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Peano Derivatives and Singular Integrals of Arbitrary Order
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作者 Lu Jianke (Department of Mathematics, Wuhan University, Wuhan 430072,China) 《Wuhan University Journal of Natural Sciences》 CAS 1996年第1期9-13,共5页
The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals ... The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established. 展开更多
关键词 Peano derivatives singular integrals of arbitrary order Cauchy principal value integrals
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Pfaff-Birkhoff Variational Problem and Noether Symmetry in Terms of RiemannLiouville Fractional Derivatives of Variable Order
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作者 严斌 张毅 《Journal of Donghua University(English Edition)》 EI CAS 2017年第4期523-528,共6页
The Pfaff-Birkhoff variational problem and its Noether symmetry are studied in terms of Riemann-Liouville fractional derivatives of variable order. Based on the combination of variational principle and fractional calc... The Pfaff-Birkhoff variational problem and its Noether symmetry are studied in terms of Riemann-Liouville fractional derivatives of variable order. Based on the combination of variational principle and fractional calculus of variable order,the Pfaff-Birkhoff variational principle with Riemann-Liouville fractional derivatives of variable order is proposed, and the fractional Birkhoff's equations of variable order are derived. Then,the Noether 's theorem for the fractional Birkhoffian system of variable order is given. At last,an example is expressed to illustrate the application of the results. 展开更多
关键词 fractional Birkhoffian system Noether symmetry conserved quantity fractional derivatives of variable order
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DERIVATION AND INTEGRAL SLIDING MODE VARIABLE STRUCTURE CONTROL OF HYDRAULIC VELOCITY TRACKING SYSTEM 被引量:3
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作者 WeiJianhua GuanCheng 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2005年第2期224-227,共4页
The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a der... The velocity tracking control of a hydraulic servo system is studied. Sincethe dynamics of the system are highly nonlinear and have large extent of model uncertainties, suchas big changes in load and parameters, a derivation and integral sliding mode variable structurecontrol scheme (DI-SVSC) is proposed. An integral controller is introduced to avoid the assumptionthat the derivative of desired signal must be known in conventional sliding mode variable structurecontrol, a nonlinear derivation controller is used to weaken the chattering of system. The designmethod of switching function in integral sliding mode control, nonlinear derivation coefficient andcontrollers of DI-SVSC is presented respectively. Simulation shows that the control approach is ofnice robustness and improves velocity tracking accuracy considerably. 展开更多
关键词 Hydraulic servo system Velocity tracking integral variable structurecontrol Nonlinear derivation control
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Fractional Order Proportional Integral Derivative Controller Design and Simulation for Bioengineering Systems
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作者 Wei-Cheng Fu Chun-Yang Wang +1 位作者 Yao-Wu Shi Ying-Bin Sun 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2013年第5期46-50,共5页
This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order m... This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order mathematical model of bioengineering systems. The main contents include the design of FOPID controller and the simulation for bioengineering systems. The simulation results show that the tuning method of fractional order system based on the FOPID controller outperforms the fractional order system based on Fractional Order Proportional Integral( FOPI) controller. As it can enhance control character and improve the robustness of the system. 展开更多
关键词 ROBUSTNESS bioengineering systems fractional order proportional integral derivative controller
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ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER 被引量:3
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作者 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2004年第1期9-27,共19页
Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also gi... Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given. 展开更多
关键词 Peano derivative generalized Hermite interpolation singular integral of arbitrary order singular quadrature formula
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Numerical scheme to solve a class of variable–order Hilfer–Prabhakar fractional differential equations with Jacobi wavelets polynomials
