This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback.Two specific combinations and simultaneous resonances are selected for d...This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback.Two specific combinations and simultaneous resonances are selected for detailed examination.Initially,utilizing Hamilton’s variational principle,a nonlinear vibration control model of suspended cables under multi-frequency excitations and longitudinal time-delayed velocity feedback is developed,and the Galerkin method is employed to obtain the discrete model.Subsequently,focusing solely on single-mode discretization,analytical solutions for the two simultaneous resonances are derived using the method of multiple scales.The frequency response equations are derived,and the stability analysis is presented for two simultaneous resonance cases.The results demonstrate that suspended cables exhibit complex nonlinearity under multi-frequency excitations.Multiple solutions under multi-frequency excitation can be distinguished through the frequency–response and the detuning-phase curves.By adjusting the control gain and time delay,the resonance range,response amplitude,and phase of suspended cables can be modified.展开更多
In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to for...In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.展开更多
Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in...Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment.This paper proposes a novel method for estimating target time delay using multi-bright spot echoes,assuming the target’s size and depth are known.Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise,the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes.Using the highlighting model theory and the target size information,an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles.Aiming to accurately estimate the target’s time delay,waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays.Simulation results show that,compared to the conventional matched filter,the proposed algorithm reduces the relative error by 65.9%-91.5%at a signal-to noise ratio of-25 dB,and by 66.7%-88.9%at a signal-to-reverberation ratio of−10 dB.This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.展开更多
Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is propos...Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is proposed to suppress vibration of the primary system under excitation with changing frequency. Firstly, the mechanical model of the delay coupled system is established. Then, the displacement transfer ratio of the system is obtained. The stability of the system is analyzed since delay may result in destabilization. Next, in order to design the control parameters, the vibration absorption performances of the proposed time-delayed vibration absorber are studied. The vibration absorption region is shown. The results show that time-delayed feedback control is able to change the response of the system. The effective vibration absorption frequency band is adjustable by tuning the control gain and time delay. The effective frequency band can be widened when choosing appropriate control parameters. The vibration absorption performances can be greatly improved by the time-delayed absorber. In addition, the optimum control parameters are obtained. Finally, the experimental prototype is constructed. Several tests with different control parameters are taken. The experimental and analytical results match quite well.展开更多
The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The fi...The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.展开更多
This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, th...This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, the expression of the signal-to-noise ratio （SNR） is obtained. It finds that the SNR is a non-monotonic function of the delayed times, of the amplitude of the driving square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters. Moreover, the SNR depends non-monotonically on the correlate rate of the dichotomous noise.展开更多
This paper considers the stochastic resonance for a time-delayed mono-stable system, driven by correlated multiplicative and additive white noise. It finds that the output signal-to-noise ratio （SNR） varies non-mono...This paper considers the stochastic resonance for a time-delayed mono-stable system, driven by correlated multiplicative and additive white noise. It finds that the output signal-to-noise ratio （SNR） varies non-monotonically with the delayed times. The SNR varies non-monotonically with the increase of the intensities of the multiplicative and additive noise, with the increase of the correlation strength between the two noises, as well as with the system parameter.展开更多
Subject of the halo-chaos control in beam transport networks （channels） has become a key concerned issue for many important applications of high-current proton beam since 1990＇. In this paper, the magnetic field ad...Subject of the halo-chaos control in beam transport networks （channels） has become a key concerned issue for many important applications of high-current proton beam since 1990＇. In this paper, the magnetic field adaptive control based on the neural network with time-delayed feedback is proposed for suppressing beam halo-chaos in the beam transport network with periodic focusing channels. The envelope radius of high-current proton beam is controlled to reach the matched beam radius by suitably selecting the control structure and parameter of the neural network, adjusting the delayed-time and control coefficient of the neural network.展开更多
