用非线性反馈函数法研究蔡电子线路的混沌同步

应用非线性控制的基本思想及李雅普诺夫函数方法，将解析与数值法相结合对著名的蔡电子线路，找到了一些非线性反馈函数并实现了混沌同步。该方法具有同步时间短、适应性较广，对某些非线性系统较为简便、有效等优点。     

超混沌同步的非线性控制法

用李雅普诺夫函数法与尝试法相结合的方法，构造了１组典型的非线性反馈函数，实现了２个超混沌Ｒｏｓｓｌｅｒ系统的同步。     

Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions

In this paper the nonlinear feedback functional method is presented for study of synchronization of spatiotemporal chaos in coupled map lattices with five connection forms.Some of nonlinear feedback functions are given.The noise effect on synchronization and sporadic nonlinear feedback are discussed.     

Chua电路混沌系统的同步分析

Chua电路是混沌系统中倍受人关注,具有广阔应用前景的混沌电路,如何同步混沌系统是应用的前提条件,用三种方法分析了Chua电路混沌系统的同步问题,为在电路上实现Chua电路混沌系统的同步提供了理论基础和技术指导。     

用FIR滤波器—PPSV实现混沌和超混沌控制

利用数字ＦＩＲ滤波器和正比于系统变量的脉冲反馈法的级联控制非线性连续系统中的混沌和超混沌。以实数Ｌｏｒｅｎｚ系统和复数洛仑兹－哈肯系统为例进行了数值研究。结果表明：ＦＲＩ－ＰＰＳＶ级联控制法比仅用ＦＩＲ滤波法或ＰＰＳＶ法更能有效地控制非线性连续系统中的混沌和超混沌,且抗噪性能ＰＰＳＶ法有显著提高。     

Laser-RF synchronization based on digital phase detector

Laser oscillator synchronization with RF reference signal is ultra-important for a modem light source based on the accelerator.For Tsinghua Thomson scattering X-ray source,we have synchronized the mode-locked laser oscillator to RF reference signal with 48.2 fs RMS relative jitter.Both fundamental and harmonic signals derived from photo diode detection are used for laser-RF synchronization in our scheme.The fundamental signal is for coarse laser-RF synchronization and multiple laser oscillator synchronization.The harmonic signal is for high precise phase locking.The digital phase detector is implemented in the synchronization scheme for less noise,replacing the mixing to DC phase detection scheme.The digital processing algorithm for synchronization is commonly used in low-level RF control field.In order to test the phase locking loop logic without damaging the real laser oscillator,a laser oscillator emulator was developed for phase locking.This paper will report the laser-RF synchronization scheme and its performance.The laser oscillator emulator system will also be introduced here.     

Stability analysis and nonlinear dynamics of natural circulation boiling water reactors

Numerous experimental and numerical investigations have been reported in literature on the effect of various parameters on the dynamics of natural circulation boiling water reactors (NCBWRs). Different findings were reported in literature regarding the effect of void reactivity coefficient and fuel time constant on Type-I and Type-II instabilities. The present work contains stability analysis and nonlinear dynamics of NCBWR using a lumped parameter model. The purpose of the stability analysis is to resolve different, seemingly contradictory parametric trends reported by previous authors. Stability analysis for three different system configurations has been done using the same mathematical model and compared with the findings reported in literature. It has been observed that the effects of void reactivity coefficient and fuel time constant are influenced by geometrical parameters and are different for different systems. Nonlinear dynamics and bifurcations have been studied numerically, for one of the system configurations, for boiling channels with and without riser. The possibility of existence of stable and unstable limit cycles, period doublings, and chaotic oscillations has been investigated. The effect of void reactivity coefficient on the nonlinear dynamics has been studied in both Type-I and Type-II regions. In the Type-I region, subcritical Hopf bifurcation leading to unstable limit cycle, as well as supercritical Hopf bifurcation leading to stable limit cycle have been found. The boiling channels with and without riser have been observed to undergo chaotic oscillations under strong reactivity feedback in the Type-II region. It has been found that the presence of riser aggravates chaotic oscillations.     

