be preserved adequately by both models. Nevertheless a general underestimation of rare events was observed. Natural correlations between vapour pressure and minimum temperature could be conserved as well as annual cycles of the hydro-logical and meteorological regime. But the simulated spectrums of extremes, especially, of precipitation and temperature, are more limited than the observed spectrums. While LARS-WG already finds application in practice, the results show that the data derived from the presented weather generator is as useful and reliable as those from the established model for the simulation of the water balance.

Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems

To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.

基于Chan氏算法和Taylor级数展开法的协同定位方法

该文分析讨论了Chan和泰勒两种TDOA定位算法的优缺点,并在此基础上提出了基于 Chan氏算法(1994)和Taylor级数展开法(1976)的协同定位方法。通过在不同信道环境下对协同定位 方法进行仿真,表明该方法在信道环境恶劣时能够有效地提高定位精度。

Taylor级数展开法定位及其性能分析

讨论适合于TDOA定位的信道模型,分析1种典型TDOA定位算法———Taylor级数展开法,并针对其收敛问题提出改进方法。结合不同信道环境和蜂窝基站位置分布,对Taylor级数展开法的性能进行仿真,并就各种环境参数对算法性能的影响,与其它算法进行分析比较。

基于能量函数高阶Taylor级数展开技术的直接法

本文提出了一种基于能量函数高阶Ｔａｙｌｏｒ级数展开技术的电力系统暂态稳定性直接法。该方法首先推导出动能、势能和总能量的各阶导数，然后形成动能、势能和总能量的高阶Ｔａｙｌｏｒ级数展开式，井在此基础上快速求取临界故障切除时间。实例分析表明，本文方法具有准确度高、速度快的特点，可以用于电力系统暂态稳定性的快速分析。

快速高阶Taylor级数法暂态稳定计算

本文从解析发电机节点入手,分析和研究了发电机与系统网络座标系之间座标变换矩阵的导数规律。并结合因子表技术,得到了在计及发电机暂态凸极效应的情况下,发电机与系统网络接口处各种时变量的各阶导数的递推公式,形成了快速高阶Taylor级数法暂态稳定计算方法。分析和计算结果表明该方法具有准确、快速和递推的优点,在电力系统暂态稳定计算与分析中有很大的实用价值。

基于隐式Taylor级数法的电力系统暂态稳定计算

基于快速高阶Taylor级数法暂态稳定计算,结合隐式积分梯形公式,推导了隐式Taylor级数法。对该方法的数值稳定性进行了分析,得到了一种可调谐的隐式Taylor级数法。该方法保留了显式Taylor级数法准确、快速、递推和编程简单的优点,并明显提高了数值计算稳定性。分析与计算表明,该方法具有隐式积分数值稳定性好、可以采用较大的积分步长、能够适应较长动态过程仿真计算的特点,同时又具有显式积分编程简单可靠、便于扩展的优点。

基于移相器统一特性和高阶Taylor级数展开技术的暂态稳定计算方法

根据移相器的共同性质，对暂态稳定计算中的移相器作了统一处理，得出了移相器支路对网络节点导纳矩阵影响的统一形式。将此形式与高阶Taylor级数展开技术相结合，形成了能灵活统一地处理各种移相器并具有快速计算能力的暂态稳定计算方法。

Taylor级数法暂态稳定计算中阶数的动态控制

在对Taylor级数法暂态稳定计算的计算量进行定量分析的基础上，根据计算精度的要求，提出了Taylor级数法暂态稳定计算中阶数的动态控制。分析与计算结果表明，由于在计算过程中按计算精度的要求动态选取求导阶数，从而在保证计算精度的前提下，有效地提高了Taylor级数法暂态稳定计算的解算效益，具有实用价值。

多群模式Taylor级数法暂态稳定计算

Taylor级数法自引入到电力系统暂态稳定分析领域以来,因其高效的计算效率而倍受青睐,但其求解的是不等值N机系统的微分方程,因此计算效率未发挥到极致。文中从减少微分方程个数角度,借助于同调分群技术得出多群模式等值参数,并推导了多群模式下发电机的电磁功率、功角新的Taylor级数表达式,该方法保留了Taylor级数简洁、循环递推的特点,具有更高的计算效率。新英格兰10机系统算例分析表明:采用等值参数的多群模式Taylor级数法,在保持准确性的同时,减少了模拟的微分方程个数,极大提高了暂态稳定分析效率。