时变切换时滞反馈镇定混沌系统不稳定周期轨线

为提高经典时滞反馈控制镇定不稳定周期轨线的效果, 扩大受控周期轨线的稳定区域, 本文基于时变切换策略对经典时滞反馈控制进行改进, 提出了时变切换时滞反馈控制. 时变切换时滞反馈控制的控制信号仅在特定的时段中存在, 而在其他时段上不存在控制信号, 这与经典时滞反馈控制中具有固定的控制信号是不同的. 通过实例分析, 研究了时变切换时滞反馈控制在镇定不稳定周期轨线中的具体性能. 以反馈增益系数为变量, 计算受控周期轨线的最大条件Lyapunov指数, 得到了受控周期轨线的稳定区域随切换频率变化的关系曲线. 结果表明, 随着切换频率增大, 受控周期轨线的稳定区域呈现非平滑地变化. 当选取恰当的切换频率时, 时变切换时滞反馈控制的稳定区域显著大于经典时滞反馈控制的稳定区域. 在混沌控制的工程实践中, 控制信号常常受到一定的限制. 要实现对目标周期轨线的稳定控制, 就需要受控周期轨线具有足够大的稳定区域. 因此, 与经典时滞反馈控制相比, 本文提出的时变切换时滞反馈控制具有更广泛的应用前景.      

基于非线性谐振电路的双稳态俘能器的俘能与动力学特性研究

双稳态俘能器可实现宽频和高效的俘能效果.目前的研究主要在双稳态结构中接入单一电阻电路进行俘能.本文将非线性RLC (电阻-电感-电容)谐振电路引入到三弹簧式双稳态结构中,构建两自由度非线性系统,以实现俘能特性的提升.设计永磁体与线圈的构型,获得了非线性机电耦合系数.推导并得到了两自由度非线性俘能器的控制方程.利用谐波平衡法推导得到了系统的电流与位移的频率响应关系.基于雅可比矩阵对解的稳定性进行了判别.将解析解与数值解进行了对比验证.结果表明,在双稳态俘能器中引入非线性二阶谐振电路不仅有利于低频俘能,还可进一步提升俘能响应,拓宽俘能带宽.相同的电路参数下,与线性电路相比非线性电路可通过电流的倍频现象实现结构更低频率的能量俘获.减小谐振电路与双稳态结构共振频率之比,增加基础激励幅值,减小静平衡点之间的距离均可提升俘能器的俘能效果.通过调控谐振电路与双稳态共振频率之比和基础激励幅值等参数,可实现系统单倍周期响应、多倍周期响应及混沌响应之间的切换.     

Bistable buckled beam and force actuation: Experimental validations

This paper presents recent experimental results on the switching of a simply supported buckled beam. Moreover, the present work is focussed on the experimental validation of a switching mechanism of a bistable beam presented in details in Camescasse et al. (2013). An actuating force is applied perpendicularly to the beam axis. Particular attention is paid to the influence of the force position on the beam on the switching scenario. The experimental set-up is described and special care is devoted to the procedure of experimental tests highlighting the main difficulties and how these difficulties have been overcome. Two situations are examined: (i) a beam subject to mid-span actuation and (ii) off-center actuation. The bistable beam responses to the loading are experimentally determined for the buckling force and actuating force as a function of the vertical position of the applied force (displacement control). A series of photos demonstrates the scenarios for both situations and the bifurcation between buckling modes are clearly shown, as well. The influence of the application point of the force on the bifurcation force is experimentally studied which leads to a minimum for the bifurcation actuating force. All the results extracted from experimental tests are compared to those coming from the modeling investigation presented in a previous work (Camescasse et al., 2013) which ascertains the proposed model for a bistable beam.     

Numerical study of vortex interactions behind two circular cylinders in bistable flow regime

A two-dimensional discrete-vortex model was used to investigate vortex interaction inside the near wakes of two circular cylinders in side-by-side arrangement within bistable flow regime. Two phases of vortex evolution are mainly identified in the near wakes: a symmetric shedding phase, characterized by two antiphase vortex streets, and a flip-flopping phase, characterized by biased gap flow, switching at irregular intervals. For the flip-flopping phase, vortex amalgamation, vortex pairing and dipole are found. Vortex dynamics of the flow is presented and its possible effects on the flow parameters are discussed. The initiation and transition from the symmetric to flip-flopping phase are caused by the asymmetry of one of the gap vortices. Flow visualization and quantitative results obtained seem to support the findings from the model.     

