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 paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability...In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.展开更多
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 d...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展开更多
A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation i...A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.展开更多
We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a n...We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.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
Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block...Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system,so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approach–The mathematical model of information interaction between trains is established based on algebraic graph theory,so that the train can obtain the state information of adjacent trains,and then realize the distributed cooperative control of each train.In the controller design,the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon,so as to suppress the chattering of sliding mode control,and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.Findings–The simulation results show that compared with proportional integral derivative(PID)control and ordinary sliding mode control,the control accuracy of the proposed algorithm in terms of speed is,respectively,improved by 25%and 75%.The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control,the error value tends to 0,and the operation trend tends to be consistent.Therefore,the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/value–The algorithm can reduce the influence of external interference in the actual operating environment,realize efficient and stable tracking of trains,and ensure the safety of train control.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
Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterp...Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system.展开更多
In this paper we investigate the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on the Lyapunov stability theory and adaptive control technique, a single adaptive-feedback cont...In this paper we investigate the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on the Lyapunov stability theory and adaptive control technique, a single adaptive-feedback controller is developed to synchronize a class of fractional-order chaotic systems. The presented controller which only contains a single driving variable is simple both in design and in implementation. Numerical simulation and circuit experimental results for fractional-order chaotic system are provided to illustrate the effectiveness of the proposed scheme.展开更多
We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability t...We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.展开更多
This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady...This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems,the FOPID fuzzy controller has been proven to provide better results.This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques.This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer,social spider optimization,in order to improve the response of fractional dynamical systems.This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima.The integral time of absolute error(ITAE)used in this study was the error function.The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value.It reached a value of 88.22 while the best value obtained in previous work was 98.87.A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time,low-percentage overshoot,and very small steady-state error.However,the other strategies were good for one factor,but not for the others.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
In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractio...In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.展开更多
In this paper,a new model identification method is developed for a class of delay fractional-order system based on the process step response.Four characteristic functions are defined to characterize the features of th...In this paper,a new model identification method is developed for a class of delay fractional-order system based on the process step response.Four characteristic functions are defined to characterize the features of the normalized fractionalorder model.Based on the time scaling technology,two identification schemes are proposed for parameters' estimation.The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly.The other scheme employs optimal searching method to adjust the fractional order for the best model identification.The proposed two identification schemes are both applicable to any stable complex process,such as higher-order,under-damped/over-damped,and minimum-phase/nonminimum-phase processes.Furthermore,an optimal PID tuning method is proposed for the delay fractionalorder systems.The requirements on the stability margins and the negative feedback are cast as real part constraints(RPC)and imaginary part constraints(IPC).The constraints are implemented by trigonometric inequalities on the phase variable,and the optimal PID controller is obtained by the minimization of the integral of time absolute error(ITAE) index.Identification and control of a Titanium billet heating process is given for the illustration.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
Palladium(Pd)-based sulfides have triggered extensive interest due to their unique properties and potential applications in the fields of electronics and optoelectronics.However,the synthesis of large-scale uniform Pd...Palladium(Pd)-based sulfides have triggered extensive interest due to their unique properties and potential applications in the fields of electronics and optoelectronics.However,the synthesis of large-scale uniform PdS and PdS_(2)nanofilms(NFs)remains an enormous challenge.In this work,2-inch wafer-scale PdS and PdS_(2) NFs with excellent stability can be controllably prepared via chemical vapor deposition combined with electron beam evaporation technique.The thickness of the pre-deposited Pd film and the sulfurization temperature are critical for the precise synthesis of PdS and PdS_(2) NFs.A corresponding growth mechanism has been proposed based on our experimental results and Gibbs free energy calculations.The electrical transport properties of PdS and PdS_(2) NFs were explored by conductive atomic force microscopy.Our findings have achieved the controllable growth of PdS and PdS_(2) NFs,which may provide a pathway to facilitate PdS and PdS_(2) based applications for next-generation high performance optoelectronic devices.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
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.
基金supported by the National Natural Science Foundation of China(Grant Nos. 61573194, 51775284)the Natural Science Foundation of Jiangsu Province of China(Grant Nos. BK20181389, BK20171441)+1 种基金the Key Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province(Grant No. 2018SJZDI142)the Australian Research Council(Grant No. DP120104986)
文摘In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.11672111,11432012,11602089)the Program for New Century Excellent Talents in Fujian Province University,and the Technological Project of Huaqiao University(Grant Nos.ZQN-YX307,ZQNYX505)
文摘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
基金supported by the National Natural Science Foundation of China (U1703262,62163035,61866036,62006196,61963033,62163035)the Tianshan Innovation Team Program (2020D14017)the Tianshan Xuesong Program (2018XS02).
