This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability cri...This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability criterion in a wider sense and obtain a more common means to analyze the stability of fractional-order systems conveniently. Finally, this paper illustrates the generalized stability criteria with an example to show the effect of the parameters variation on the fractional-order control systems.展开更多
The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. I...The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.展开更多
The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilib...The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilibrium is proposed.The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincar′e map.To further demonstrate the physical realizability of the presented novel chaotic system,a chaotic circuit is designed.By using fractional-order operators,a controller is designed based on the state-feedback method.According to the Gronwall inequality,Laplace transform and Mittag-Leffler function,a new control scheme is explored for the whole closed-loop system.Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero.Finally,the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.展开更多
The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertaint...The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.展开更多
An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.Howe...An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.展开更多
In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy u...In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy used the robust Fractional-Order(FO)Proportional-Integral(PI)control technique.The FOPI control contains a non-integer order which is preferred over the integer-order control owing to its benefits.It offers extra flexibility in design and demonstrates superior outcomes such as high robustness and effectiveness.The optimal gains of the FOPI controller have been determined using a recent Manta Ray Foraging Optimization(MRFO)algorithm.During the optimization process,the FOPI controller’s parameters are assigned to be the decision variables whereas the objective function is the error racking that to be minimized.To prove the superiority of the MRFO algorithm,an empirical comparison study with the homologous particle swarm optimization and genetic algorithm is achieved.The obtained results proved the superiority of the introduced strategy in tracking and control performances against various conditions such as voltage dips and wind speed variation.展开更多
This study introduces an enhanced adaptive fractional-order nonsingular terminal sliding mode controller(AFONTSMC)tailored for stabilizing a fully submerged hydrofoil craft(FSHC)under external disturbances,model uncer...This study introduces an enhanced adaptive fractional-order nonsingular terminal sliding mode controller(AFONTSMC)tailored for stabilizing a fully submerged hydrofoil craft(FSHC)under external disturbances,model uncertainties,and actuator saturation.A novel nonlinear disturbance observer modified by fractional-order calculus is proposed for flexible and less conservative estimation of lumped disturbances.An enhanced adaptive fractional-order nonsingular sliding mode scheme augmented by disturbance estimation is also introduced to improve disturbance rejection.This controller design only necessitates surpassing the estimation error rather than adhering strictly to the disturbance upper bound.Additionally,an adaptive fast-reaching law with a hyperbolic tangent function is incorporated to enhance the responsiveness and convergence rates of the controller,thereby reducing chattering.Furthermore,an auxiliary actuator compensator is developed to address saturation effects.The resultant closed system of the FSHC with the designed controller is globally asymptotically stable.展开更多
Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge i...Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge in core power control research.In comparing with the integer-order models,fractional-order models describe the variation of core power more accurately,thus provide a comprehensive and realistic depiction for the power and state changes of reactor core.However,current fractional-order controllers cannot adjust their parameters dynamically to response the environmental changes or demands.In this paper,we aim at the stable control and dynamic responsiveness of core power.Based on the strong selflearning ability of artificial neural network(ANN),we propose a composite controller combining the ANN and FOPID controller.The FOPID controller is firstly designed and a back propagation neural network(BPNN)is then utilized to optimize the parameters of FOPID.It is shown by simulation that the composite controller enables the real-time parameter tuning via ANN and retains the advantage of FOPID controller.展开更多
The elimination of the vertical tail in tailless aircraft results in a significant decrease in heading static stability,causing substantial coupling among the three control channels.In addition,in specific operational...The elimination of the vertical tail in tailless aircraft results in a significant decrease in heading static stability,causing substantial coupling among the three control channels.In addition,in specific operational scenarios,the tailless aircraft is prone to electromagnetic interference,leading to the generation of high-frequency noise and consequently compromising their control performance.To address these issues,a decoupling control method based on a fractional-order error extended state observer(FOEESO)is proposed.A nonlinear model of a tailless aircraft with thrust vectoring capabilities is first developed.The decoupling control design for the three control channels is then implemented using FOEESO,with the asymptotic convergence conditions outlined.The proposed method is evaluated through simulations and compared to coupled control and linear extended state observer(LESO)techniques.Numerical simulations demonstrate that the FOEESO-based control methodology achieves effective decoupling,exhibiting 6.9%and 11.7%reductions in integral absolute error(IAE)relative to LESO under nominal operational conditions and critical fault scenarios,respectively.These improvements thereby highlight FOEESO’s capability to enhance closed-loop stability and tracking precision in tailless aircraft control systems.展开更多
This paper is concerned with fractional-order PI~λD~μcontrollers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of a fractional-order controller and fractional-o...This paper is concerned with fractional-order PI~λD~μcontrollers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of a fractional-order controller and fractional-order control systems are outlined. The effects on control systems of order variation for fractional-order PI~λD~μ controllers are investigated by qualitative analysis and simulation. The conclusions and simulation examples are given. The results show the fractional-order PI~λD~μ controller is not sensitive to variation of its order.展开更多