转子系统振动变参控制中的瞬态响应

本文以可变参数的挤压油膜阻尼器作为控制元件，研究了转子在稳态转速及加速运动过程中进行变参控制时的瞬态响应问题。结果说明了对转子系统的振动进行分段变参控制，无论是在稳态还是在加速运动过程中，一般都可以取得满意的控制效果，不仅可以减小转子系统的振动，而且还可以使转子系统平稳地通过具有较大振动的共振区，但变参位置不应在多值转速区内。     

Global stabilization of periodic orbits using a proportional feedback control with pulses

We investigate the stabilization of periodic orbits of one-dimensional discrete maps by using a proportional feedback method applied in the form of pulses. We determine a range of the parameter μ values representing the strength of the feedback for which all positive solutions of the controlled equation converge to a periodic orbit.     

Stability and Hopf bifurcations of an optoelectronic time-delay feedback system

The local dynamics around the trivial solution of an optoelectronic time-delay feedback system is investigated in the paper, and the effect of the feedback strength on the stability is addressed. The linear stability analysis shows that as the feedback strength varies, the system undergoes exactly two times of stability switch from a stable status to an unstable status or vice versa, and at each of the two end points of the stable interval, a Hopf bifurcation occurs. To gain insight of the bifurcated periodic solution, the Lindstedt–Poincaré method that involves easy computation, rather than the center manifold reduction that involves a great deal of tedious computation as done in the literature, is used to calculate the bifurcated periodic solution, and to determine the direction of the bifurcation. Two case studies are made to demonstrate the efficiency of the method.     

Effect of delay combinations on stability and Hopf bifurcation of an oscillator with acceleration-derivative feedback

This paper presents new observations of delayed AD (acceleration-derivative) controller in active vibration control and in bifurcation control of a Duffing oscillator. Based on the stability analysis of the linear delayed oscillator, it is found that combination of the two delays in acceleration feedback and velocity feedback has a significant influence on the stable region in the parameter plane of the gains. By calculating the real part of the rightmost characteristic roots of the controlled oscillator with fixed delays, it is shown that a delayed acceleration feedback with positive gain can work much better than the corresponding delayed negative acceleration feedback, which is used in classic control theory. For given feedback gains, by calculating the critical delay values, it is shown that a delayed positive acceleration feedback can result in a much larger stable delay interval than the corresponding delayed negative acceleration feedback does. As an application of these results to a delayed Duffing oscillator with acceleration-derivative feedback, a delayed positive acceleration feedback can be well used to postpone the occurrence of Hopf bifurcation in the delayed nonlinear oscillators.     

负反馈诱发神经电振荡的反常现象的复杂动力学

传统观念认为,负反馈容易使系统达到稳定平衡点而正反馈容易引起振荡.本研究基于神经元理论模型,提出了负反馈可以诱发稳定平衡点、也就是静息、变为振荡、也就是放电的新观点.在Hopf分岔点附近,作用在静息上的一次足够大的负向脉冲电流的抑制性刺激,能够引起一个动作电位及随后的衰减振荡的后电位;而能够在后电位上诱发出动作电位的负脉冲电流强度阈值也是衰减振荡的.在模型中,引入具有时滞($\tau$)的负反馈来模拟抑制性自突触,一个动作电位诱发的负反馈自突触电流会作用到比动作电位延迟$\tau$的后电位上.随时滞增加,能够诱发出放电的负反馈增益强度阈值呈现出具有衰减振荡特点的类似多重相干共振的特性,衰减振荡的周期与电流阈值曲线的周期以及分岔点附近的放电周期相关.另外,负反馈还能诱发出放电与静息共存的复杂行为.本研究的结果不仅揭示了负反馈的新的反常调控作用,还有助于理解在现实神经系统中存在的慢抑制性自突触的潜在功能.      

On the aerodynamic characteristics of inclined stay cable sheaths in the critical flow regime

This paper studies the presence of the bistable flow activity around inclined cable models. It presents results from wind tunnel test on static original High-Density Polyethylene cable covers in a range of Reynolds numbers from the subcritical to the critical regime, inclined at angles of 90°(vertical), 60°and 45°. It has already been shown that, in the critical regime, turbulent transition in the boundary layers around a circular cylinder exhibits bistable behavior at zero inclination, i.e. the boundary layer on either side is intermittently turbulent or laminar, leading to intermittent asymmetry of the flow and resulting aerodynamic loads. The present wind tunnel tests consist in measuring the pressure patterns around inclined circular cylinders using numerous pressure taps. Bifurcation diagrams are created in order to quantify the occurrence of bistability and Proper Orthogonal Decomposition is used to identify the geometrical flow modes that are governed by the bistability. The results show that the bistable phenomenon is only identified in the Reynolds number range corresponding to the first transition between the TrBL0 and TrBL1 regimes. Furthermore, the inclination angle seems to have a significant impact on the energy of the flow mode related to unsteady asymmetric reattachment. This paper also treats the potential sensitivity of the aerodynamic drag and lift forces to the circularity defect of the covers and presents the positive impact of the helical fillet on controlling the bistable activity at a critical inclination angle of 60°.     