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作者 B.Bagherzadeh Tavasani A.H.Refahi Sheikhani H.Aminikhah 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2022年第1期35-51,共17页
In this paper,we introduced a numerical approach for solving the fractional differential equations with a type of variable-order Hilfer-Prabhakar derivative of orderμ(t)andν(t).The proposed method is based on the Ja... In this paper,we introduced a numerical approach for solving the fractional differential equations with a type of variable-order Hilfer-Prabhakar derivative of orderμ(t)andν(t).The proposed method is based on the Jacobi wavelet collocation method.According to this method,an operational matrix is constructed.We use this operational matrix of the fractional derivative of variable-order to reduce the solution of the linear fractional equations to the system of algebraic equations.Theoretical considerations are discussed.Finally,some numerical examples are presented to demonstrate the accuracy of the proposed method. 展开更多
关键词 Hilfer-Prabhakar derivative Jacobi wavelets operational matrices variable order
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Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics 被引量:1
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作者 展德会 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期30-33,共4页
We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m(x),∞∑n=0sntm/n!m!H2n,2m(x,y),and ∞∑n=0sntm/n!m!H2n+l,2m+k(x,y).We employ the operator Herm... We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m(x),∞∑n=0sntm/n!m!H2n,2m(x,y),and ∞∑n=0sntm/n!m!H2n+l,2m+k(x,y).We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states. 展开更多
关键词 generating function two-variable Hermite polynomials Hermite polynomial method technique of integral within an ordered product of operators
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A specific state variable for a class of 3D continuous fractional-order chaotic systems
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作者 周平 程元明 邝菲 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第7期102-106,共5页
A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable ... A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its (q-order and 2q-order) time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its (q-order and 2q-order) time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method. 展开更多
关键词 fractional-order chaotic systems state variable q-order and 2q-order time derivatives chaotic synchronization
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基于矩阵解耦的精馏塔VOFFLC温控系统 被引量:2
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作者 汪洋 江厚顺 +3 位作者 许冬进 诸昌武 杨瑞洪 杨欢 《控制工程》 CSCD 北大核心 2023年第2期262-274,291,共14页
针对复杂的精馏塔MIMO温控系统的多变量、非线性、强耦合的特点和自适应需求,设计了基于矩阵解耦精馏塔的VOFFLC系统。首先,对温控系统的多变量控制模型进行改进,利用矩阵解耦理论实现对角解耦,以此改变控制通道的特性;然后,设计基于矩... 针对复杂的精馏塔MIMO温控系统的多变量、非线性、强耦合的特点和自适应需求,设计了基于矩阵解耦精馏塔的VOFFLC系统。首先,对温控系统的多变量控制模型进行改进,利用矩阵解耦理论实现对角解耦,以此改变控制通道的特性;然后,设计基于矩阵解耦的精馏塔VOFFLC温控系统,实现精馏塔的塔顶和塔底的自适应温控;最后,采用仿真实验,对所设计的多种温控系统进行性能比较。实验结果表明,VOFFLC系统可以实现控制参数的自适应,具有更强的论域容错性和鲁棒性。 展开更多
关键词 矩阵解耦 温度控制 ITAE FLC FOPID VofFLC
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Solving the Nonlinear Variable Order Fractional Differential Equations by Using Euler Wavelets 被引量:1
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作者 Yanxin Wang Li Zhu Zhi Wang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2019年第2期339-350,共12页
An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of... An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented.Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations.And the convergence of the Euler wavelets basis is given.The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy. 展开更多
关键词 EULER WAVELETS variable order FRACTIONAL differential EQUATIONS caputo FRACTIONAL derivatives OPERATIONAL matrix CONVERGENCE analysis.
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Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models 被引量:1
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作者 Yanli QIAO Xiaoping WANG +1 位作者 Huanying XU Haitao QI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第12期1771-1786,共16页
Fractional calculus has been widely used to study the flow of viscoelastic fluids recently,and fractional differential equations have attracted a lot of attention.However,the research has shown that the fractional equ... Fractional calculus has been widely used to study the flow of viscoelastic fluids recently,and fractional differential equations have attracted a lot of attention.However,the research has shown that the fractional equation with constant order operators has certain limitations in characterizing some physical phenomena.In this paper,the viscoelastic fluid flow of generalized Maxwell fluids in an infinite straight pipe driven by a periodic pressure gradient is investigated systematically.Consider the complexity of the material structure and multi-scale effects in the