线性时滞反馈引起的周期性振动共振分析

研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应. 关键词： 双稳系统 Duffing 系统 线性时滞反馈 振动共振     

时滞位置反馈对一类非线性相对转动系统混沌运动和安全盆侵蚀的控制

本文以一类典型的相对转动振动系统为研究对象,研究激励引起的系统混沌运动和安全域侵蚀,并对系统施加时滞位置反馈来抑制这两类复杂动力学行为.首先,利用Melnikov函数法获得相对转动系统的混沌运动及安全盆侵蚀的激励振幅阈值;其次,通过讨论时滞反馈系统的Hopf分岔条件获得适用于Melnikov函数法的控制参数取值范围,进而利用Melnikov函数法获得时滞受控系统的全局分岔必要条件;最后,利用四阶Rung-Kutta法和点映射法数值模拟了时滞受控系统动力学行为随参数的演变,从而验证解析结果的有效性.研究发现:在正的增益系数和较短的时滞量下,时滞位置反馈能够有效抑制相对转动系统的混沌运动和安全盆侵蚀现象.     

一类具有随机时变通信时滞的遥操作系统同步控制

针对无人机地面遥操作中存在的通信延时、丢包等实际情况,研究了一类具有随机时变通信时滞的遥操作系统的同步控制问题.建立了这种具有通信时滞的主、从遥操作系统的控制模型;采用基于Markov跳变模态参数的时变时滞函数来刻画遥控通信网络中的时滞,在随机系统框架下,通过均方意义下的稳定性分析,求解系统的同步控制问题.利用一个微小型四旋翼无人飞行器半物理仿真平台对本文方法进行验证,初步仿真结果表明,通过反馈线性化分别设计控制器,可以保证主、从端运动轨迹的有界性.     

一类非自治位置时滞反馈控制系统的亚谐共振响应

研究了弹性轨道条件下，控制回路中位置反馈信号存在时滞的磁浮系统在亚谐轨道激励作用下的响应问题. 将动力学模型在平衡点处线性化，以时滞为分岔参数，得到了系统出现Hopf分岔的条件. 用中心流形约化方法得到了包含轨道扰动系统的Poincaré规范型. 用多尺度法从理论上推导了时滞磁浮系统的亚谐共振周期解，得到了自由振动的分岔响应方程，分析了周期解中自由振动项的存在条件，研究了控制参数和激励参数与周期解的关系. 最后用数值仿真的方法分析了时滞参数、控制参数对系统响应的影响，分析结果指出，使系统保持稳定的亚谐响应的时滞边界小于无扰动时的时滞边界，时滞参数不但可以抑制亚谐响应，还能够控制混沌的产生，而控制参数可以控制系统响应中自由振动项的出现和受迫振动的幅值，适当选择这些参数可以有效抑制亚谐振动响应. 关键词： 亚谐共振响应 位置时滞反馈控制 非自治磁浮系统 分岔     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

时滞位移反馈对Helmholtz振子系统的分形侵蚀安全域的控制

对一个Helmoholtz振子系统引入线性时滞位移反馈,研究时滞位移反馈对系统的安全盆侵蚀的控制作用.将Melnikov函数法推广到时滞系统,从而给出时滞受控系统的安全盆的边界分形条件,在此基础上得出了安全盆分形的激励振幅阈值.再以时滞量为变参数,运用四阶Rung-Kutta方法和点映射方法从定量上研究了时滞对受控系统安全盆的影响规律.结果表明在弱反馈下,时滞量的增大能够提高安全盆边界分形的阈值,进而有效地抑制安全盆的分形侵蚀.说明时滞位移反馈是控制系统的安全盆侵蚀的良好方法. 关键词： 安全盆 分形侵蚀 时滞 反馈     

分数阶时滞反馈对Duffing振子动力学特性的影响

研究了含分数阶时滞耦合反馈的Duffing自治系统, 通过平均法得到了系统周期解的一阶近似解析形式, 定义了以反馈系数、分数阶阶次、时滞参数表示的等效刚度和等效阻尼系数, 发现分数阶时滞耦合反馈同时具有速度时滞反馈和位移时滞反馈的作用. 比较了三种参数条件下近似解析解与数值积分的结果, 二者的吻合精度都很高, 证明了近似解析解的正确性和准确性. 分析了反馈系数、分数阶阶次和非线性刚度系数等参数对系统分岔点、周期解稳定性、周期解的存在范围、零解的稳定性以及稳定性切换次数等系统动力学特性的影响.     

受迫Holmes-Duffing系统安全域分形及时滞速度反馈控制

以受迫Holmes-Duffing系统为研究对象, 对系统施加时滞速度反馈控制, 研究周期激励引起的系统安全域的分形侵蚀及时滞速度反馈对分形侵蚀安全盆的控制作用. 利用Melnikov函数法给出时滞受控系统的安全盆的边界分形条件. 再以时滞量为变参数, 运用四阶Runge-Kutta方法和点映射方法数值研究了时滞对受控系统安全盆的影响规律. 结果表明在弱反馈下, 时滞量的增大能够提高安全盆边界分形的阈值, 从而抑制安全盆的分形侵蚀. 说明时滞速度反馈能够有效抑制系统的安全盆侵蚀.     

