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fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

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Applied Mathematics and Mechanics(English Edition) 2019年第1期40卷 49-62页

作者： Wenjie ZHAO Shaopu YANG Guilin WEN Xuehong REN State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan University State Key Laboratory of Mechanical Behavior in Traffic Engineering Structure and System Safety Shijiazhuang Tiedao University

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain *** capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

关键词： cyclic visco-plastic constitutive fractional derivative fractional-order uni-fied visco-plastic(FVP)model rate-dependent ratcheting

fractional-order permanent magnet synchronous motor and its adaptive chaotic control

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Chinese Physics B 2012年第10期21卷 168-173页

作者：李春来禹思敏罗晓曙 College of Automation Guangdong University of Technology College of Physics and Electronics Hunan Institute of Science and Technology College of Electronic Engineering Guangxi Normal University

In this paper we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor（PMSM）.The necessary condition for the existence of chaos in the fractional-order PMSM is *** an adaptivefeedback controller is developed based on the stability theory for fractional *** presented control scheme,which contains only one single state variable,is simple and flexible,and it is suitable both for design and for implementation in *** is carried out to verify that the obtained scheme is efficient and robust against external interference for controlling the fractional-order PMSM system.

关键词： fractional-order permanent magnet synchronous motor adaptive chaotic control

fractional-order Modeling and Dynamical Analysis of a Francis Hydro-Turbine Governing System with Complex Penstocks

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Transactions of Tianjin University 2018年第1期24卷 32-44页

作者： Feifei Wang Diyi Chen Beibei Xu Hao Zhang Institute of Water Resources and Hydropower Research Northwest A&F University Department of Mathematics and Statistics Faculty of Science and EngineeringCurtin University

This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.

关键词： Hydro-turbine governing system Complex penstocks fractional-order Nonlinearity Bifurcation

Asymptotical consensus of fractional-order multi-agent systems with current and delay states

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Applied Mathematics and Mechanics(English Edition) 2019年第11期40卷 1677-1694页

作者： Xuhui WANG Xuesong LI Nanjing HUANG D.O'REGAN Department of Mathematics Sichuan UniversityChengdu 610064China School of Mathematics Statistics and Applied MathematicsNational University of IrelandGalwayIreland

In this paper,we study some new fractional-order multi-agent systems with current and delay states (FMASCD).Using the generalized Nyquist's stability criterion and Gerschgorin's circle theorem,we obtain the bounded input-bounded output (BIBO) stability and asymptotical consensus of the FMASCD under mild ***,we give some numerical examples to illustrate our main results.

关键词： fractional-order multi-agent system (FMAS) asymptotical consensus current state delay state

Open-loop and closed-loop D^(α)-type iterative learning control for fractional-order linear multi-agent systems with state-delays

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Journal of Systems Engineering and Electronics 2021年第1期32卷 197-208页

作者： LI Bingqiang LAN Tianyi ZHAO Yiyun LYU Shuaishuai School of Automation Northwestern Polytechnical UniversityXi’an 710129China School of Electrical and Control Engineering Shaanxi University of Science and TechnologyXi’an 710021China College of Electronics and Information Hangzhou Dianzi UniversityHangzhou 310018China

This study focuses on implementing consensus tracking using both open-loop and closed-loop Dα-type iterative learning control(ILC)schemes,for fractional-order multi-agent systems(FOMASs)with *** desired trajectory is constructed by introducing a virtual leader,and the fixed communication topology is considered and only a subset of followers can access the desired *** each control scheme,one controller is designed for one agent *** to the tracking error between the agent and the virtual leader,and the tracking errors between the agent and neighboring agents during the last iteration(for open-loop scheme)or the current running(for closed-loop scheme),each controller continuously corrects the last control law by a combination of communication weights in the topology to obtain the ideal control *** the rigorous analysis,sufficient conditions for both control schemes are established to ensure that all agents can achieve the asymptotically consistent output along the iteration axis within a finite-time *** numerical simulation results demonstrate the effectiveness of the control schemes,and provide some meaningful comparison results.

关键词： multi-agent system fractional-order consensus control iterative learning control virtual leader state-delay

Improved quantum bacterial foraging algorithm for tuning parameters of fractional-order PID controller

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Journal of Systems Engineering and Electronics 2018年第1期29卷 166-175页

作者： LIU Lu SHAN Liang DAI Yuewei LIU Chenglin QI Zhidong School of Automation Nanjing University of Science and Technology Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education) Institute of AutomationJiangnan University

The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population *** tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.

