In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified hi...It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified highly precise direct integration(VHPD-T method)was presented.Through introducing new variables and expanding dimensions,the system can be transformed into a timeinvariant system,in which the transfer matrix can be computed for once and used forever with a highly precise direct integration method.The method attains higher precision than the common methods(e.g.RK4 and power series)and high efficiency in computation.Some numerical examples demonstrate the validity and efficiency of the method proposed.展开更多
This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order...This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.展开更多
将神经网络与比例-积分-微分(Proportion Integral Differential,PID)相结合,设计电力可编程逻辑控制器(Programmable Logic Controller,PLC)高精度温控方法。选用GX20MH01型号的温度传感器采集温度数据;选择多层前馈神经网络作为神经...将神经网络与比例-积分-微分(Proportion Integral Differential,PID)相结合,设计电力可编程逻辑控制器(Programmable Logic Controller,PLC)高精度温控方法。选用GX20MH01型号的温度传感器采集温度数据;选择多层前馈神经网络作为神经网络结构,计算网络传播数据的误差;通过神经元输出的激活数值,引进PID控制算法,整定电力系统控制器温度参数;基于专家经验知识,将输入变量划分为若干个模糊集合,以此为依据设计模糊控制规则,高精度控制电力PLC温度。对比实验结果表明:应用设计的方法进行温度控制后,电力PLC温度值稳定在目标值,波动范围极小,控制效果良好。展开更多
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
基金supported by the National Natural Science Foundation of China(Grant No.50876066)
文摘It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified highly precise direct integration(VHPD-T method)was presented.Through introducing new variables and expanding dimensions,the system can be transformed into a timeinvariant system,in which the transfer matrix can be computed for once and used forever with a highly precise direct integration method.The method attains higher precision than the common methods(e.g.RK4 and power series)and high efficiency in computation.Some numerical examples demonstrate the validity and efficiency of the method proposed.
基金supported by the National Natural Science Foun-dation of China (11172334)
文摘This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.
文摘将神经网络与比例-积分-微分(Proportion Integral Differential,PID)相结合,设计电力可编程逻辑控制器(Programmable Logic Controller,PLC)高精度温控方法。选用GX20MH01型号的温度传感器采集温度数据;选择多层前馈神经网络作为神经网络结构,计算网络传播数据的误差;通过神经元输出的激活数值,引进PID控制算法,整定电力系统控制器温度参数;基于专家经验知识,将输入变量划分为若干个模糊集合,以此为依据设计模糊控制规则,高精度控制电力PLC温度。对比实验结果表明:应用设计的方法进行温度控制后,电力PLC温度值稳定在目标值,波动范围极小,控制效果良好。
