This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural n...The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.展开更多
The finite-time synchronization of fractional-order multi-weighted complex networks(FMCNs)with uncertain parameters and external disturbances is studied.Firstly,based on fractional calculus characteristics and Lyapuno...The finite-time synchronization of fractional-order multi-weighted complex networks(FMCNs)with uncertain parameters and external disturbances is studied.Firstly,based on fractional calculus characteristics and Lyapunov stability theory,quantized controllers are designed to guarantee that FMCNs can achieve synchronization in a limited time with and without coupling delay,respectively.Then,appropriate parameter update laws are obtained to identify the uncertain parameters in FMCNs.Finally,numerical simulation examples are given to validate the correctness of the theoretical results.展开更多
Active disturbance rejection controller（ADRC）uses tracking-differentiator（TD）to solve the contradiction between the overshoot and the rapid nature.Fractional order proportion integral derivative（PID）controller i...Active disturbance rejection controller（ADRC）uses tracking-differentiator（TD）to solve the contradiction between the overshoot and the rapid nature.Fractional order proportion integral derivative（PID）controller improves the control quality and expands the stable region of the system parameters.ADRC fractional order（ADRFO）PID controller is designed by combining ADRC with the fractional order PID and applied to reentry attitude control of hypersonic vehicle.Simulation results show that ADRFO PID controller has better control effect and greater stable region for the strong nonlinear model of hypersonic flight vehicle under the influence of external disturbance,and has stronger robustness against the perturbation in system parameters.展开更多
This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eli...This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.展开更多
This paper investigates the adaptive fuzzy finite-time output-feedback fault-tolerant control (FTC) problemfor a class of nonlinear underactuated wheeled mobile robots (UWMRs) system with intermittent actuatorfaults. ...This paper investigates the adaptive fuzzy finite-time output-feedback fault-tolerant control (FTC) problemfor a class of nonlinear underactuated wheeled mobile robots (UWMRs) system with intermittent actuatorfaults. The UWMR system includes unknown nonlinear dynamics and immeasurable states. Fuzzy logic systems(FLSs) are utilized to work out immeasurable functions. Furthermore, with the support of the backsteppingcontrol technique and adaptive fuzzy state observer, a fuzzy adaptive finite-time output-feedback FTC scheme isdeveloped under the intermittent actuator faults. It is testifying the scheme can ensure the controlled nonlinearUWMRs is stable and the estimation errors are convergent. Finally, the comparison results and simulationvalidate the effectiveness of the proposed fuzzy adaptive finite-time FTC approach.展开更多
Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an inte...Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios.展开更多
In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guar...In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.展开更多
With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rej...With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.展开更多
A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult ...A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.展开更多
In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear...In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM.All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer(NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.展开更多
The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(M...The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.展开更多
This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and extern...This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.展开更多
To keep multiple missiles to fly in a formation, a robust controller for missile formation is designed. Based on the leader-follower formation mode, two formation relative motion models in different coordinate frames ...To keep multiple missiles to fly in a formation, a robust controller for missile formation is designed. Based on the leader-follower formation mode, two formation relative motion models in different coordinate frames are established and compared. The three-dimension model built in a follower reference coordinate frame is chosen due to its control inputs decoupling, then this model is decoupled into three subsystems. For each subsystem a robust formation controller is proposed based on the disturbance observer and f＇mite-time control theory when the external disturbance exits. The stability of the closed-loop system adopting the controller is proved theoretically. Simulation resuits show that the follower can foUow the leader and keep the desired formation despite the external disturbance, which validates the effectiveness of the proposed robust formation controller.展开更多
A new calculation method of fractional order [proportional integral ]( FO [PI ]) controller parameters is proposed. And the systematic design schemes of fractional order [proportional integral ]( FO[PI]) controllers b...A new calculation method of fractional order [proportional integral ]( FO [PI ]) controller parameters is proposed. And the systematic design schemes of fractional order [proportional integral ]( FO[PI]) controllers based on vector method are discussed in detail. The FO[PI]controller parameters algorithm based on the vector method can be programmed in MATLAB. According to MATLAB programs of the FO[PI]controller parameters algorithm,the FO[PI] controllers are designed following the different phase margins,different gain crossover frequency and different plants,respectively. From the simulation results,the calculated parameters based on MATLAB program is unique and the designed FO[PI] controllers work efficiently.展开更多