We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed co...We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.展开更多
For the purpose of investigating two complex networks' hybrid synchronization,a controller with fractional-order is provided.Regarding hybrid synchronization which includes the outer synchronization and inner sync...For the purpose of investigating two complex networks' hybrid synchronization,a controller with fractional-order is provided.Regarding hybrid synchronization which includes the outer synchronization and inner synchronization,some hybrid synchronization's sufficient conditions according to the Lyapunov stability theorem and the LaSalle invariance principle are proposed.Theoretical analysis suggests that,only when the state of driving-response networks is outer synchronization and each network is in inner synchronization,two coupled networks' hybrid synchronization under some suitable conditions could be reached.Finally,theoretical results are illustrated and validated with the given numerical simulations.展开更多
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 deduced.And an a...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 deduced.And an adaptivefeedback controller is developed based on the stability theory for fractional systems.The 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 practice.Simulation is carried out to verify that the obtained scheme is efficient and robust against external interference for controlling the fractional-order PMSM system.展开更多
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to ac...This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional...This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.展开更多
Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. T...Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control （FASMC） method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are en- hanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.展开更多
This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractiona...This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.展开更多
A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fract...A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.展开更多
This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this...This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet prac- tical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.展开更多
基金Supported by the Natural Science Foundation of Chongqing City (No. CSTC2004BB2165) and Research Foundation of Chongqing University of Posts and Telecommunications (No. A2005-47)
文摘This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability criterion in a wider sense and obtain a more common means to analyze the stability of fractional-order systems conveniently. Finally, this paper illustrates the generalized stability criteria with an example to show the effect of the parameters variation on the fractional-order control systems.
文摘The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.
基金supported by the National Natural Science Foundation of China(61573184)Jiangsu Natural Science Foundation of China(SBK20130033)+1 种基金Six Talents Peak Project of Jiangsu Province(2012-XXRJ-010)Fundamental Research Funds for the Central Universities(NE2016101)
文摘The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilibrium is proposed.The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincar′e map.To further demonstrate the physical realizability of the presented novel chaotic system,a chaotic circuit is designed.By using fractional-order operators,a controller is designed based on the state-feedback method.According to the Gronwall inequality,Laplace transform and Mittag-Leffler function,a new control scheme is explored for the whole closed-loop system.Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero.Finally,the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.
基金supported by the Estonian Research Council(PRG658)。
文摘The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.
基金This research was funded by the Deputyship for Research and Innovation,Ministry of Education,Saudi Arabia,through the University of Tabuk,Grant Number S-1443-0123.
文摘An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.
文摘In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy used the robust Fractional-Order(FO)Proportional-Integral(PI)control technique.The FOPI control contains a non-integer order which is preferred over the integer-order control owing to its benefits.It offers extra flexibility in design and demonstrates superior outcomes such as high robustness and effectiveness.The optimal gains of the FOPI controller have been determined using a recent Manta Ray Foraging Optimization(MRFO)algorithm.During the optimization process,the FOPI controller’s parameters are assigned to be the decision variables whereas the objective function is the error racking that to be minimized.To prove the superiority of the MRFO algorithm,an empirical comparison study with the homologous particle swarm optimization and genetic algorithm is achieved.The obtained results proved the superiority of the introduced strategy in tracking and control performances against various conditions such as voltage dips and wind speed variation.
基金Supported by Natural Science Basic Research Program of Shaanxi under Grant No.2023-JC-QN-0751,No.2023-JC-QN-0778Fundamental Research Funds for the Central Universities,CHD under Grant No.300102324102+1 种基金the National Natural Science Foundation of China under Grant Nos.72471035,52271313Fundamental Research Funds for the Central Universities under Grant No.XK2040021004025.
文摘This study introduces an enhanced adaptive fractional-order nonsingular terminal sliding mode controller(AFONTSMC)tailored for stabilizing a fully submerged hydrofoil craft(FSHC)under external disturbances,model uncertainties,and actuator saturation.A novel nonlinear disturbance observer modified by fractional-order calculus is proposed for flexible and less conservative estimation of lumped disturbances.An enhanced adaptive fractional-order nonsingular sliding mode scheme augmented by disturbance estimation is also introduced to improve disturbance rejection.This controller design only necessitates surpassing the estimation error rather than adhering strictly to the disturbance upper bound.Additionally,an adaptive fast-reaching law with a hyperbolic tangent function is incorporated to enhance the responsiveness and convergence rates of the controller,thereby reducing chattering.Furthermore,an auxiliary actuator compensator is developed to address saturation effects.The resultant closed system of the FSHC with the designed controller is globally asymptotically stable.