The traditional passive absorber is fully effective within a narrow and certain frequency band.To solve this problem,a time-delayed acceleration feedback is introduced to convert a passive absorber into an active one....The traditional passive absorber is fully effective within a narrow and certain frequency band.To solve this problem,a time-delayed acceleration feedback is introduced to convert a passive absorber into an active one.Both the inherent and the intentional time delays are included.The former mainly comes from signal acquiring and processing,computing,and applying the actuation force,and its value is fixed.The latter is introduced in the controller,and its value is actively adjustable.Firstly,the mechanical model is established and the frequency response equations are obtained.The regions of stability are delineated in the plane of control parameters.Secondly,the design scheme of control parameters is performed to help select the values of the feedback gain and time delay.Thirdly,the experimental studies are conducted.Effects of both negative and positive feedback control are investigated.Experimental results show that the proper choices of control parameters may broaden the effective frequency band of vibration absorption.Moreover,the time-delayed absorber greatly suppresses the resonant response of the primary system when the passive absorber totally fails.The experimental results are in good agreement with the theoretical predictions and numerical simulations.展开更多
Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delay...Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Ito differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.展开更多
A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to de...A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .展开更多
The stochastic resonance behavior of coupled stochastic resonance(SR)system with time-delay under mass and frequency fluctuations was studied.Firstly,the approximate system model of the time-delay system was obtained ...The stochastic resonance behavior of coupled stochastic resonance(SR)system with time-delay under mass and frequency fluctuations was studied.Firstly,the approximate system model of the time-delay system was obtained by the theory of small time-delay approximation.Then,the random average method and Shapiro-Loginov algorithm were used to calculate the output amplitude ratio of the two subsystems.The simulation analysis shows that increasing the time-delay and the input signal amplitude appropriately can improve the output response of the system.Finally,the system is applied to bearing fault diagnosis and compared with the stochastic resonance system with random mass and random frequency.The experimental results show that the coupled SR system taking into account the actual effect of time-delay and couple can more effectively extract the frequency of the fault signal,and thus realizing the diagnosis of the fault signal,which has important engineering application value.展开更多
The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Partic...The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle incell simulation results show that the method is very effective and has some advantages for high-current beam experimentsand engineering.展开更多
The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly ...The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.展开更多
This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A ge...This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.展开更多
Recently, the conditions of observers that can estimate directly Kx（t） for an arbitrarily given K, and that are free of the effect of time delayed states of the system, are formulated. This paper points out that, be...Recently, the conditions of observers that can estimate directly Kx（t） for an arbitrarily given K, and that are free of the effect of time delayed states of the system, are formulated. This paper points out that, because of the equivalence in formulation, the existing conditions for unknown input observers can be used to establish directly a new set of sufficient conditions for that recent observer. This new set of sufficient conditions is much simpler, and therefore much more useful and significant, than the sufficient conditions derived in that recent paper. This new set of sufficient conditions also reveals some basic mistakes of that recent paper. In addition, this paper reveals the severe restrictiveness of this new set of conditions and proposes a fundamentally new observer design formulation that can relax that set of conditions significantly.展开更多
The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the las...The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the laser field isobtained.The mean,normalized variance and skewness of the steady-state laser intensity are calculated.It is found thatthe time-delayed feedback control can suppress the intensity fluctuation of the laser system.The numerical simulationsare in good agreement with the approximate analytic results.展开更多
We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optica...We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor a can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of a. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.展开更多
Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-pa...Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.展开更多
Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the syste...Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant No.12432001)Natural Science Foundation of Hunan Province(Grant Nos.2023JJ60527,2023JJ30152,and 2023JJ30259)the Natural Science Foundation of Changsha(KQ2202133).
