Piezoelectric stages use piezoelectric actuators and flexure hinges as driving and amplifying mechanisms,respectively.These systems have high positioning accuracy and high-frequency responses,and they are widely used ...Piezoelectric stages use piezoelectric actuators and flexure hinges as driving and amplifying mechanisms,respectively.These systems have high positioning accuracy and high-frequency responses,and they are widely used in various precision/ultra-precision positioning fields.However,the main challenge with these devices is the inherent hysteresis nonlinearity of piezoelectric actuators,which seriously affects the tracking accuracy of a piezoelectric stage.Inspired by this challenge,in this work,we developed a Hammerstein model to describe the hysteresis nonlinearity of a piezoelectric stage.In particular,in our proposed scheme,a feedback-linearization algorithm is used to eliminate the static hysteresis nonlinearity.In addition,a composite controller based on equivalent-disturbance compensation was designed to counteract model uncertainties and external disturbances.An analysis of the stability of a closed-loop system based on this feedback-linearization algorithm and composite controller was performed,and this was followed by extensive comparative experiments using a piezoelectric stage developed in the laboratory.The experimental results confirmed that the feedback-linearization algorithm and the composite controller offer improved linearization and trajectory-tracking performance.展开更多
In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabili...In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.展开更多
Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was poin...Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.展开更多
The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation o...The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.展开更多
In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for h...In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for hovering control is presented. It is proved that the nonlinear system of the small-scale helicopter can be transformed to a linear system using the dynamic feedback linearization technique. Finally, simulations are carried out to validate the nonlinear controller.展开更多
The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented ba...The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.展开更多
This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor...This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.展开更多
This paper deals with the design of an observer-based nonlinear control for continuous stirred tank reactors(CSTR).A variable structure observer is constructed to estimate the whole process state variables.This observ...This paper deals with the design of an observer-based nonlinear control for continuous stirred tank reactors(CSTR).A variable structure observer is constructed to estimate the whole process state variables.This observer is basically the conventional Luenberger observer with an additional switching term used to guarantee the robustness against modeling errors.The observer is coupled with a nonlinear controller,designed based on input-output linearization for controlling the reactor temperature.The asymptotical stability of the closed-loop system is shown by the Lyapunov stability theorem.Finally,computer simulations are developed for showing the performance of the proposed approach.展开更多
This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feed...This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.展开更多
In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restri...In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restricted to lie on a surface. Donders＇ intuition was that under such a restriction, the head orientation would be a function of its pointing direction. In this paper, we revisit Donders＇ Law and show that indeed the proposed intuition is true for a restricted class of head-orientations satisfying a class of quadratic Donders＇ surfaces, if the head points to a suitable neighborhood of the frontal pointing direction. Moreover, on a suitably chosen subspace of the 3D rotation group SO（3）, we describe a head movement dynamical system with input control signals that are the three external torques on the head provided by muscles. Three output signals are also suitably chosen as follows. Two of the output signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders＇ surface. We claim that the square system is locally feedback linearizable on the subspace chosen, and the linear dynamics is decomposed into parts, transverse and tangential to the Donders＇ surface. We demonstrate our approach by synthesizing a tracking and path-following controller. Additionally, for different choices of the Donders＇ surface parameters, head gaits are visualized by simulating different movement patterns of the head-top vector, as the head-pointing vector rotates around a circle.展开更多
The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control w...The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.展开更多
A sliding mode control approach based on the feedback linearization is proposed for the electrically controllable clutch of AMT vehicles. The nonlinear dynamic model for the hydraulic actuator associated with clutch i...A sliding mode control approach based on the feedback linearization is proposed for the electrically controllable clutch of AMT vehicles. The nonlinear dynamic model for the hydraulic actuator associated with clutch is established. By means of the exact feedback linearization procedure of differential geometry, an equivalent, fully controllable and linear model is derived via a homomorphic transformation for the AMT clutch system.Furthermore, a sliding mode control is introduced to improve robustness. The tracking tests are performed using the sliding mode control on a Santana LX passenger car, and the experimental results prove that this nonlinear controller is of fine robustness and high degree of tracking accuracy.展开更多
A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic so...A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model展开更多
Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a c...Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a class of non_affine control systems. The mathematical model describing motion of nonlinear viscoelastic plates is established, and it is simplified by the Galerkin method. The phase space portrait and the power spectrum are employed to demonstrate chaos in the system. The deflection is treated as an output, and is controlled to given periodic goals.展开更多
A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low ...A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low accuracy when used in the multivariable systems or in large search space. The new algorithm combines the particle swarm algorithm and the chaotic optimization, using randomness and ergodicity of chaos to overcome the premature convergence of the particle swarm optimization. At the same time, a new neural network feedback linearization control system is built to control the single-machine infinite-bus system. The network parameters are trained by the chaos particle swarm algorithm, which makes the control achieve optimization and the control law of prime mover output torque obtained. Finally, numerical simulation and practical application validate the effectiveness of the method.展开更多
It is a complicated nonlinear controlling problem to conduct a two-dimensional trajectory correction of rockets.By establishing the aerodynamic correction force mathematical model of rockets on nose cone swinging,the ...It is a complicated nonlinear controlling problem to conduct a two-dimensional trajectory correction of rockets.By establishing the aerodynamic correction force mathematical model of rockets on nose cone swinging,the linear control is realized by the dynamic inverse nonlinear controlling theory and the three-time-scale separation method.The control ability and the simulation results are also tested and verified.The results show that the output responses of system track the expected curve well and the error is controlled in a given margin.The maximum correction is about±314 m in the lengthwise direction and±1 212 m in the crosswise direction from the moment of 5 s to the drop-point time when the angle of fire is 55°.Thus,based on the dynamic inverse control of feedback linearization,the trajectory correction capability of nose cone swinging can satisfy the requirements of two-dimensional ballistic correction,and the validity and effectiveness of the method are proved.展开更多
Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators ...Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.展开更多
Aiming to improve the control accuracy of the vehicle height for the air suspension system,deeply analyzing the processes of variable mass gas thermodynamics and vehicle dynamics,a nonlinear height control model of th...Aiming to improve the control accuracy of the vehicle height for the air suspension system,deeply analyzing the processes of variable mass gas thermodynamics and vehicle dynamics,a nonlinear height control model of the air suspension vehicle was built. To deal with the nonlinear characteristic existing in the lifting and lowering processes,the nonlinear model of vehicle height control was linearized by using a feedback linearization method. Then,based on the linear full vehicle model,the sliding model controller was designed to achieve the control variables. Finally,the nonlinear control algorithm in the original coordinates can be achieved by the inverse transformation of coordinates. To validate the accuracy and effectiveness of the sliding mode controller,the height control processes were simulated in Matlab,i. e.,the lifting and lowering processes of the air suspension vehicle were taken when vehicle was in stationary and driving at a constant speed. The simulation results show that,compared to other controllers,the designed sliding model controller based on the feedback linearization can effectively solve the ＂overshoot＂problem,existing in the height control process,and force the vehicle height to reach the desired value,so as to greatly improve the speed and accuracy of the height control process. Besides,the sliding mode controller can well regulate the roll and pitch motions of the vehicle body,thereby improving the vehicle＇s ride comfort.展开更多
In this paper,a fifth-order fully differential interface circuit( IC) is presented to improve the noise performance for micromechanical sigma-delta( Σ-Δ) accelerometer. A lead compensator is adopted to ensure the st...In this paper,a fifth-order fully differential interface circuit( IC) is presented to improve the noise performance for micromechanical sigma-delta( Σ-Δ) accelerometer. A lead compensator is adopted to ensure the stability of the closed-loop high-order system. A low noise capacitance detection circuit is described with a correlated-double-sampling( CDS) technique to decrease 1 /f noise and offset of the operational amplifier. This paper also proposes a self-test technique for the interface circuit to test the harmonic distortion. An electrostatic force feedback linearization circuit is presented to reduce the harmonic distortion resulting in larger dynamic range( DR). The layout of the IC is implemented in a standard 0. 6 μm CMOS technology and operates at a sampling frequency of 250 kHz. The interface consumes 20 mW from a 5 V supply. The post-simulation results indicate that the noise floor of the digital accelerometer is about- 140 dBV /Hz1 /2at low frequency. The sensitivity is 2. 5 V /g and the nonlinearity is 0. 11%. The self-test function is achieved with 98. 2 dB thirdorder harmonic distortion detection based on the electrostatic force feedback linearization.展开更多
A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to conve...A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was de- signed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track vari- able desired output, which could be a time variant function or an equilibrium points. Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.展开更多
基金supported by the National Key R&D Program of China (Grant No.2022YFB3206700)the Independent Research Project of the State Key Laboratory of Mechanical Transmission (Grant No.SKLMT-ZZKT-2022M06)the Innovation Group Science Fund of Chongqing Natural Science Foundation (Grant No.cstc2019jcyj-cxttX0003).