The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions...The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results.展开更多
Normally all real world process in a process industry will have time delay.For those processes with time delays,obtaining satisfactory closed loop performances becomes very difficult.In this work,three interacting cyl...Normally all real world process in a process industry will have time delay.For those processes with time delays,obtaining satisfactory closed loop performances becomes very difficult.In this work,three interacting cylindrical tank process is considered for study and the objective of the work is to compensate for time delays using smith predictor structure and to maintain the level in the third tank.Input/Output data is generated for the three interacting tank process.It is approximated as Integer First Order Plus Dead Time system(IFOPDT)and Fractional First Order Plus Dead Time system(FFOPDT).Smith predictor based fractional order Proportional Integral controller and Integer order Proportional Integral controller is designed for the IFOPDT and FFOPDT model using frequency response technique and their closed loop performance indices are compared and tabulated.The servo and regulatory responses are simulated using Matlab/Simulink.展开更多
We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incomm...We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate. The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.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
This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that ...This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that can achieve the finite-time synchronization of any-order fractional-order chaotic systems under stochastic disturbances. This controller has good robustness and anti-interference performance. With the concept of the finite-time stability theory given, some judgment criterions for the synchronization of fractional-order chaotic systems are proved. This method can not only make the error systems have a faster convergence rate but also can be implemented in engineering easily. The numerical simulations of two specific examples demonstrate the effectiveness of the method. At the same time, the synchronised time of finite-time synchronization is shorter and faster than the complete synchronization and the time can be adjusted according to the parameters in the controller.展开更多
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11371049 and 61772063)the Fundamental Research Funds for the Central Universities,China(Grant No.2016JBM070)
文摘The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.
文摘The finite-time synchronization of fractional-order multi-weighted complex networks(FMCNs)with uncertain parameters and external disturbances is studied.Firstly,based on fractional calculus characteristics and Lyapunov stability theory,quantized controllers are designed to guarantee that FMCNs can achieve synchronization in a limited time with and without coupling delay,respectively.Then,appropriate parameter update laws are obtained to identify the uncertain parameters in FMCNs.Finally,numerical simulation examples are given to validate the correctness of the theoretical results.
基金Supported by the Innovation Foundation of Aerospace Science and Technology(CASC200902)~~
文摘Active disturbance rejection controller（ADRC）uses tracking-differentiator（TD）to solve the contradiction between the overshoot and the rapid nature.Fractional order proportion integral derivative（PID）controller improves the control quality and expands the stable region of the system parameters.ADRC fractional order（ADRFO）PID controller is designed by combining ADRC with the fractional order PID and applied to reentry attitude control of hypersonic vehicle.Simulation results show that ADRFO PID controller has better control effect and greater stable region for the strong nonlinear model of hypersonic flight vehicle under the influence of external disturbance,and has stronger robustness against the perturbation in system parameters.
基金the National Natural Science Foundation of China(62203356)Fundamental Research Funds for the Central Universities of China(31020210502002)。
文摘This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.
基金the National Natural Science Foundation of China under Grant U22A2043.
文摘This paper investigates the adaptive fuzzy finite-time output-feedback fault-tolerant control (FTC) problemfor a class of nonlinear underactuated wheeled mobile robots (UWMRs) system with intermittent actuatorfaults. The UWMR system includes unknown nonlinear dynamics and immeasurable states. Fuzzy logic systems(FLSs) are utilized to work out immeasurable functions. Furthermore, with the support of the backsteppingcontrol technique and adaptive fuzzy state observer, a fuzzy adaptive finite-time output-feedback FTC scheme isdeveloped under the intermittent actuator faults. It is testifying the scheme can ensure the controlled nonlinearUWMRs is stable and the estimation errors are convergent. Finally, the comparison results and simulationvalidate the effectiveness of the proposed fuzzy adaptive finite-time FTC approach.
