Nonlinear feedback synchronization of hyperchaos in higher dimensional systems

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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。     

An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects

The point reactor kinetics equations of multi-group of delayed neutrons in the presence Newtonian temperature feedback effects are a system of stiff nonlinear ordinary differential equations which have not any exact analytical solution. The efficient technique for this nonlinear system is based on changing this nonlinear system to a linear system by the predicted value of reactivity and solving this linear system using the fundamental matrix of the homogenous linear differential equations. The nonlinear point reactor kinetics equations are rewritten in the matrix form. The solution of this matrix form is introduced. This solution contains the exponential function of a variable coefficient matrix. This coefficient matrix contains the unknown variable, reactivity. The predicted values of reactivity in the explicit form are determined replacing the exponential function of the coefficient matrix by two kinds, Backward Euler and Crank Nicholson, of the rational approximations. The nonlinear point kinetics equations changed to a linear system of the homogenous differential equations. The fundamental matrix of this linear system is calculated using the eigenvalues and the corresponding eigenvectors of the coefficient matrix. Stability of the efficient technique is defined and discussed. The efficient technique is applied to the point kinetics equations of six-groups of delayed neutrons with step, ramp, sinusoidal and the temperature feedback reactivities. The results of these efficient techniques are compared with the traditional methods.     

A stochastically perturbed nonlinear point reactor model

We present an exact analysis of the fluctuations of neutron density in a stochastically perturbed nonlinear point reactor model in the absence of delayed neutrons. The reactivity and feedback coefficients are assumed to have white noise Gaussian component. The time development of probability distribution is obtained from the Fokker-Planck equation. It is found that for small density of neutron population the stationary probability distribution is more sensitive to the random change in the reactivity than in the feedback coefficient, whereas for large neutron density the probability distribution is more sensitive to the random change in the feedback coefficient than in the reactivity.     

兰州重离子加速器冷却储存环主环加速过程的束流反馈

正在建设中的兰州重离子加速器冷却储存环（HIRFL-CSR）主环用于束流的加速。在加速过程中,为了保证束流的谐振加速,须准备2个束流反馈环(相位反馈环和束流径向位置反馈环)来保证主导磁场与高频频率的同步。本文基于Laplace变换及数值计算结果，分析了束流反馈环对同步加速器中束流动力学行为的影响。     

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。     

Integrated operation of diagnostic and control systems

In fusion research the ability to generate and sustain high performance fusion plasmas gains more and more importance. Optimal combinations of magnetic shape, temperature and density profiles as well as the confinement time are identified as advanced regimes. Safe operation in such regimes will be crucial for the success of ITER and later fusion reactors. The operational space, on the other hand, is characterized by nonlinear dependencies between plasma parameters. Various MHD limits must be avoided in order to minimize the risk of a disruption.Sophisticated feedback control schemes help to tackle this challenge. But these in turn require detailed information on plasma state in time to allow proper reaction. Control system and diagnostic systems therefore must establish a symbiotic relationship to carry out such schemes. Today, all major fusion devices implement such a concept.An implementation of such a concept with sustained integration is presented using the example of ASDEX Upgrade. It covers data communication via a real-time network, synchronization mechanisms for data-driven algorithm execution as well as operational aspects and exception handling for failure detection and recovery. A modular distributed software framework offers standardized user algorithm interfaces, automated workflow procedures and the application of various computer and network hardware components. Designed with a special focus on reliability, robustness and flexibility, it is a sound base for exploring ITER-relevant plasma regimes and control strategies.     

自由电子激光器中稳定波长反馈的理论研究

改进了一维含时间变量的自由电子激光振荡器程序，加入稳定波长反馈,考虑了电子束能量变化引起的电子束脉冲间隔的变化。对稳定波长反馈引起的输出激光功率的调制振荡现象进行了理论研究,证实了实验观测,计算得到的调制频率和深度实验结果很好吻合。发现这种类极限环振荡的产生机制来源于主要由超辐射引起的频率蠕变,电子在有质动力势阱中的同步振荡亦有重要影响。研究、分析了稳定波长反馈系统的稳定性和对反馈系统带宽的要求。对于随机因素引起的波长变化,所需反馈系统的带宽取决于随机变化的频率。而对于自由电子激光内在非线性效应引起的波长变化,稳定波长所需带宽频率很高,很难实现,效果也不明显。对于高增益高功率自由电子激光,由于边带的发展,采用负反馈稳定波长的可行性及其后果还需要进一步研究。     