Dynamic analysis of multiple nuclear-coupled boiling channels based on a multi-point reactor model

This work investigates the non-linear dynamics and stabilities of a multiple nuclear-coupled boiling channel system based on a multi-point reactor model using the Galerkin nodal approximation method. The nodal approximation method for the multiple boiling channels developed by Lee and Pan [Lee, J.D., Pan, C., 1999. Dynamics of multiple parallel boiling channel systems with forced flows. Nucl. Eng. Des. 192, 31–44] is extended to address the two-phase flow dynamics in the present study. The multi-point reactor model, modified from Uehiro et al. [Uehiro, M., Rao, Y.F., Fukuda, K., 1996. Linear stability analysis on instabilities of in-phase and out-of-phase modes in boiling water reactors. J. Nucl. Sci. Technol. 33, 628–635], is employed to study a multiple-channel system with unequal steady-state neutron density distribution. Stability maps, non-linear dynamics and effects of major parameters on the multiple nuclear-coupled boiling channel system subject to a constant total flow rate are examined. This study finds that the void-reactivity feedback and neutron interactions among subcores are coupled and their competing effects may influence the system stability under different operating conditions. For those cases with strong neutron interaction conditions, by strengthening the void-reactivity feedback, the nuclear-coupled effect on the non-linear dynamics may induce two unstable oscillation modes, the supercritical Hopf bifurcation and the subcritical Hopf bifurcation. Moreover, for those cases with weak neutron interactions, by quadrupling the void-reactivity feedback coefficient, period-doubling and complex chaotic oscillations may appear in a three-channel system under some specific operating conditions. A unique type of complex chaotic attractor may evolve from the Rossler attractor because of the coupled channel-to-channel thermal-hydraulic and subcore-to-subcore neutron interactions. Such a complex chaotic attractor has the imbedding dimension of 5 and the fractal dimension ranging from 1.26 to 1.35.     

Nonlinear analysis for a nuclear-coupled two-phase natural circulation loop

The objective of this paper is to develop a nonlinear numerical model to investigate the stability and nonlinear dynamics of a nuclear-coupled two-phase natural circulation loop. Some stability maps, parametric effects and transient characteristics of this natural circulation loop have been studied. Results indicate that the system indeed has two instability regions, the type-I and type-II instabilities, as is well known for a natural circulation loop. Parameters may induce different effects on the system stability in type-I and type-II unstable regions. In particular, the void-reactivity feedback destabilizes the system in both regions of low and high operating powers. Moreover, by strengthening nuclear feedback effect, period-doubled bifurcation may prevail in the system at relatively high inlet subcoolings and eventually a chaotic attractor appears with a fractal dimension of 1.79 ± 0.01 and an embedding dimension of 5.     

传热管在内外流体作用下的振动特性研究

为研究传热管在内外流体共同作用下的动力学行为,引入尾流振子模型,同时考虑轴向伸长引起的几何非线性的影响,建立了弹性管-内外流体耦合系统的分析模型,并利用Galerkin方法离散非线性耦合方程。基于数值计算,分析了内外流体流速、几何非线性参数对传热管振动响应的影响,得到了传热管在后屈曲时的分叉图、相图。结果显示,传热管在后屈曲时会表现出一系列丰富的动力学行为,如倒分叉、周期运动和混沌运动。     

摇摆条件下自然循环流动不稳定性非线性演化特性研究

针对摇摆运动下自然循环流动不稳定性的非线性演化特性进行了分析。应用非线性时间序列分析方法对不同流动状态的时间序列进行幅度谱分析、吸引子重构,并基于相空间重构理论,计算包括关联维数（CD）、Kolmogorov熵（K熵）和最大李雅普诺夫指数（MLE）在内的几何不变量的值,根据计算结果分析了摇摆运动下两相自然循环系统流动不稳定性的非线性演化特性。分析结果表明：随着无量纲功率的增大,系统几何不变量的值先增加后减小,系统由极限环运动经倍周期分岔发展成混沌振荡,最终回到稳定流动;系统非线性特征先增强后减弱,是由于热驱动力、流动阻力和摇摆引起的驱迫外力之间的相互反馈及耦合程度不同所致。     

Controlling Chaos of Semiconductor Laser Using Sliding Variable Structure Strategy

CHEL3300激光器首次尝试采用1套磁脉冲压缩快关控制的L-C反转电路实现3个独立的激光腔放电。通过调整磁脉冲压缩开关到各个放电腔电路的电感确保3个放电腔按照“天光一号”系统1次分束的要求以20ns的时间间隔依次放电。     

Gamma-Ray Energy of 4DK

Abstract

The stability of a power reactor with multiple transport lags and nonlinear characteristics embodied in the controller is analyzed by parameter plane method. The analysis covers two reactor models: (a) A rather simple model, symbolically representing the features of a nonlinear controller, one transport lag and the reactor with temperature feedback, and (b) A more realistic model depicting a practical chemical fine-control reactor system characterized by multiple transport lags and mixing effect associated with the chemical fluid, the nonlinear characteristics of chemical injection valves, and the spatial distribution of poison inside the reactor, as well as the reactor temperature feedback. These analyses yield much useful information about the stability of both systems, such as the conditions of reactor stability and of the occurrence of limit cycles, as well as the aspects of discontinuous change of the limit cycle frequency. Use of this parameter plane method will greatly simplify evaluation of the stability of even a fairly complex reactor control system that depends not only on the system parameters but also on the nonlinear controller characteristics and initial input signal amplitude.     