关键词： bacterial foraging algorithm fractional-order quantum rotation gate proportion integration differentiation(PID) servo system

Hypersonic reentry trajectory planning by using hybrid fractional-order particle swarm optimization and gravitational search algorithm

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Chinese Journal of Aeronautics 2021年第1期34卷 50-67页

作者： Khurram SHAHZAD SANA Weiduo HU School of Astronautics Beihang UniversityBeijing 102206China

This paper proposes a novel hybrid algorithm called fractional-order Particle Swarm optimization Gravitational Search Algorithm(FPSOGSA)and applies it to the trajectory planning of the hypersonic lifting reentry flight *** proposed method is used to calculate the control profiles to achieve the two objectives,namely a smoother trajectory and enforcement of the path constraints with terminal *** smoothness of the trajectory is achieved by scheduling the bank angle with the aid of a modified scheme known as a Quasi-Equilibrium Glide(QEG)*** aerodynamic load factor and the dynamic pressure path constraints are enforced by further planning of the bank angle with the help of a constraint enforcement *** maximum heating rate path constraint is enforced through the angle of attack *** Common Aero Vehicle(CAV)flight vehicle is used for the simulation purpose to test and compare the proposed method with that of the standard Particle Swarm Optimization(PSO)method and the standard Gravitational Search Algorithm(GSA).The simulation results confirm the efficiency of the proposed FPSOGSA method over the standard PSO and the GSA methods by showing its better convergence and computation efficiency.

关键词： fractional-order Gravitational search algorithm Particle swarm optimization Reentry gliding vehicle Trajectory optimization

Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems

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Science China(Technological Sciences) 2020年第9期63卷 1854-1862页

作者： WANG Zhen WANG XinHe XIA JianWei SHEN Hao MENG Bo College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China School of Mathematics Science Liaocheng UniversityLiaocheng252059China School of Electrical Engineering and Information Anhui University of TechnologyMaanshan243002China

An adaptive sliding mode control(ASMC) method, based on fractional-order disturbance-observer(FODOB), is presented for a class of fractional-order nonlinear time-delay systems(FONTDS) with uncertainties to solve the target output tracking *** external disturbances are estimated by FODOB, and the unknown internal perturbations of the system are adaptively estimated by sliding mode control(SMC). Furthermore, Gronwall's inequality approach is used to ensure that the output tracking error is uniformly bounded for FONTDS. Firstly, a fractional-order sliding mode control(FOSMC) based FODOB is proposed for a fractional-order linear time-delay system(FOLTDS). Secondly, combined with adaptive estimation, the ASMC of FONTDS is studied. Finally, a numerical example of FONTDS is used to verify the effectiveness of the proposed methods.

关键词： adaptive sliding mode control fractional-order disturbance-observer time-delay uncertainty

Stochastic averaging technique for SDOF strongly nonlinear systems with delayed feedback fractional-order PD controller

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Science China(Technological Sciences) 2019年第2期62卷 287-297页

作者： CHEN LinCong LIANG Xiao ZHU WeiQiu ZHAO YaoBing College of Civil Engineering Huaqiao University Departments of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University

A stochastic averaging technique is proposed to study the randomly excited single-degree-of-freedom(SDOF) strongly nonlinear systems with delayed feedback fractional-order proportional-derivative(PD) controller. The delayed feedback fractional-order PD control force is approximated by an equivalent non-delay feedback control force combining with a quasi-linear elastic force and a quasi-linear damping force. The averaged It? stochastic differential equation for amplitude of the equivalent nonlinear system is derived by the generalized harmonic functions. The analytical stationary probability density function(PDF) is obtained with solving the reduced Fokker-Planck-Kolmogorov(FPK) equation. Two examples of van der Pol oscillator and RayleighDuffing oscillator are studied to illustrate the application and effectiveness of the proposed method. Numerical results display that the proposed method can yield to the high precision, and the time delay could ruin the control effectiveness, but also even amplifies the response of the system more than that of uncontrolled system. Furthermore, the study finds that the parameters of fractional-order α and time delay may cause the stochastic P-bifurcation. It is indicated that the delayed feedback fractional-order PD controller can offer a potentially effective tool for anti-control of stochastic bifurcation

关键词： αstochastic averaging strongly nonlinear system time delay fractional-order PD^a controller