viscoelastic fluid flow.The modified time fractional Maxwell models and the corresponding governing equations with distributed/variable order time fractional derivatives are proposed.Based on the L1-approximation formula of Caputo fractional derivatives,the implicit finite difference schemes for the distributed/variable order time fractional governing equations are presented,and the numerical solutions are derived.In order to test the correctness and availability of numerical schemes,two numerical examples are established to give the exact solutions.The comparisons between the numerical solutions and the exact solutions have been made,and their high consistency indicates that the present numerical methods are effective.Then,this paper analyzes the velocity distributions of the distributed/variable order fractional Maxwell governing equations under specific conditions,and discusses the effects of the weight coefficient(α)in distributed order time fractional derivatives,the orderα(r,t)in variable fractional order derivatives,the relaxation timeλ,and the frequencyωof the periodic pressure gradient on the fluid flow velocity.Finally,the flow rates of the distributed/variable order fractional Maxwell governing equations are also studied. 展开更多
关键词 distributed order time fractional derivative variable order time fractional derivative finite difference scheme viscoelastic fluid
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Optimum Design of Fractional Order PID Controller for an AVR System Using an Improved Artificial Bee Colony Algorithm 被引量:15
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作者 ZHANG Dong-Li TANG Ying-Gan GUAN Xin-Ping 《自动化学报》 EI CSCD 北大核心 2014年第5期973-980,共8页
关键词 PID控制器 优化设计 VR系统 群算法 分数阶 工蜂 自动电压调节器 搜索范围
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Linear and nonlinear control of a robotic excavator 被引量:3
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作者 顾军 MA Xian-dong +1 位作者 倪俊芳 孙立宁 《Journal of Central South University》 SCIE EI CAS 2012年第7期1823-1831,共9页
Various control systems for a robotic excavator named LUCIE (Lancaster University Computerized and Intelligent Excavator),were investigated. The excavator is being developed to dig trenches autonomously. One stumbling... Various control systems for a robotic excavator named LUCIE (Lancaster University Computerized and Intelligent Excavator),were investigated. The excavator is being developed to dig trenches autonomously. One stumbling block is the achievement of adequate,accurate,quick and smooth movement under automatic control. Here,both classical and modern approaches are considered,including proportional-integral-derivative (PID) control tuned by conventional Zigler-Nichols rules,linear proportional-integral-plus (PIP) control,and a novel nonlinear PIP controller based on a state-dependent parameter (SDP) model structure,in which the parameters are functionally dependent on other variables in the system. Implementation results for the excavator joint arms control demonstrate that SDP-PIP controller provides the improved performance with fast,smooth and accurate response in comparison with both PID and linearized PIP control. 展开更多
关键词 非线性控制 挖掘机器人 控制系统 自动化控制 PIP 状态调整 响应性能 PID
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Research on the Control Strategy of Variable Nozzle Turbocharger for Natural Gas Engine 被引量:2
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作者 郝利君 黄英 +1 位作者 张付军 葛蕴珊 《Journal of Beijing Institute of Technology》 EI CAS 2010年第1期37-41,共5页
A variable nozzle turbocharger (VNT) was applied to a 2.2-liter L4 natural gas engine,and a VNT control system was designed to operate it.Based on VNT matching test results,a VNT control strategy was studied,in whic... A variable nozzle turbocharger (VNT) was applied to a 2.2-liter L4 natural gas engine,and a VNT control system was designed to operate it.Based on VNT matching test results,a VNT control strategy was studied,in which VNT adjustment is carried out through pre-calibrated VNT handling rod position,combined with a closed-loop target boost pressure feedback using proportional-integral-derivative(PID) algorithm.Experimental results showed that the VNT control system presented in this thesis can lead to optimized performance of VNT,increase engine volumetric efficiency over a wide speed range,improve engine dynamic characteristics and upgrade economic performance. 展开更多
关键词 natural gas engine variable nozzle turbocharger (VNT) proportional-integral-derivative(PID) control control strategy experimental study
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Existence and Uniqueness for the Boundary Value Problems of Nonlinear Fractional Differential Equation
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作者 Yufeng Sun Zheng Zeng Jie Song 《Applied Mathematics》 2017年第3期312-323,共12页
