Tolerance of start-up control of rotation in parametric pendulum by delayed feedback

In this Letter, we propose a control method for establishing periodic rotation inherent in parametric pendulum based on a delayed feedback control. The experiments elucidate the existing range of periodic rotation in the domain of delay. The range of existence possibly represents the tolerance of proposed control with mistuned delay. It is confirmed that forced synchronization governs the existence and the width. The result assures that the frequency synchronization characteristics overcome the mistuned difference of delay in the control through entrainment.     

振荡摆参量过程研究

在弱调制的情况下,利用摄动方法研究了振荡摆(θ<5°)参量过程解的性质.     

用气垫摆测物体的转动惯量

介绍用自己研制的气垫摆测量物体的转动惯量,叙述了相关理论,推导了计算公式,给出了实验结果。     

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincar map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.     

放置不同物体三线摆转动周期变化规律研究

针对三线摆上放置的常用物体,如:圆盘、圆环、两圆柱体等,探讨放置物体前后、质量分布及位置改变时转动周期的变化规律.结果表明:理论分析与实验结果有较好的一致性.     

Experimental evidence for chaotic behaviour of a parametrically forced pendulum

Experimental evidence is presented for chaotic type nonperiodic motions of a parametrically forced pendulum. A bifurcation diagram is measured directly, showing successive subharmonic bifurcations to ?/4, onset of a periodic motion and the appearance of periodic motions via intermittency. The experimentally determined threshold values of the amplitude of the driving force for the first period doublings and the onset of a periodic motion are found to be in good agreement with the theoretical predictions.     

Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms

In this paper we present a numerical method to compute derivatives of the rotation number for parametric families of circle diffeomorphisms with high accuracy. Our methodology is an extension of a recently developed approach to compute rotation numbers based on suitable averages of iterates of the map and Richardson extrapolation. We focus on analytic circle diffeomorphisms, but the method also works if the maps are differentiable enough. In order to justify the method, we also require the family of maps to be differentiable with respect to the parameters and the rotation number to be Diophantine. In particular, the method turns out to be very efficient for computing Taylor expansions of Arnold Tongues of families of circle maps. Finally, we adapt these ideas to study invariant curves for parametric families of planar twist maps.     

Application of focused beams for parametric reflection control

The effect of parametric reflection of a signal beam from a focused reference beam has been investigated. It is shown that focusing reduces a pump power reflection threshold but causes certain distortions due to the reduction of the area of the parametric mirror and occurrence of its longitudinal curvature. These effects limit the width and angle of incidence of the signal beam. To decrease the sum wave power, it is proposed to introduce an additional dispersion mismatch.     

自由摆的平板控制系统设计

为了实现对基于自由摆的平板的控制,建立了基于自由摆的平板控制系统.首先分析平板的控制转角与自由摆转角的关系,推导出关系式,再对控制单元、反馈单元进行分析比较给出方案,采用32位LPC2138(ARM7)处理器为平板控制系统的中央控制单元,实现由高精度电位器测量出摆动角度后由步进电机控制的平板在周期摆动中做相应反馈调整,然后在现有器件的基础上编制出控制软件,在设备上进行调试,最后对系统的精度进行分析并进行实际测量.测量结果表明激光笔在摆动中照射在靶板上的光斑偏离基准线最大0.89cm,基本满足对平板的控制要求.     

Adaptive control and synchronization for chaotic systems with parametric uncertainties

An adaptive control scheme using only part of the system states for the stabilization of one chaotic system and the synchronization of two chaotic systems is presented. The system parameters are allowed to have a large range of time varying uncertainties around their fixed unknown nominal values both in the stabilization and the synchronization control problems. Simulation results also illustrate the effectiveness of the proposed control scheme.     

Instabilities in the main parametric resonance area of a mechanical system with a pendulum

Vibrations of an autoparametric system, composed of a nonlinear mechanical oscillator with an attached damped pendulum, around the principal resonance region, are investigated in this paper. Approximate analytical solutions of the model are determined on the basis of the Harmonic Balance Method (HBM). Correctness of the analytical results is verified by numerical simulations and experimental tests performed on an especially prepared experimental rig. The influence of all essential parameters such as damping, excitation amplitude and frequency, nonlinear stiffness of the spring, on the localisation of the instability region and the system dynamics is presented in the work. Regions of regular system oscillations, chaotic motions, and full rotation of the pendulum are confirmed experimentally.     

磁力摆相位锁定机制的实验研究

周期驱动下的磁力摆在一定条件下可以实现与驱动信号的相位锁定,从而产生稳定的等幅振动.本文测量了磁力摆相位锁定建立的暂态过程以及相位锁定点与控制参数的关系.基于单摆的非线性以及磁场驱动力与相位差的定性依赖关系,所有实验结果都可以得到很好的解释.     

Chen系统的非共振参数控制

本文利用非共振参数策动实现对Chen系统的非反馈方式混沌控制.使用远大于系统平均频率的周期信号作为控制输入,将控制系统中的系统变量分解为按系统平均频率变化的慢变量和按外加控制信号频率变化的快变量,然后利用平均法对控制系统进行处理得到慢变系统;根据慢变系统的动力学性质,得出所用控制参数应满足的条件.数值仿真结果表明此方法可以使控制系统迅速达到目标状态,并且在控制信号受到噪声干扰时,在一定信噪比范围内仍能对系统进行有效的控制,证明了该方法的可行性. 关键词： 平均法 Chen系统 混沌控制     

Experimental observation of four-photon entanglement from parametric down-conversion

We observe polarization entanglement between four photons produced from a single down-conversion source. The nonclassical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well suited for implementing advanced quantum communication schemes such as multiparty quantum key distribution, secret sharing, and telecloning.     

Experimental observation of parametric excitation in Tonks-Dattner resonances

It is shown that in a certain range of the h. f. power, the h. f. (T-D resonances) and the l. f. (ion sound wave and its harmonics) oscillations are parametrically excited in a certain region of the hysteresis loop.     

Experimental study of parametric autoresonance in Faraday waves

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.     

Windows95环境中转速测量和直流电机转速控制方法

介绍在Windows95环境中用Visual Basic5.0编写转速测量和直流电机转速控制方法的过程。     

单频外激励弹簧摆的鞍结分岔控制

对弹簧摆的振动幅值控制进行研究,设计了反馈控制器,对弱非线性系统用近似解析方法求出了控制系统的幅值控制方程,得到了控制参数与幅值的函数关系,使多自由度非线性系统的鞍结分岔得到控制.这项工作可以推广到其他多自由度非线性系统的分岔控制. 关键词： 外激励弹簧摆 鞍结分岔 振动幅值 反馈控制     

Optimal analytical and numerical approximations to the (un)forced (un)damped parametric pendulum oscillator

The (un)forced (un)damped parametric pendulum oscillator (PPO) is analyzed analytically and numerically using some simple, effective, and more accurate techniques. In the first technique, the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions. In the second approach, some approximations to (un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method. In the third approach, He's frequency-amplitude principle is applied for deriving some approximations to the (un)damped PPO. In the forth approach, He's homotopy technique is employed for analyzing the forced (un)damped PPO numerically. In the fifth approach, the p-solution Method, which is constructed based on Krylov–Bogoliúbov Mitropolsky method, is introduced for deriving an approximation to the forced damped PPO. In the final approach, the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically. All proposed techniques are compared to the fourth-order Runge–Kutta (RK4) numerical solution. Moreover, the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations. The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science, e.g. waves and oscillations in plasma physics.