不连续机械系统混沌运动的控制

首先指出：预紧弹性约束，干摩擦等不连续力学因素将导致系统Ｐｏｉｎｃａｒｅ映射在控制目标附近不可微，故ＯＧＹ等控制策略无法胜任这类系统的混沌运动控制。为控制这类系统的混沌运动，提出了由实验数据区分所合Ｐｏｉｎｃａｒｅ映射以及分区进行极点配置形成控制策略。对具有预紧弹性约束的受迫振子的仿真实验表明，这种控制策略是成功的。     

引导混沌运动到周期运动的自适应控制策略

提出一种自适应控制策略，对控制参数作线性反馈将非线性动力系统由混沌运动引导到指定的周期运动．所解决的关键问题是将反馈控制强度的确定转化为扩维相空间中的极点配置问题．给出了将该策略用于控制Ｌｏｇｉｓｔｉｃ映射和受迫Ｄｕｆｉｎｇ振子的仿真．     

A Modified Exact Linearization Control for Chaotic Oscillators

The control of chaotic oscillations is investigated in this paper. A control methodology, termed input-output linearization, is modified by locally linearizing the nonlinear control law in the small neighborhood of the control goal. Its suitability for controlling chaotic oscillators is analyzed. The forced Duffing oscillator is treated as a numerical example of controlling chaotic motion to a given fixed point and a given period-2 motion. The control signals and time needed to achieve the desired goals of the modified method are compared with those of the original method. The robustness of the control law is demonstrated.     

Nonlinear dynamic analysis and sliding mode control for?a?gyroscope system

This paper employs differential transformation (DT) method to analyze and control the dynamic behavior of a gyroscope system. The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic, quasiperiodic, and chaotic responses of the center of gravity. Furthermore, the results reveal the changes which take place in the dynamic behavior of the gyroscope system as the external force is increased. The current analytical results by DT method are found to be in good agreement with those of Runge?CKutta (RK) method. In order to suppress the chaotic behavior in gyroscope system, the sliding mode controller (SMC) is used and guaranteed the stability of the system from chaotic motion to periodic motion. Numerical simulations are shown to verify the results. The proposed DT method and controlling scheme provide an effective means of gaining insights into the nonlinear dynamics and controlling of gyroscope systems.     

Dither signals with particular application to the control of windscreen wiper blades

This study verifies chaotic motion of an automotive wiper system, which consists of two blades driven by a DC motor via the two connected four-bar linkages and then elucidates a system for chaotic control. A bifurcation diagram reveals complex nonlinear behaviors over a range of parameter values. Next, the largest Lyapunov exponent is estimated to identify periodic and chaotic motions. Finally, a method for controlling a chaotic automotive wiper system will be proposed. The method involves applying another external input, called a dither signal, to the system. Some simulation results are presented to demonstrate the feasibility of the proposed method.     

不平衡量对非线性多转子系统动力特性的影响

用近代非线性动力学理论分析了弹性支承有间隙和摩擦的非线性刚性多转子系统的复杂运动.建立了支座有间隙和有摩擦的弹性支承的力学模型.导出了这类多转子系统的运动微分方程组.用数值方法得到系统在某些参数区域内的轴心轨迹图,Poincare映射图和分岔图等.以转子不平衡量为控制参数讨论了进出混沌区的不同路径和系统各种形式的拟周期,倍周期和混沌运动.分析结果为定性地改善转子系统的稳定运行状态提供了理论依据.     

弹性支承有间隙的复合转子系统的混沌特性

用近代非线性动力学理论分析了支承有间隙的调整对对称刚性复合转子系统的复杂运动,用数值方法得到系统在某些参数区域内的轴心轨迹图、Poincare映射图和分岔图,讨论了转速变化时出现的周期、倍周期、拟周期和混沌运动,分析结果为定性地改善转子系统的稳定运动状态提供了理论依据。     

Chaotic motion of a nonlinear thermoelastic elliptic plate

In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived, with the effects of large deflection of plate and thermoelasticity taken into account. The Melnikov function method is used to give the critical condition for chaotic motion. A demonstrative example is discussed through the Poincaré mapping, phase portrait and time history. Finally the path to chaotic motion is also discussed. Through the theoretical analysis and numerical computation some beneficial conclusions are obtained. Foundation item: the National natural Science Foundation of China (19672038); the Natural Science Foundation of Shanxi Provence (1880342).     