文摘Piezoelectric stages use piezoelectric actuators and flexure hinges as driving and amplifying mechanisms,respectively.These systems have high positioning accuracy and high-frequency responses,and they are widely used in various precision/ultra-precision positioning fields.However,the main challenge with these devices is the inherent hysteresis nonlinearity of piezoelectric actuators,which seriously affects the tracking accuracy of a piezoelectric stage.Inspired by this challenge,in this work,we developed a Hammerstein model to describe the hysteresis nonlinearity of a piezoelectric stage.In particular,in our proposed scheme,a feedback-linearization algorithm is used to eliminate the static hysteresis nonlinearity.In addition,a composite controller based on equivalent-disturbance compensation was designed to counteract model uncertainties and external disturbances.An analysis of the stability of a closed-loop system based on this feedback-linearization algorithm and composite controller was performed,and this was followed by extensive comparative experiments using a piezoelectric stage developed in the laboratory.The experimental results confirmed that the feedback-linearization algorithm and the composite controller offer improved linearization and trajectory-tracking performance.
基金Supported by the National Natural Science Foundation of China (61863022)the Natural Science Foundation of Gansu Province(20JR10RA329)Scientific Research and Innovation Fund Project of Gansu University of Chinese Medicine in 2019 (2019KCYB-10)。
文摘In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.
文摘Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.
基金supported by the National Natural Science Foundation of China(51679201)
文摘The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.
基金supported by the National Natural Science Foundation of China (No.60975023)
文摘In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for hovering control is presented. It is proved that the nonlinear system of the small-scale helicopter can be transformed to a linear system using the dynamic feedback linearization technique. Finally, simulations are carried out to validate the nonlinear controller.
文摘The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.
基金Project supported by the National Natural Science Foundations of China (Grant Nos 70571030 and 90610031)the Advanced Talents’ Foundation of Jiangsu University of China (Grant No 07JDG054)
文摘This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.
文摘This paper deals with the design of an observer-based nonlinear control for continuous stirred tank reactors(CSTR).A variable structure observer is constructed to estimate the whole process state variables.This observer is basically the conventional Luenberger observer with an additional switching term used to guarantee the robustness against modeling errors.The observer is coupled with a nonlinear controller,designed based on input-output linearization for controlling the reactor temperature.The asymptotical stability of the closed-loop system is shown by the Lyapunov stability theorem.Finally,computer simulations are developed for showing the performance of the proposed approach.
基金supported by Russian Foundation for Basic Research(No.15-08-06859a)and by the Ministry of Education and Science of the Russian Federation in the framework of the basic part of the state order(No.2.8629.2017).
文摘This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.
文摘In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restricted to lie on a surface. Donders＇ intuition was that under such a restriction, the head orientation would be a function of its pointing direction. In this paper, we revisit Donders＇ Law and show that indeed the proposed intuition is true for a restricted class of head-orientations satisfying a class of quadratic Donders＇ surfaces, if the head points to a suitable neighborhood of the frontal pointing direction. Moreover, on a suitably chosen subspace of the 3D rotation group SO（3）, we describe a head movement dynamical system with input control signals that are the three external torques on the head provided by muscles. Three output signals are also suitably chosen as follows. Two of the output signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders＇ surface. We claim that the square system is locally feedback linearizable on the subspace chosen, and the linear dynamics is decomposed into parts, transverse and tangential to the Donders＇ surface. We demonstrate our approach by synthesizing a tracking and path-following controller. Additionally, for different choices of the Donders＇ surface parameters, head gaits are visualized by simulating different movement patterns of the head-top vector, as the head-pointing vector rotates around a circle.
文摘The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.
基金This project is imbursed by elite university teacher supporting plan
文摘A sliding mode control approach based on the feedback linearization is proposed for the electrically controllable clutch of AMT vehicles. The nonlinear dynamic model for the hydraulic actuator associated with clutch is established. By means of the exact feedback linearization procedure of differential geometry, an equivalent, fully controllable and linear model is derived via a homomorphic transformation for the AMT clutch system.Furthermore, a sliding mode control is introduced to improve robustness. The tracking tests are performed using the sliding mode control on a Santana LX passenger car, and the experimental results prove that this nonlinear controller is of fine robustness and high degree of tracking accuracy.
文摘A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model
文摘Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a class of non_affine control systems. The mathematical model describing motion of nonlinear viscoelastic plates is established, and it is simplified by the Galerkin method. The phase space portrait and the power spectrum are employed to demonstrate chaos in the system. The deflection is treated as an output, and is controlled to given periodic goals.
