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 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
The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, ...The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.展开更多
An externally excited Duffing oscillator under feedback control is discussed and analyzed under the worst resonance case.Multiple time scales method is applied for this system to find analytic solution with the existe...An externally excited Duffing oscillator under feedback control is discussed and analyzed under the worst resonance case.Multiple time scales method is applied for this system to find analytic solution with the existence and nonexistence of the time delay on control loop.An appropriate stability analysis is also performed and appropriate choices for the feedback gains and the time delay are found in order to reduce the amplitude peak.Different response curves are involved to show and compare controller effects.In addition,analytic solutions are compared with numerical approximation solutions using Rung-Kutta method of fourth order.展开更多
In this paper,we used time delay feedback to minimize the vibrations of a hybrid Rayleigh–van der Pol–Duffing oscillator.This system is a one-degree-offreedom containing the cubic and fifth nonlinear terms and an ex...In this paper,we used time delay feedback to minimize the vibrations of a hybrid Rayleigh–van der Pol–Duffing oscillator.This system is a one-degree-offreedom containing the cubic and fifth nonlinear terms and an external force.We applied the multiple scales method to get the solution from first approximation.Graphically and numerically,we studied the system before and after adding time delay feedback at the primary resonance case(ffi!).We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.展开更多
In the paper, several different methods are adopted to control Lü system. With direct feedback method, Lü system can be stabilized at one equilibrium point or a limit cycle surrounding its equilibrium. With ...In the paper, several different methods are adopted to control Lü system. With direct feedback method, Lü system can be stabilized at one equilibrium point or a limit cycle surrounding its equilibrium. With adaptive time-delayed feedback method, feedback coefficient and delay time can be adjusted adaptively to stabilize Lü system at its original unstable periodic orbit. With minimal energy method, Lü system can also be stabilized at fixed point or limit cycle. Numerical simulations show the effectiveness of our methods.展开更多
The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing contr...The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.展开更多
运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数...运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数,对非自治时滞反馈系统的主共振分岔响应进行了控制.研究结果表明,适当选取参数不仅可以改变分岔响应曲线的拓扑形态,还可以改变分岔点的位置.展开更多
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(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Supported by the "973" Project of P. R. China (G1998020300)
文摘The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.
文摘An externally excited Duffing oscillator under feedback control is discussed and analyzed under the worst resonance case.Multiple time scales method is applied for this system to find analytic solution with the existence and nonexistence of the time delay on control loop.An appropriate stability analysis is also performed and appropriate choices for the feedback gains and the time delay are found in order to reduce the amplitude peak.Different response curves are involved to show and compare controller effects.In addition,analytic solutions are compared with numerical approximation solutions using Rung-Kutta method of fourth order.
文摘In this paper,we used time delay feedback to minimize the vibrations of a hybrid Rayleigh–van der Pol–Duffing oscillator.This system is a one-degree-offreedom containing the cubic and fifth nonlinear terms and an external force.We applied the multiple scales method to get the solution from first approximation.Graphically and numerically,we studied the system before and after adding time delay feedback at the primary resonance case(ffi!).We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.
文摘In the paper, several different methods are adopted to control Lü system. With direct feedback method, Lü system can be stabilized at one equilibrium point or a limit cycle surrounding its equilibrium. With adaptive time-delayed feedback method, feedback coefficient and delay time can be adjusted adaptively to stabilize Lü system at its original unstable periodic orbit. With minimal energy method, Lü system can also be stabilized at fixed point or limit cycle. Numerical simulations show the effectiveness of our methods.
基金Supported by the National Natural Science Foundation of China (Grant No. 10772159)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335125)+1 种基金Zhejiang Natural Science Foundation (Grant No. Y7080070)Fujian Provincial Science and Technology Project (Grant No. 2005YZ1021)
文摘The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.
文摘运用多尺度法研究了一类van der Pol-Duffing系统的Hopf分岔问题和分岔控制问题.首先,分析了自治的van der Pol-Duffin g系统的Hopf分岔问题,并设计了线性和非线性联合的状态反馈控制器,对其进行了Hopf分岔控制.然后,设计了线性时滞参数,对非自治时滞反馈系统的主共振分岔响应进行了控制.研究结果表明,适当选取参数不仅可以改变分岔响应曲线的拓扑形态,还可以改变分岔点的位置.