This paper studies the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Ban... This paper studies the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach’s contraction principle and the Schauder’s fixed point theorem. In addition, an example is given to demonstrate the application of our main results. 展开更多
关键词 FRACTIONAL order Differential EQUATIONS BOUNDARY Value Problem Caputo FRACTIONAL derivative FRACTIONAL integral Fixed Point
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Research on Stick-Slip Vibration Suppression Method of Drill String Based on Machine Learning Optimization
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作者 Kanhua Su Jian Wei +3 位作者 Meng Li Hao Li Wenghao Da Lang Zhang 《Sound & Vibration》 EI 2023年第1期97-117,共21页
During the drilling process,stick-slip vibration of the drill string is mainly caused by the nonlinear friction gen-erated by the contact between the drill bit and the rock.To eliminate the fatigue wear of downhole dr... During the drilling process,stick-slip vibration of the drill string is mainly caused by the nonlinear friction gen-erated by the contact between the drill bit and the rock.To eliminate the fatigue wear of downhole drilling tools caused by stick-slip vibrations,the Fractional-Order Proportional-Integral-Derivative(FOPID)controller is used to suppress stick-slip vibrations in the drill string.Although the FOPID controller can effectively suppress the drill string stick-slip vibration,its structure isflexible and parameter setting is complicated,so it needs to use the cor-responding machine learning algorithm for parameter optimization.Based on the principle of torsional vibration,a simplified model of multi-degree-of-freedom drill string is established and its block diagram is designed.The continuous nonlinear friction generated by cutting rock is described by the LuGre friction model.The adaptive learning strategy of genetic algorithm(GA),particle swarm optimization(PSO)and particle swarm optimization improved(IPSO)by arithmetic optimization(AOA)is used to optimize and adjust the controller parameters,and the drill string stick-slip vibration is suppressed to the greatest extent.The results show that:When slight drill string stick-slip vibration occurs,the FOPID controller optimized by machine learning algorithm has a good effect on suppressing drill string stick-slip vibration.However,the FOPID controller cannot get the drill string system which has fallen into serious stick-slip vibration(stuck pipe)out of trouble,and the machine learning algorithm is required to mark a large amount of data on adjacent Wells to train the model.Set a reasonable range of drilling parameters(weight on bit/drive torque)in advance to avoid severe stick-slip vibration(stuck pipe)in the drill string system. 展开更多
关键词 Stick-slip vibration machine learning fractional order proportional integral derivative(FOPID)control optimization algorithm
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一种适用于复杂电网下的高精度锁相环
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作者 黄海宏 刘远朋 王海欣 《电机与控制学报》 EI CSCD 北大核心 2024年第3期43-55,共13页
针对现有并网逆变器在电网电压谐波复杂的情况下难以精确锁定电压频率和相位的问题,结合传统锁相环结构与自适应算法的理论提出一种高精度的锁相方法。依据对传统锁相环在复杂电网下的弊端分析,确定了锁相环采用传统低通滤波器、带通滤... 针对现有并网逆变器在电网电压谐波复杂的情况下难以精确锁定电压频率和相位的问题,结合传统锁相环结构与自适应算法的理论提出一种高精度的锁相方法。依据对传统锁相环在复杂电网下的弊端分析,确定了锁相环采用传统低通滤波器、带通滤波器时的滤波效果与延时的矛盾关系。根据最小均方算法的高自适应特性与快速跟踪特点,结合锁相环中坐标变换公式,确定算法的输入输出以及权重矩阵,构建基于派克变换的最小均方算法矩阵模型。通过将所需的电压正序分量设置为不断更新的权重矩阵来进行高精度的滤波,同时通过引入均方瞬时误差和自相关估计均值来进行变步长控制,提高滤波更新速度,以适用于复杂程度不确定的电网电压进行自适应滤波锁相。对仿真和样机实验的结果表明:采用基于派克变换的最小均方算法的改进型双二阶广义积分锁相方法,可以在不降低动态响应速度的前提下,提高锁相环的滤波效果,进而提高并网逆变器在电网畸变严重场景下锁定电压频率和相位的跟踪精度。 展开更多
关键词 锁相环 自适应滤波 双二阶广义积分 最小均方算法 变步长
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引入PID反馈的SHAEKF算法估算电池SOC
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作者 蔡黎 向丽红 +1 位作者 晏娟 徐青山 《电池》 CAS 北大核心 2024年第1期47-51,共5页
电池荷电状态(SOC)的估算精度是电动汽车电池组的重要指标。为提升SOC估算精度,在融合Sage-Husa扩展卡尔曼滤波(SHEKF)算法与自适应扩展卡尔曼滤波(AEKF)算法的基础上,增加比例积分微分(PID)反馈环节,形成改进算法。采用粒子群优化(PSO... 电池荷电状态(SOC)的估算精度是电动汽车电池组的重要指标。为提升SOC估算精度,在融合Sage-Husa扩展卡尔曼滤波(SHEKF)算法与自适应扩展卡尔曼滤波(AEKF)算法的基础上,增加比例积分微分(PID)反馈环节,形成改进算法。采用粒子群优化(PSO)算法对二阶RC等效电路模型进行参数辨识;用开源电池数据集对模型和算法进行实验和分析。改进的SHAEKF算法在电池动态应力测试(DST)、北京动态应力测试(BJDST)和美国联邦城市驾驶(FUDS)等工况下的平均估计误差都在1%以内,与单纯的融合算法SHAEKF算法相比,最大误差可减小5%。 展开更多
关键词 荷电状态(SOC)估算 二阶RC等效电路模型 比例积分微分(PID) 粒子群优化(PSO)算法 自适应扩展卡尔曼滤波(AEKF)
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变限积分函数导数运算的应用研究
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作者 祝福 《商丘职业技术学院学报》 2024年第1期78-81,共4页
变限积分函数是证明牛顿-莱布尼兹公式的重要工具,是高等数学中微分和积分知识相互联结的纽带.通过对变限积分函数及其性质进行推广,并收集与变限积分有关典型例题,论述变限积分函数在解题的应用.
关键词 变限积分函数 换元 导数 应用
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含参量积分函数的奇偶性
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作者 张清邦 《大学数学》 2024年第2期87-91,共5页
先给出了含参量积分函数是奇(偶)函数的充要条件,及含参量的变限积分函数的是奇(偶)函数的充分条件;然后应用所得结论得到了含参量的变限积分函数的导数是奇(偶)函数的充分条件,以及第十三届全国大学生数学竞赛补赛第二题的一种解法.
关键词 含参量积分函数 含参量的变限积分函数 导数 奇偶性
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