实现混沌同步的非线性变量反馈控制法

应用非线性变量反馈控制法，通过李雅普诺夫函数方法和尝试法，分别构造了一些非线性反馈函数，并用以实现了对Ｒｏｓｓｌｅｒ系统和改进的Ｌｏｒｅｎｚ系统的混沌同步。２种方法起着相互补充的作用。     

统一混沌系统的脉冲控制与同步

对统一混沌系统的脉冲控制稳定性与同步问题进行了理论分析，利用脉冲微分方程理论给出了脉冲控制稳定与同步的充分条件，并对脉冲控制时间间隔的范围作了估计。最后，通过仿真进行了验证。     

Impulsive Stabilization of Uncertain Dynamical Systems and Chaos Control

Chaos control and synchronization have received significant attention. Impulsive control is one of main methods among them and arises in a wide variety of applications except at chaotic systems, such as orbital transfer of satellites, ecosystems management and control of money supply in a financial market.     

Dynamics of multiple parallel boiling channel systems with forced flows

This work investigates the nonlinear dynamics of multiple parallel boiling channels with forced flows by using the Galerkin nodal approximation method. The stability maps for multiple-channel systems subject to a constant total mass flow rate are constructed on the basis of the average heat flux and mass flow rate on the parameter plane of the subcooling and phase change numbers. The limit cycle oscillations for 3-, 4- and 5-channel systems indicate that the most heated channel exhibits the largest magnitude of oscillation, and is out-of-phase with the other channels. Owing to that the boiling assembly contains only a small number of channels, the above system becomes unstable due to channel-to-channel interaction with an increase of the channel number. This work also elucidates the dynamics of a 3-channel system with a periodic total mass flow rate. In addition, complicated nonlinear oscillations are predicted for different operating points with high inlet subcooling numbers in the stable region. The system dynamics are highly sensitive to the frequency of the forcing function. Periodic, quasi-periodic and chaotic oscillations may appear in the forcing function system. Unstable oscillations appear when either the frequency of the forcing function is equal or extremely close to the system’s natural frequency or the two frequencies are frequency-locking.     

Methodology of Nuclear Reactor Monitoring and Diagnostics Using Information Dimension Application to Power Oscillation

Abstract

Reactor noise analysis method based on information dimension is applied to the monitoring and diagnosing of power oscillation. The method focuses on the utilization of the slope of the correlation integral (SOCI) which determines the information dimension of attractors. For practical application, the information dimension is expected to be the same as the fractal dimension of attractors; it can be used to classify different asymptotic regimes of nonlinear dynamical systems. We examined a real power oscillation using SOCI and the results implied that the oscillation was just a noisy limit cycle, although it is not possible to assert that there is no chaotic character in the oscillation because large oscillatory time-series data sets are not available. In addition, the application of SOCI to the real-time monitoring of power oscillation is proposed and examined.     

Conditions for the existence of chaotic oscillations in nuclear reactors

It is shown on the basis of point kinetics equations with delayed neutrons that if the impulse feedback function is negative, nonmonotonic, and possesses several maxima and the coefficient of amplification of feedback is sufficiently large, then chaotic self-excited oscillations of the following type arise in nuclear reactors. Neutron bursts with random intensity occur in random time interals in the reactor, and the neutron density between the bursts oscillates at a low level. The mechanism for the appearance of chaos is described and one-dimensional mappings which approximately determine the chaotic dynamics are constructed. Three types of reactors (boiling water, with gaseous core, pulsed) where such chaotic oscillations can arise are indicated. The results obtained point the way to determining other types of reactors with stochastic behavior. 4 figures, 10 references. This work is supported by a grant (No. 87 Gr-98) in fundamental studies in the field of power engineering and electronics (Ministry of Education, Moscow Power-Engineering Institute) “Chaotic dynamics of nuclear reactors” and a grant in fundamental studies in the field of automatics and telemechanics, computer technology, information technology, cybernetics, metrology, and communication (Ministry of Education, St. Petersburg State Electrical Engineering University) “Chaotic dynamics of nonlinear control systems.” Scientific-Research Institute of Mechanics at Nizhnii Novgorod State University. Translated from Atomnaya énergiya, Vol. 88, No. 6, pp. 432–438, June, 2000.     

Consideration on the coherence functions of at-power reactor noise

This paper is concerned with a basic study of the second order coherence functions in terms of at-power reactions noise. Significant properties arising in ordinary and partial coherence patterns, such as the effect of feedback, that of increase in the noise source intensity are investigated by means of simulation study which is based on the at-power model presented by Seifritz. Furthermore, numerical results from nonlinear model are compared with those from the linearized one.