基金This work is supported by National Natural Science Foundation of China （50776005）.
文摘A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low accuracy when used in the multivariable systems or in large search space. The new algorithm combines the particle swarm algorithm and the chaotic optimization, using randomness and ergodicity of chaos to overcome the premature convergence of the particle swarm optimization. At the same time, a new neural network feedback linearization control system is built to control the single-machine infinite-bus system. The network parameters are trained by the chaos particle swarm algorithm, which makes the control achieve optimization and the control law of prime mover output torque obtained. Finally, numerical simulation and practical application validate the effectiveness of the method.
基金Project(9140A05030109HK01)supported by Equipment Pre-research Foundation,China
文摘It is a complicated nonlinear controlling problem to conduct a two-dimensional trajectory correction of rockets.By establishing the aerodynamic correction force mathematical model of rockets on nose cone swinging,the linear control is realized by the dynamic inverse nonlinear controlling theory and the three-time-scale separation method.The control ability and the simulation results are also tested and verified.The results show that the output responses of system track the expected curve well and the error is controlled in a given margin.The maximum correction is about±314 m in the lengthwise direction and±1 212 m in the crosswise direction from the moment of 5 s to the drop-point time when the angle of fire is 55°.Thus,based on the dynamic inverse control of feedback linearization,the trajectory correction capability of nose cone swinging can satisfy the requirements of two-dimensional ballistic correction,and the validity and effectiveness of the method are proved.
基金Sponsored by the Doctoral Fund of Ministry of Education of China(20070288022)the Natural Science Foundation of Jiangsu Province of China(BK2008404)the Young Teacher Academic Foundation of Nanjing University of Technology(39710013)
文摘Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.
基金Supported by the National Natural Science Foundation of China(5137504651205021)the Basic Research Foundation of Beijing Institute of Technology(20120342002)
文摘Aiming to improve the control accuracy of the vehicle height for the air suspension system,deeply analyzing the processes of variable mass gas thermodynamics and vehicle dynamics,a nonlinear height control model of the air suspension vehicle was built. To deal with the nonlinear characteristic existing in the lifting and lowering processes,the nonlinear model of vehicle height control was linearized by using a feedback linearization method. Then,based on the linear full vehicle model,the sliding model controller was designed to achieve the control variables. Finally,the nonlinear control algorithm in the original coordinates can be achieved by the inverse transformation of coordinates. To validate the accuracy and effectiveness of the sliding mode controller,the height control processes were simulated in Matlab,i. e.,the lifting and lowering processes of the air suspension vehicle were taken when vehicle was in stationary and driving at a constant speed. The simulation results show that,compared to other controllers,the designed sliding model controller based on the feedback linearization can effectively solve the ＂overshoot＂problem,existing in the height control process,and force the vehicle height to reach the desired value,so as to greatly improve the speed and accuracy of the height control process. Besides,the sliding mode controller can well regulate the roll and pitch motions of the vehicle body,thereby improving the vehicle＇s ride comfort.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61204121)the National Hi-Tech Research and Development Program of China(Grant No.2013AA041107)
文摘In this paper,a fifth-order fully differential interface circuit( IC) is presented to improve the noise performance for micromechanical sigma-delta( Σ-Δ) accelerometer. A lead compensator is adopted to ensure the stability of the closed-loop high-order system. A low noise capacitance detection circuit is described with a correlated-double-sampling( CDS) technique to decrease 1 /f noise and offset of the operational amplifier. This paper also proposes a self-test technique for the interface circuit to test the harmonic distortion. An electrostatic force feedback linearization circuit is presented to reduce the harmonic distortion resulting in larger dynamic range( DR). The layout of the IC is implemented in a standard 0. 6 μm CMOS technology and operates at a sampling frequency of 250 kHz. The interface consumes 20 mW from a 5 V supply. The post-simulation results indicate that the noise floor of the digital accelerometer is about- 140 dBV /Hz1 /2at low frequency. The sensitivity is 2. 5 V /g and the nonlinearity is 0. 11%. The self-test function is achieved with 98. 2 dB thirdorder harmonic distortion detection based on the electrostatic force feedback linearization.
基金Supported by National Natural Science Foundation of China (60374013) and Natural Science Foundation of Zhejiang Province (Y104414, M603217)
文摘A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was de- signed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track vari- able desired output, which could be a time variant function or an equilibrium points. Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.