时滞状态正反馈在振动控制中的新特征

控制理论中广泛采用负反馈,而正反馈的应用不多, 一个重要原因是正反馈将系统的变化放大而使系统的稳定性变差. 如果反馈环节具有时滞, 那么正反馈未必使系统稳定性变差. 本文以线性振动系统为例, 采用稳定性切换方法和利用确定时滞系统稳定性的最大实部特征根, 详细研究了时滞状态正反馈在镇定系统不稳定运动和改善系统稳定性方面的作用. 我们发现,时滞位移正反馈明显优于时滞位移负反馈, 表现为: (1). 正反馈控制可以用较小的时滞去镇定不稳定运动和改善系统稳定性; (2). 正反馈控制可容许的时滞范围很大, 而负反馈控制的可容许时滞范围很小; (3). 正反馈对应的闭环系统的最大实部特征根的实部的极小值可显著小于负反馈对应的闭环系统的最大实部特征根的实部的极小值, 因而在相同的初始条件下, 正反馈作用下的闭环系统比之负反馈作用下的闭环系统可以更快地稳定到平衡点. 我们还发现, 对时滞速度反馈与时滞加速度反馈来说, 负反馈优于正反馈; 而对相同的反馈增益, 时滞位移正反馈优于时滞速度正反馈和时滞加速度正反馈. 关键字镇定,振动控制,时滞正反馈, 稳定性切换, 特征根      

ew Features of Positive Time-Delayed Feedbacks in Vibration Control

控制理论中广泛采用负反馈,而正反馈的应用不多, 一个重要原因是正反馈将系统的变化放大而使系统的稳定性变差. 如果反馈环节具有时滞, 那么正反馈未必使系统稳定性变差. 本文以线性振动系统为例, 采用稳定性切换方法和利用确定时滞系统稳定性的最大实部特征根, 详细研究了时滞状态正反馈在镇定系统不稳定运动和改善系统稳定性方面的作用. 我们发现,时滞位移正反馈明显优于时滞位移负反馈, 表现为: (1). 正反馈控制可以用较小的时滞去镇定不稳定运动和改善系统稳定性; (2). 正反馈控制可容许的时滞范围很大, 而负反馈控制的可容许时滞范围很小; (3). 正反馈对应的闭环系统的最大实部特征根的实部的极小值可显著小于负反馈对应的闭环系统的最大实部特征根的实部的极小值, 因而在相同的初始条件下, 正反馈作用下的闭环系统比之负反馈作用下的闭环系统可以更快地稳定到平衡点. 我们还发现, 对时滞速度反馈与时滞加速度反馈来说, 负反馈优于正反馈; 而对相同的反馈增益, 时滞位移正反馈优于时滞速度正反馈和时滞加速度正反馈. 关键字镇定,振动控制,时滞正反馈, 稳定性切换, 特征根     

{L}_{2}-gain analysis and output feedback control for continuous-time switched systems with actuator saturation

This paper is concerned with the problem of \(L_2\) -gain analysis for a class of continuous-time switched systems with actuator saturation. Different from the existing results using the state-dependent switching approach, a linear parameter-varying output feedback controller with the time-dependent switching mechanism is designed such that the overall system is exponentially stable and with disturbance tolerance capacity and \(L_2\) gain. Further, the proposed controller is insured by introducing the slack matrices to have less conservatism, which maximizes the ellipsoid where the state trajectories starting from the origin will remain. Sufficient conditions for the existence of the switching and output feedback control law are derived in terms of linear matrix inequalities. Finally, a practical example is given to show the effectiveness of the proposed method.     

Chimera states in ensembles of bistable elements with regular and chaotic dynamics

We consider ensembles of bistable elements with nonlocal interaction. It is shown that the bistability of units in the case of nonlocal interaction leads to the formation of chimera structures of a special type, which we have called double-well chimeras. Their distinctive feature consists in the formation of incoherence clusters with an irregular distribution of elements between two attractive sets existing in an individual element (two “potential wells”). Ensembles of different bistable units are considered, namely ensembles of cubic maps, FitzHugh–Nagumo oscillators in the regime of two stable equilibrium points and Chua’s circuits. The spatiotemporal behavior of the ensembles is studied in the cases of regular and chaotic dynamics in time, and different types of chimera structures are revealed.     

Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping

A strategy is proposed to solve the fixed final state optimalcontrol problem using the simple cell mapping method. A non-uniform timestep simple cell mapping is developed to create a general database fromwhich solutions of various optimal control problems can be obtained. Atwo-stage backward search algorithm is proposed to eliminate degeneratedpaths often associated with the simple cell mapping. The proposed methodcan accurately delineate the switching curves and eliminate false limitcycles in the solution. The method is applied to two optimal controlproblems with bang-bang control. The well-known minimum time controlproblem of moving a point mass from any initial condition to the originof the phase plane is studied first. This example has exact solutionsavailable which provide a yardstick to examine the accuracy of themethod. The cell size dependence of the solution accuracy is studiednumerically. The second example is a variable stiffness feedback controlproblem with tuning range saturation. The strategy proposed is able toprovide the switching curves in the phase plane. This result has notbeen obtained before.     

Limit cycles,tori, and complex dynamics in a second-order differential equation with delayed negative feedback

We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined.     

Uniqueness of the Bistable Traveling Wave for Mutualist Species

For a system of reaction–diffusion equations that models the interaction of n mutualist species, the existence of the bistable traveling wave solution has been proved where the nonlinear reaction terms possess a certain type of monotonicity. However the problem of whether there can be two distinct traveling waves remains open. In this paper we use a homotopy approach incorporated with the Liapunov–Schmidt method to show that the bistable traveling wave solution is unique. Our method developed in this paper can also be applied to study the existence and uniqueness of traveling wave solutions for some competition models.     

非均匀铁弹畴变对离面极化压电陶瓷应力强度因子的影响研究

基于文献中报道的试验结果，本文考虑非均匀的畴变过程区，它包含一个位于中心的饱和区和环绕饱和区的渐变区．为了描述外加应力引起的部分铁弹畴变，本文采用一个显式的基于最小能量原理的非均匀畴变准则．考虑离面极化的压电陶瓷，假设其初始极化矢量平行于离面方向．畴变后的电畴位于面内，具体方位由最大释放功来确定．基于非均匀畴变准则，本文给出了裂尖处非均匀畴变区几何及畴变体积分数的分布．并在静止裂纹和稳态扩展裂纹两种特殊情况下计算了铁弹畴变对裂尖处应力强度因子的影响．结果表明：(1) 静止裂纹尖端处的畴变减小了材料的起裂强度；(2) 准静态稳态裂纹附近的畴变增加了材料的断裂强度．且理论预测的R曲线渐近值与试验结果定量吻合．     

Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics

In this paper, a general form for multi-axial constitutive laws for ferroelectric ceramics is constructed. The foundation of the theory is an assumed form for the Helmholtz free energy of the material. Switching surfaces and associated flow rules are postulated in a modified stress and electric field space such that a positive dissipation rate during switching is guaranteed. The resulting tangent moduli relating increments of stress and electric field to increments of strain and electric displacement are symmetric since changes in the linear elastic, dielectric and piezoelectric properties of the material are included in the switching surface. Finally, parameters of the model are determined for two uncoupled cases, namely non-remanent straining ferroelectrics and purely ferroelastic switching, and then for the fully coupled ferroelectric case.     

Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise

Stochastic resonance in an underdamped bistable system subjected to a weak asymmetric dichotomous noise is investigated numerically. Dichotomous noise is a non-Gaussian color noise and more complex than Gaussian white noise, whose waiting time complies with the exponential distribution. Utilizing an efficiently numerical algorithm, we acquire the asymmetric dichotomous noise accurately. Then the system responses and the averaged power spectrum as the signatures of the stochastic resonance are calculated by the fourth-order Runge?CKutta algorithm. The effects of the noise strength, the forcing frequency, and the asymmetry of dichotomous noise on the system responses and the effects of the forcing frequency on the averaged power spectrum are discussed, respectively. It is found that the increasing of the noise strength or the forcing frequency could strengthen the passage between the stable points of the system, and the system responses also display the asymmetry for the asymmetric dichotomous noise, which has not been discovered in other investigated results. Additionally, the averaged power spectrum exhibits the sharp peaks, which indicates the occurrence of stochastic resonance, and we also discover two critical forcing frequencies: one denoting the transformation of the peaks and another for the optimum on stochastic resonance.