文摘Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge in core power control research.In comparing with the integer-order models,fractional-order models describe the variation of core power more accurately,thus provide a comprehensive and realistic depiction for the power and state changes of reactor core.However,current fractional-order controllers cannot adjust their parameters dynamically to response the environmental changes or demands.In this paper,we aim at the stable control and dynamic responsiveness of core power.Based on the strong selflearning ability of artificial neural network(ANN),we propose a composite controller combining the ANN and FOPID controller.The FOPID controller is firstly designed and a back propagation neural network(BPNN)is then utilized to optimize the parameters of FOPID.It is shown by simulation that the composite controller enables the real-time parameter tuning via ANN and retains the advantage of FOPID controller.
文摘The elimination of the vertical tail in tailless aircraft results in a significant decrease in heading static stability,causing substantial coupling among the three control channels.In addition,in specific operational scenarios,the tailless aircraft is prone to electromagnetic interference,leading to the generation of high-frequency noise and consequently compromising their control performance.To address these issues,a decoupling control method based on a fractional-order error extended state observer(FOEESO)is proposed.A nonlinear model of a tailless aircraft with thrust vectoring capabilities is first developed.The decoupling control design for the three control channels is then implemented using FOEESO,with the asymptotic convergence conditions outlined.The proposed method is evaluated through simulations and compared to coupled control and linear extended state observer(LESO)techniques.Numerical simulations demonstrate that the FOEESO-based control methodology achieves effective decoupling,exhibiting 6.9%and 11.7%reductions in integral absolute error(IAE)relative to LESO under nominal operational conditions and critical fault scenarios,respectively.These improvements thereby highlight FOEESO’s capability to enhance closed-loop stability and tracking precision in tailless aircraft control systems.
基金Sponsored by Shanghai Science and Technology Development Funds (Grant No.011607033).
文摘This paper is concerned with fractional-order PI~λD~μcontrollers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of a fractional-order controller and fractional-order control systems are outlined. The effects on control systems of order variation for fractional-order PI~λD~μ controllers are investigated by qualitative analysis and simulation. The conclusions and simulation examples are given. The results show the fractional-order PI~λD~μ controller is not sensitive to variation of its order.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171238)the Ministry of Education Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRTO0742)
文摘We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61201227)the Funding of China Scholarship Council,the Natural Science Foundation of Anhui Province(Grant No.1208085MF93)the 211 Innovation Team of Anhui University(Grant Nos.KJTD007A and KJTD001B)
文摘For the purpose of investigating two complex networks' hybrid synchronization,a controller with fractional-order is provided.Regarding hybrid synchronization which includes the outer synchronization and inner synchronization,some hybrid synchronization's sufficient conditions according to the Lyapunov stability theorem and the LaSalle invariance principle are proposed.Theoretical analysis suggests that,only when the state of driving-response networks is outer synchronization and each network is in inner synchronization,two coupled networks' hybrid synchronization under some suitable conditions could be reached.Finally,theoretical results are illustrated and validated with the given numerical simulations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61172023,60871025,and 10862001)the Natural Science Foundation of Guangdong Province,China (Grant Nos. S2011010001018 and 8151009001000060)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20114420110003)
文摘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 deduced.And an adaptivefeedback controller is developed based on the stability theory for fractional systems.The 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 practice.Simulation is carried out to verify that the obtained scheme is efficient and robust against external interference for controlling the fractional-order PMSM system.
文摘This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
基金Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 11MG49)
文摘This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.
基金supported by the National Natural Science Foundation of China(Grant No.51507134)the Science Fund from the Education Department of Shaanxi Province,China(Grant No.15JK1537)
文摘Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control （FASMC） method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are en- hanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.
基金supported by the National Natural Science Foundation of China(Grant Nos.51207173 and 51277192)
文摘This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.
基金supported by the National Natural Science Foundation of China (Grant No. 51109180)the Personal Special Fund of Northwest Agriculture and Forestry University,China (Grant No. RCZX-2009-01)
文摘A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.
基金Project supported by the National Natural Science Foundation of China(Nos.11672231 and11672233)the Natural Science Foundation of Shaanxi Province(No.2016JM1010)+1 种基金the Fundamental Research Funds for the Central Universities(No.3102017AX008)the Seed Foundation of Innovation and Creation for Graduate Students at the Northwestern Polytechnical University of China(No.Z2017187)
文摘This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet prac- tical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China(61403149,61573298)Natural Science Foundation of Fujian Province(2015J01261,2016J05165)Foundation of Huaqiao University(Z14Y0002)