有界噪声激励下带有时滞反馈的随机Mathieu-Duffing系统的响应

研究了参数激励下带有时滞反馈的随机Mathieu-Duffing方程的主参数共振响应问题.运用多尺度方法分离了系统的快慢变量.分析了系统的分岔性质,发现调谐参数、时滞、时滞项的系数以及非线性项的强度等都可以影响系统的分岔行为,适当选择这些参数可以改变系统的分岔响应.同时,还讨论了非零解的稳定性,得到了非零解稳定的充要条件,而且发现在随机激励的带宽较小时,系统的多解现象仍然存在,分岔和跳跃现象仍会发生,数值模拟验证了理论推导的有效性. 关键词： 随机Mathieu-Duffing系统 多尺度 稳定性 分岔     

Genesio混沌系统的线性反馈控制实验

构建了Genesio混沌系统的硬件实现电路,采用线性反馈对该系统进行控制,根据Hurwitz稳定性判据,得到将系统控制到稳定状态的反馈增益的取值范围.通过硬件电路实验对理论分析进行验证,结果表明线性反馈可以将Genesio混沌系统有效地控制到不动点和稳定的周期态.     

循环平稳声场的声源定位研究

旋转机械产生的辐射声场具有循环平稳特性,传统的平面近场声全息技术无法准确反映其调制特性,往往在边频带上出现虚假的能量的分布. 采用循环谱密度取代功率谱密度作为重建物理量,则可准确提取循环平稳声场的调制和载波信息. 考虑到循环谱密度的计算量以及特征提取的准确性,提出了循环谱密度组合切片分析法,并分析了加性白噪声对重建的影响. 仿真分析及实验结果表明,此方法有较强的噪声抑制能力,全息重建的结果可准确反映声源的位置. 关键词： 循环平稳声场 近场声全息 噪声源定位     

Vibration control by recursive time-delayed acceleration feedback

This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.     

基于延时光电反馈控制两段式半导体激光器的双稳及自脉动特性

提出一种将延时光电反馈引入两段式双稳半导体激光器（TBLD）的吸收区，从而达到控制其双稳及自脉动特性的方案.利用速率方程模型，分析了反馈增益及延迟时间对TBLD双稳及不稳定特性的控制作用.数值模拟的结果表明：TBLD的稳定区域随延迟时间呈周期性变化；双稳区域随延迟时间的增大而变窄；在一定的取值范围内，增大延迟时间有利于增强双稳的稳定性；负反馈更容易出现不稳定性. 关键词： 两段式双稳半导体激光器 动态双稳 自脉动 延时光电反馈     

Transverse and torsional complex vibration systems for ultrasonic seam welding of metal plates

Transverse and torsional complex vibration systems for ultrasonic seam welding of metal plate specimens, using a 27 kHz complex vibration disk welding tip vibrating in transverse and torsional vibration modes, were studied. Using a complex vibration welding system with a welding tip vibrating in elliptical or circular locus, thick plate specimens can be welded with a more uniform and larger area compared to a conventional ultrasonic welding system. The disk welding tip vibrates in an elliptical or circular locus. The complex vibration system can continuously weld multiple parts of metal plate specimens such as heat sinks with a large number of fins.     

Vibration amplitude control for a van der Pol–Duffing oscillator with time delay

Periodic solutions for the fundamental resonance response of a van der Pol–Duffing system under time-delayed position and velocity feedbacks are investigated. Using the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the fundamental resonance response are derived. Their fixed points correspond to limit cycles (phase-locked periodic solutions) for the original system. In the uncontrolled system, periodic solutions exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical requirements. It is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude can be accomplished. Therefore, the results obtained show that an effective vibration amplitude control is possible if appropriate time delay and feedback gains are chosen.     

Nonlinear analysis,design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

This paper combines cubic nonlinearity and time delay to improve the performance of vibration isolation. Nonlinear dynamics properties, design methodology and isolation performance are studied for a piecewise bilinear vibration isolation system with the time-delayed cubic velocity feedback control. By the multi-scale perturbation method, the equivalent stiffness and damping are first defined to interpret the effect of feedback control loop on dynamics behaviours, such as frequency island phenomenon. Then, a design criterion is proposed to suppress the jump phenomenon induced by the saddle-node bifurcation. With the purpose of obtaining the desirable vibration isolation performance, stability conditions are obtained to find appropriate feedback parameters including gain and time delay. Last, the influence of the feedback parameters on vibration transmissibility is assessed. Results show that the strategy developed in this paper is practicable and feedback parameters are significant factors to alter dynamics behaviours, and more importantly, to improve the isolation effectiveness for the bilinear isolation system.     

Suppression of dynamic instabilities in erbium-doped fiber amplifiers with a combined gain control system

We report an improved transient response of an Er(3+) -doped fiber-optic amplifier with combined electronic feedforward (EFF) and optical feedback (OFB) control systems. We find, theoretically and experimentally, that the time delay of an EFF response leads to control instabilities in the form of erbium-doped fiber amplifier gain auto-oscillations, which can be suppressed by an appropriate choice of OFB wavelength and control system design.     

Novel design for bifurcation control in a delayed fractional dual congestion model

This letter puts forward an ingenious feedback control method with parametric delay to manipulate bifurcation control for a delayed fractional dual congestion model. By employing time delay as a bifurcation parameter, the local dynamics involving stability and Hopf bifurcation is examined. The control efforts can be realized with or without time delay in the strength of feedback control. It suggests that the stability performance is consumedly elevated by exploiting the parametric delay feedback controller, yet Hopf bifurcation engenders ahead of time in the event of the absence of the controller. Moreover, the impact of the order or linear feedback gain on the bifurcation point is numerically discussed via aborative calculation. Numerical simulations are eventually actualized to corroborate the proposed scheme.