Control of Chaotic Motion in a Spinning Spacecraft with a Circumferential Nutational Damper

Control of chaotic vibrations in a simplified model of a spinning spacecraft with a circumferential nutational damper is achieved using two techniques. The control methods are implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in practice, may arise in the platform of a dual-spin spacecraft under malfunction of the control system or from an unbalanced rotor or from vibrations in appendages. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude and consequently could have disastrous affects on its operation. The two control methods, recursive proportional feedback (RPF) and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamical systems. Each technique is outlined and the effectiveness of the two strategies in controlling chaotic motion exhibited by the present system is compared and contrasted. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincaré map, Lyapunov characteristic exponents and bifurcation diagrams.     

Chaotic attitude motion of a magnetic rigid spacecraft in an elliptic orbit and its control

This paper deals with the chaotic attitude motion of a magnetic rigid spacecraft with internal damping in an elliptic orbit. The dynamical model of the spacecraft is established. The Melnikov analysis is carried out to prove the existence of a complicated nonwandering Cantor set. The dynamical behaviors are numerically investigated by means of time history, Poincaré map, Lyapunov exponents and power spectrum. Numerical simulations demonstrate the chaotic motion of the system. The input-output feedback linearization method and its modified version are applied, respectively, to control the chaotic attitude motions to the given fixed point or periodic motion. The project supported by the National Natural Science Foundation of Chine (10082003)     

Periodic and chaotic dynamics of a sliding driven oscillator with dry friction

We have performed a numerical study of the dynamics of a harmonically forced sliding oscillator with two degrees of freedom and dry friction. The study of the four-dimensional dynamical system corresponding to the two non-linear motion equations can be reduced, in this case, to the study of a three-dimensional Poincaré map. The behaviour of the system has been investigated calculating bifurcation diagrams, time series, periodic and chaotic attractors and basins of attraction. Furthermore, a systematic study of the stability of periodic solutions and their bifurcations has been carried out applying the Floquet theory. The results show rich dynamics being very sensitive to the changes in forcing amplitudes (control parameter), where periodic and chaotic states alternatively appear. It is shown how the system exhibits different types of bifurcational phenomena (saddle-node, symmetry-breaking, period-doubling cascades and intermittent transitions to chaos) into relatively narrow intervals of the control parameter. Moreover, a collection of chaotic attractors was computed to show the evolution of the chaotic regime. Finally, basins of attraction were calculated. In all the cases studied, the basins exhibit fractal structure boundaries and, when more of two attractors are coexisting, we have found Wada basin boundaries.     

Dynamic delayed feedback control for stabilizing the giant swing motions of an underactuated three-link gymnastic robot

This paper investigates the dynamics of the giant swing motions of an underactuated three-link gymnastic robot moving in a vertical plane by means of dynamic delayed feedback control (DDFC). DDFC, being one of useful methods to overcome the so-called odd number limitation in controlling a chaotic discrete-time system, is extended to control a continuous-time system such as a 3-link gymnastic robot with passive joint. Meanwhile, a way to calculate the error transfer matrix and the input matrix which are necessary for discretization is proposed, based on a Poincaré section which is defined to regard the target system as a discrete-time system. Moreover, the stability of the closed-loop system by the proposed control strategy is discussed. Furthermore, some numerical simulations are presented to show the effectiveness in controlling a chaotic motion of the 3-link gymnastic robot to a periodic giant swing motion.     

Chaotic behavior in the nonlinear elastic beam

The dynamic response of the non-linear elastic simply supported beam subjected to axial forces and transverse periodic load is studied. Melnikov method is used to consider the dynamic behavior of the system whose post-buckling path is steady. The effect of the higher order terms in the controlling equation is taken into account. It is found that the fifth-order terms have a great influence on the dynamic behavior of the system. The result shows that there exist either homoclinic orbits or heteroclinic orbits in the system. In this paper, the critical values of the system entering chaotic states are given. The diagram of an example is shown. The project is supported by the National Natural Sciences Foundation of China.     

Finite-time chaos control of unified chaotic systems with uncertain parameters

This paper is concerned with finite-time chaos control of unified chaotic systems with uncertain parameters. Based on the finite-time stability theory in the cascade-connected system, a nonlinear control law is presented to achieve finite-time chaos control. The controller is simple and easy to be constructed. Simulation results for Lorenz, Lü, and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme. Supported by the National Natural Science Foundation of China (Grant No. 60674024).     