文摘This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback.Two specific combinations and simultaneous resonances are selected for detailed examination.Initially,utilizing Hamilton’s variational principle,a nonlinear vibration control model of suspended cables under multi-frequency excitations and longitudinal time-delayed velocity feedback is developed,and the Galerkin method is employed to obtain the discrete model.Subsequently,focusing solely on single-mode discretization,analytical solutions for the two simultaneous resonances are derived using the method of multiple scales.The frequency response equations are derived,and the stability analysis is presented for two simultaneous resonance cases.The results demonstrate that suspended cables exhibit complex nonlinearity under multi-frequency excitations.Multiple solutions under multi-frequency excitation can be distinguished through the frequency–response and the detuning-phase curves.By adjusting the control gain and time delay,the resonance range,response amplitude,and phase of suspended cables can be modified.
基金co-supported by the National Natural Science Foundation of China (Nos. 61333011, 91216304 and 61121003)
文摘In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.
基金Supported by the State Key Laboratory of Acoustics and Marine Information Chinese Academy of Sciences(SKL A202507).
文摘Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment.This paper proposes a novel method for estimating target time delay using multi-bright spot echoes,assuming the target’s size and depth are known.Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise,the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes.Using the highlighting model theory and the target size information,an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles.Aiming to accurately estimate the target’s time delay,waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays.Simulation results show that,compared to the conventional matched filter,the proposed algorithm reduces the relative error by 65.9%-91.5%at a signal-to noise ratio of-25 dB,and by 66.7%-88.9%at a signal-to-reverberation ratio of−10 dB.This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.
基金the National Natural Science Foundation of China (Grants 11572224 and 11772229).
文摘Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is proposed to suppress vibration of the primary system under excitation with changing frequency. Firstly, the mechanical model of the delay coupled system is established. Then, the displacement transfer ratio of the system is obtained. The stability of the system is analyzed since delay may result in destabilization. Next, in order to design the control parameters, the vibration absorption performances of the proposed time-delayed vibration absorber are studied. The vibration absorption region is shown. The results show that time-delayed feedback control is able to change the response of the system. The effective vibration absorption frequency band is adjustable by tuning the control gain and time delay. The effective frequency band can be widened when choosing appropriate control parameters. The vibration absorption performances can be greatly improved by the time-delayed absorber. In addition, the optimum control parameters are obtained. Finally, the experimental prototype is constructed. Several tests with different control parameters are taken. The experimental and analytical results match quite well.
基金Project supported by the National Natural Science Foundation of China (Nos. 12122208, 11972254,and 11932015)。
文摘The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.
基金supported by the Doctor Foundation of Southwest University of Science and Technology of China (Grant No. 08zx7108)
文摘This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, the expression of the signal-to-noise ratio （SNR） is obtained. It finds that the SNR is a non-monotonic function of the delayed times, of the amplitude of the driving square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters. Moreover, the SNR depends non-monotonically on the correlate rate of the dichotomous noise.
文摘This paper considers the stochastic resonance for a time-delayed mono-stable system, driven by correlated multiplicative and additive white noise. It finds that the output signal-to-noise ratio （SNR） varies non-monotonically with the delayed times. The SNR varies non-monotonically with the increase of the intensities of the multiplicative and additive noise, with the increase of the correlation strength between the two noises, as well as with the system parameter.
基金The project supported by the Key Projects of National Natural Science Foundation of China under Grant No. 70431002 and National Natural Science Foundation of China under Grants Nos. 70371068 and 10247005
文摘Subject of the halo-chaos control in beam transport networks （channels） has become a key concerned issue for many important applications of high-current proton beam since 1990＇. In this paper, the magnetic field adaptive control based on the neural network with time-delayed feedback is proposed for suppressing beam halo-chaos in the beam transport network with periodic focusing channels. The envelope radius of high-current proton beam is controlled to reach the matched beam radius by suitably selecting the control structure and parameter of the neural network, adjusting the delayed-time and control coefficient of the neural network.
