The critical point set plays a central role in the theory of Tchebyshev approximation. Generally, in multivariate Tchebyshev approximation, it is not a trivial task to determine whether a set is critical or not. In th...The critical point set plays a central role in the theory of Tchebyshev approximation. Generally, in multivariate Tchebyshev approximation, it is not a trivial task to determine whether a set is critical or not. In this paper, we study the characterization of the critical point set of S^01（△） in geometry, where A is restricted to some special triangulations （bitriangular, single road and star triangulations）. Such geometrical characterization is convenient to use in the determination of a critical point set.展开更多
针对存在临界点的A类被控对象及不存在临界点的B类被控对象,分别采用其-180?和-120?相位点的频率和增益提出了PID (Proportional-integral-derivative)控制器参数的优化整定方法.基于Tchebyshev多项式和分数阶积分器求取被控对象-180?或...针对存在临界点的A类被控对象及不存在临界点的B类被控对象,分别采用其-180?和-120?相位点的频率和增益提出了PID (Proportional-integral-derivative)控制器参数的优化整定方法.基于Tchebyshev多项式和分数阶积分器求取被控对象-180?或-120?相位点的频率和增益,建立其积分滞后模型.采用负载扰动下跟踪误差平方和(Sum of squares of tracking errors, SSE)最小作为优化指标,使闭环系统具有强的鲁棒性的最大灵敏度和最大补灵敏度为约束方程,针对两类被控对象,分别建立了基于-180?和-120?相位点频率和增益的PID控制器比例、积分与微分三个参数的优化整定规则.通过与其他常用PID控制方法的仿真与物理对比实验,表明所提方法的优越性.展开更多
This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis fo...This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] （r〈s）.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1027102260373093+3 种基金605330601110136661100130)the Innovation Foundation of the Key Laboratory of High-Temperature Gasdynamics of Chinese Academy of Sciences
文摘The critical point set plays a central role in the theory of Tchebyshev approximation. Generally, in multivariate Tchebyshev approximation, it is not a trivial task to determine whether a set is critical or not. In this paper, we study the characterization of the critical point set of S^01（△） in geometry, where A is restricted to some special triangulations （bitriangular, single road and star triangulations）. Such geometrical characterization is convenient to use in the determination of a critical point set.
文摘针对存在临界点的A类被控对象及不存在临界点的B类被控对象,分别采用其-180?和-120?相位点的频率和增益提出了PID (Proportional-integral-derivative)控制器参数的优化整定方法.基于Tchebyshev多项式和分数阶积分器求取被控对象-180?或-120?相位点的频率和增益,建立其积分滞后模型.采用负载扰动下跟踪误差平方和(Sum of squares of tracking errors, SSE)最小作为优化指标,使闭环系统具有强的鲁棒性的最大灵敏度和最大补灵敏度为约束方程,针对两类被控对象,分别建立了基于-180?和-120?相位点频率和增益的PID控制器比例、积分与微分三个参数的优化整定规则.通过与其他常用PID控制方法的仿真与物理对比实验,表明所提方法的优越性.
基金Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
文摘This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] （r〈s）.