The global bifurcation and chaos for the coupling between longitudinal and transverse vibration of a thin elastic plate in large overall motion

This paper presents the global bifurcation and chaotic behavior for the coupling of longitudinal and transverse vibration of a thin elastic plate in large overall motion. First the parametric equations of the homoclinic orbits of such a system is obtained. Then, by using the Melnikov method and digital computer simulation. the behavior of bifurcation and chaos of this vibration system is investigated in the cases of different resonances. The obvious difference between the transverse vibration and the coupling of transverse and longitudinal vibration is also shown.The project supported by the National Natural Science Foundation of China.     

Noise-induced chaos in the elastic forced oscillators with real-power damping force

The chaotic behavior of the elastic forced oscillators with real-power exponents of damping and restoring force terms under bounded noise is investigated. By using random Melnikov method, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the random frequency increases, and decrease as the real-power exponent of damping term increase. The threshold of bounded noise amplitude for the onset of chaos is determined by the numerical calculation via the largest Lyapunov exponents. The effects of bounded noise and real-power exponent of damping term on bifurcation and Poincaré map are also investigated. Our results may provide a valuable guidance for understanding the effect of bounded noise on a class of generalized double well system.     

An adaptive delayed feedback control method for stabilizing chaotic time-delayed systems

This paper addresses a new adaptive delayed feedback control technique for stabilizing a class of chaotic time-delayed systems with a variable parameter. In the proposed scheme, the feedback gain of a delayed feedback controller is automatically tuned according to an adaptation law in order to stabilize unstable fixed points of the system. Such a mechanism provides a way to cope with unexpected changes in the parameters of the system. The adaptation algorithm is constructed based on the Lyapunov?CKrasovskii??s stability theorem. The control technique provides the advantages of increased stability and optimality, adaptability to the changes in the parameters, high privacy, simplicity, and noninvasiveness. The effectiveness of the control scheme is demonstrated using numerical simulations for a well-known chaotic time-delayed system.     

NONLINEAR COMPLEX DYNAMIC PHENOMENA OF THE PERTURBED METALLIC BAR CONSIDERING DISSIPATING EFFECT

IntroductionTotheweaklydamped ,periodicallyforcedsine_Gordonequation ,A .R .Bishop[1～ 3]analyzeditssolutionunderperiodicboundaryconditionandconcludedthatitssolutionwouldshowdifferentspatialstructuresandlong_timeasymptoticstatesalongwiththevariationofpara…     

Chaotic attitude and reorientation maneuver for completely liquid-filled spacecraft with flexible appendage

The present paper investigates the chaotic attitude dynamics and reorientation maneuver for completely viscous liquid-filled spacecraft with flexible appendage. All of the equations of motion are derived by using Lagrangian mechanics and then transformed into a form consisting of an unperturbed part plus perturbed terms so that the system＇s nonlinear characteristics can be exploited in phase space. Emphases are laid on the chaotic attitude dynamics produced from certain sets of physical parameter values of the spacecraft when energy dissipation acts to derive the body from minor to major axis spin. Numerical solutions of these equations show that the attitude dynamics of liquid-filled flexible spacecraft possesses characteristics common to random, non- periodic solutions and chaos, and it is demonstrated that the desired reorientation maneuver is guaranteed by using a pair of thruster impulses. The control strategy for reorientation maneuver is designed and the numerical simulation results are presented for both the uncontrolled and controlled spins transition.     

Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system

This paper analyzes the hyperchaotic behaviors of the newly presented simplified Lorenz system by using a sinusoidal parameter variation and hyperchaos control of the forced system via feedback. Through dynamic simulations which include phase portraits, Lyapunov exponents, bifurcation diagrams, and Poincaré sections, we find the sinusoidal forcing not only suppresses chaotic behaviors, but also generates hyperchaos. The forced system also exhibits some typical bifurcations such as the pitchfork, period-doubling, and tangent bifurcations. Interestingly, three-attractor coexisting phenomenon happens at some specific parameter values. Furthermore, a feedback controller is designed for stabilizing the hyperchaos to periodic orbits, which is useful for engineering applications.