基金supported by the National Natural Science Foundation of China(Grant No.61773142).
文摘Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios.
基金supported by the National Natural Science Foundation of China (62073015,62173036,62122014)。
文摘In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples.
基金the 2021 Key Project of Natural Science and Technology of Yangzhou Polytechnic Institute,Active Disturbance Rejection and Fault-Tolerant Control of Multi-Rotor Plant ProtectionUAV Based on QBall-X4(Grant Number 2021xjzk002).
文摘With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.
文摘A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.
文摘In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM.All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer(NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.
基金supported by the Board of Research in Nuclear Sciences of the Department of Atomic Energy,India(2012/36/69-BRNS/2012)
文摘The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.
文摘This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.
基金Supported by the National Natural Science Foundation of China(10872029)
文摘To keep multiple missiles to fly in a formation, a robust controller for missile formation is designed. Based on the leader-follower formation mode, two formation relative motion models in different coordinate frames are established and compared. The three-dimension model built in a follower reference coordinate frame is chosen due to its control inputs decoupling, then this model is decoupled into three subsystems. For each subsystem a robust formation controller is proposed based on the disturbance observer and f＇mite-time control theory when the external disturbance exits. The stability of the closed-loop system adopting the controller is proved theoretically. Simulation resuits show that the follower can foUow the leader and keep the desired formation despite the external disturbance, which validates the effectiveness of the proposed robust formation controller.
基金Sponsored by the Basic Research Program of Jilin Provincial Science & Technology Department(Grant No.20130102025JC)
文摘A new calculation method of fractional order [proportional integral ]( FO [PI ]) controller parameters is proposed. And the systematic design schemes of fractional order [proportional integral ]( FO[PI]) controllers based on vector method are discussed in detail. The FO[PI]controller parameters algorithm based on the vector method can be programmed in MATLAB. According to MATLAB programs of the FO[PI]controller parameters algorithm,the FO[PI] controllers are designed following the different phase margins,different gain crossover frequency and different plants,respectively. From the simulation results,the calculated parameters based on MATLAB program is unique and the designed FO[PI] controllers work efficiently.
基金Natural Science Foundation of Shanghai,China (No.19ZR1400500)。
文摘The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results.
文摘Normally all real world process in a process industry will have time delay.For those processes with time delays,obtaining satisfactory closed loop performances becomes very difficult.In this work,three interacting cylindrical tank process is considered for study and the objective of the work is to compensate for time delays using smith predictor structure and to maintain the level in the third tank.Input/Output data is generated for the three interacting tank process.It is approximated as Integer First Order Plus Dead Time system(IFOPDT)and Fractional First Order Plus Dead Time system(FFOPDT).Smith predictor based fractional order Proportional Integral controller and Integer order Proportional Integral controller is designed for the IFOPDT and FFOPDT model using frequency response technique and their closed loop performance indices are compared and tabulated.The servo and regulatory responses are simulated using Matlab/Simulink.
基金Project supported by the National Natural Science Foundation of China （Grant No. 11171238）, the Science Found of Sichuan University of Science and Engineering （Grant Nos. 2012PY17 and 2014PY06）, the Fund from Artificial Intelligence Key Laboratory of Sichuan Province （Grant No. 2014RYJ05）, and the Opening Project of Sichuan Province University Key Laborstory of Bridge Non-destruction Detecting and Engineering Computing （Grant No. 2013QYJ01）.
文摘We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate. The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.
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.
文摘This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that can achieve the finite-time synchronization of any-order fractional-order chaotic systems under stochastic disturbances. This controller has good robustness and anti-interference performance. With the concept of the finite-time stability theory given, some judgment criterions for the synchronization of fractional-order chaotic systems are proved. This method can not only make the error systems have a faster convergence rate but also can be implemented in engineering easily. The numerical simulations of two specific examples demonstrate the effectiveness of the method. At the same time, the synchronised time of finite-time synchronization is shorter and faster than the complete synchronization and the time can be adjusted according to the parameters in the controller.