基金supported by the State Key Program of National Natural Science Foundation of China(grant No. 11032009)National Natural Science Foundation of China(grant No.11272236)
文摘The traditional passive absorber is fully effective within a narrow and certain frequency band.To solve this problem,a time-delayed acceleration feedback is introduced to convert a passive absorber into an active one.Both the inherent and the intentional time delays are included.The former mainly comes from signal acquiring and processing,computing,and applying the actuation force,and its value is fixed.The latter is introduced in the controller,and its value is actively adjustable.Firstly,the mechanical model is established and the frequency response equations are obtained.The regions of stability are delineated in the plane of control parameters.Secondly,the design scheme of control parameters is performed to help select the values of the feedback gain and time delay.Thirdly,the experimental studies are conducted.Effects of both negative and positive feedback control are investigated.Experimental results show that the proper choices of control parameters may broaden the effective frequency band of vibration absorption.Moreover,the time-delayed absorber greatly suppresses the resonant response of the primary system when the passive absorber totally fails.The experimental results are in good agreement with the theoretical predictions and numerical simulations.
基金Supported by the National Natural Science Foundation of China(61863022)the Key Project of Gansu Province Natural Science Foundation(23JRRA882)。
文摘Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Ito differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.
基金the National Natural Science Foundation of China (10772159)Specialized Research Fund for the Doctoral Program of Higher Education of China (20060335125)
文摘A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .
基金Project(61771085)supported by the National Natural Science Foundation of ChinaProject(KJQN 201900601)supported by the Research Project of Chongqing Educational Commission,China。
文摘The stochastic resonance behavior of coupled stochastic resonance(SR)system with time-delay under mass and frequency fluctuations was studied.Firstly,the approximate system model of the time-delay system was obtained by the theory of small time-delay approximation.Then,the random average method and Shapiro-Loginov algorithm were used to calculate the output amplitude ratio of the two subsystems.The simulation analysis shows that increasing the time-delay and the input signal amplitude appropriately can improve the output response of the system.Finally,the system is applied to bearing fault diagnosis and compared with the stochastic resonance system with random mass and random frequency.The experimental results show that the coupled SR system taking into account the actual effect of time-delay and couple can more effectively extract the frequency of the fault signal,and thus realizing the diagnosis of the fault signal,which has important engineering application value.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10247005,70071047,and 19875080
文摘The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle incell simulation results show that the method is very effective and has some advantages for high-current beam experimentsand engineering.
基金Project(KYLX15_0256)supported by the Funding of Jiangsu Innovation Program for Graduate Education,ChinaProject(SV2015-KF-01)supported by the Open Project of State Key Laboratory for Strength and Vibration of Mechanical Structures,ChinaProject(XZA15003)supported by the Fundamental Research Funds for the Central Universities,China
文摘The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10902085)
文摘This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.
文摘Recently, the conditions of observers that can estimate directly Kx（t） for an arbitrarily given K, and that are free of the effect of time delayed states of the system, are formulated. This paper points out that, because of the equivalence in formulation, the existing conditions for unknown input observers can be used to establish directly a new set of sufficient conditions for that recent observer. This new set of sufficient conditions is much simpler, and therefore much more useful and significant, than the sufficient conditions derived in that recent paper. This new set of sufficient conditions also reveals some basic mistakes of that recent paper. In addition, this paper reveals the severe restrictiveness of this new set of conditions and proposes a fundamentally new observer design formulation that can relax that set of conditions significantly.
文摘The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the laser field isobtained.The mean,normalized variance and skewness of the steady-state laser intensity are calculated.It is found thatthe time-delayed feedback control can suppress the intensity fluctuation of the laser system.The numerical simulationsare in good agreement with the approximate analytic results.
基金Supported by Research Project of Hubei Provincial Department of Education under Grant No.Q20101609Foundation of Wuhan Textile University under Grant No.105040
文摘We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor a can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of a. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.
基金Project supported by the National Natural Science Foundation of China(Grant No.60551002)the Natural Science Foundation of Hunan Province,China(Grant No.2018JJ3680).
文摘Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.
基金Project supported by the National Nature Science Foundation of China(Grant No.11205044)the Fundamental Research Funds for the Central Universities(Grant No.10ML40)
文摘Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.