文摘A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.
基金supported by the Anhui Provincial Development and Reform Commission New Energy Vehicles and Intelligent Connected Automobile Industry Technology Innovation Project。
文摘We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.
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supported by the Natural Science Foundation of China under Grant 52162050R&D plan project for science and technology of China Railway(No.N2021G045).
文摘Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system,so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approach–The mathematical model of information interaction between trains is established based on algebraic graph theory,so that the train can obtain the state information of adjacent trains,and then realize the distributed cooperative control of each train.In the controller design,the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon,so as to suppress the chattering of sliding mode control,and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.Findings–The simulation results show that compared with proportional integral derivative(PID)control and ordinary sliding mode control,the control accuracy of the proposed algorithm in terms of speed is,respectively,improved by 25%and 75%.The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control,the error value tends to 0,and the operation trend tends to be consistent.Therefore,the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/value–The algorithm can reduce the influence of external interference in the actual operating environment,realize efficient and stable tracking of trains,and ensure the safety of train control.
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. 60702023)the Natural Science Foundation of Zhejiang Province, China (Grant No. R1110443)
文摘Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system.
基金Project supported by the Natural Science Foundation of Hebei Province,China (Grant No. A2010000343)
文摘In this paper we investigate the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on the Lyapunov stability theory and adaptive control technique, a single adaptive-feedback controller is developed to synchronize a class of fractional-order chaotic systems. The presented controller which only contains a single driving variable is simple both in design and in implementation. Numerical simulation and circuit experimental results for fractional-order chaotic system are provided to illustrate the effectiveness of the proposed scheme.
基金Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2010000343).
文摘We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.
文摘This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems,the FOPID fuzzy controller has been proven to provide better results.This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques.This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer,social spider optimization,in order to improve the response of fractional dynamical systems.This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima.The integral time of absolute error(ITAE)used in this study was the error function.The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value.It reached a value of 88.22 while the best value obtained in previous work was 98.87.A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time,low-percentage overshoot,and very small steady-state error.However,the other strategies were good for one factor,but not for the others.
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supported by National Natural Science Foundation of China(61573194,61374180,61573096)China Postdoctoral Science Foundation Funded Project(2013M530229)+3 种基金China Postdoctoral Science Special Foundation Funded Project(2014T70463)Six Talent Peaks High Level Project of Jiangsu Province(ZNDW-004)Science Foundation of Nanjing University of Posts and Telecommunications(NY213095)Australian Research Council(DP120104986)
文摘In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.
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)
文摘In this paper,a new model identification method is developed for a class of delay fractional-order system based on the process step response.Four characteristic functions are defined to characterize the features of the normalized fractionalorder model.Based on the time scaling technology,two identification schemes are proposed for parameters' estimation.The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly.The other scheme employs optimal searching method to adjust the fractional order for the best model identification.The proposed two identification schemes are both applicable to any stable complex process,such as higher-order,under-damped/over-damped,and minimum-phase/nonminimum-phase processes.Furthermore,an optimal PID tuning method is proposed for the delay fractionalorder systems.The requirements on the stability margins and the negative feedback are cast as real part constraints(RPC)and imaginary part constraints(IPC).The constraints are implemented by trigonometric inequalities on the phase variable,and the optimal PID controller is obtained by the minimization of the integral of time absolute error(ITAE) index.Identification and control of a Titanium billet heating process is given for the illustration.
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supported by National Natural Science Foundation of China (No.11974301)Key Research and Development Program of Hunan Province (No.2022GK2007)+2 种基金Key Project from Department Education of Hunan Province (No.22A0123)Scientific Research Fund of Hunan Provincial Education Department (No.21B0136)National college students innovation and entrepreneurship training program (No.S202310530016)。
文摘Palladium(Pd)-based sulfides have triggered extensive interest due to their unique properties and potential applications in the fields of electronics and optoelectronics.However,the synthesis of large-scale uniform PdS and PdS_(2)nanofilms(NFs)remains an enormous challenge.In this work,2-inch wafer-scale PdS and PdS_(2) NFs with excellent stability can be controllably prepared via chemical vapor deposition combined with electron beam evaporation technique.The thickness of the pre-deposited Pd film and the sulfurization temperature are critical for the precise synthesis of PdS and PdS_(2) NFs.A corresponding growth mechanism has been proposed based on our experimental results and Gibbs free energy calculations.The electrical transport properties of PdS and PdS_(2) NFs were explored by conductive atomic force microscopy.Our findings have achieved the controllable growth of PdS and PdS_(2) NFs,which may provide a pathway to facilitate PdS and PdS_(2) based applications for next-generation high performance optoelectronic devices.
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.