核反应堆中通量密度的一种非线性控制方法

针对核反应堆动态非线性模型模型,提出一种非线性状态反馈的中子通量密度恒值控制的新方法。与传统的古典控制方法相比,此方法不必对模型进行近似线性化处理,因而,控制精度较讥,适用的时域范围较广,控制律也不太复杂。仿真结果验证了这种非线性控制律的有效性和优越性。     

Optimal control of a boiling water nuclear reactor

Application of optimal control to a boiling water nuclear reactor is the theme of this paper. The optimal control problem of a linearized model of a reactor is treated as a regulator problem and feedback control laws are derived to drive the system to steady state in the presence of disturbances. The weighting matrices in the performance index of the regulator problem are suitably changed to yield acceptable closed-loop responses for specific disturbances. The disturbances considered are (i) impulse change in temperature of water at inlet to plenum chamber and (ii) step change in throttle valve area. Then the feedback control laws are implemented on the nonlinear model to illustrate their effectiveness both for large and small disturbances.     

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。     

Research on stability of a reactor with power reactivity feedback

The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equation qualitative theory, the model of a reactor with power reactivity feedback is judged unstable. The equilibrium point is a saddle-node point. A portion of the trajectory in the neighborhood of the equilibrium point is parabolic fan curve, the other are hyperbolic fan curve. Based on phase locus near the equilibrium point, it is pointed out that the model is still stable within physical limits. The difference between stability in the mathematical sense and in the physical sense is indicated.     

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.     

200MW 核供热堆的非线性动态模型

本文为２００ＭＷ核供热堆建立了一个用于大功率运行范围控制系统仿真的非线性动态模型。模型除了采用点中子动态方程、集中参数的慢化剂温度和燃料温度负反馈等压水堆控制系统常用的建模方法之外，为了使模型适用于大功率运行范围，还重点考虑了主回路自然循环对堆芯内冷却剂和燃料棒之间的传热系数、主换热器换热系数、主回路时间常数的影响，以及二回路流量变化引入的非线性。仿真结果表明，模型具有较高的精度，可用于控制系统仿真。     

Research reactor power controller design using an output feedback nonlinear receding horizon control method

A constrained, output feedback nonlinear receding horizon control (NRHC) method is applied to design a research reactor power controller. The method uses a nonlinear plant model subject to state, control and terminal set constraints; a nonlinear cost function; and a high gain observer. The controller regulates reactor power from 1% to 100% of full power; considers known disturbances, such as reactivity insertions and changes in core inlet flow and temperature; and includes upper limits constraints on neutron flux, neutron flux rate, core outlet temperature and core inlet–outlet temperature difference. Simulation results show an excellent performance for power regulation and known disturbances rejection: all process variables are kept within the admissible limits avoiding the actuation of the safety systems.     

Application of a reduced order model to BWR corewide stability analysis

The determination of system stability parameters from power readings is a problem usually solved by time series techniques such as autoregressive modeling. These techniques are capable of determining the system stability, but ignore the physics of the process and focus on the determination of a nth order linear model. A nonlinear reduced order system is used in conjunction with estimation techniques to present a different approach for stability determination. The simulation of the reduced order model shows the importance of the feedback reactivity imposed by the thermal-hydraulics; the dominant contribution to this feedback is provided by the void reactivity, being a function of power, burnup, power distribution, and in general of the operating conditions of the system. The feedback reactivity is estimated from power measurements and used in conjunction with a reduced order model to determine the system stability properties in terms of the decay ratio.     

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.     

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.     

Spectrum behavior for the nonlinear fractional point reactor kinetics model

The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.     

Power density axial oscillations induced by Xenon dynamics: Parameter identification via genetic algorithms

In this paper we describe the axial flux oscillations in PWRs by means of the Onega and Kisner model (1978), a two-point xenon oscillation model based on the one-group, one-dimensional neutron diffusion equation with nonlinear power reactivity feedback and on the nonlinear xenon and iodine balance equations. We investigate the feasibility of using genetic algorithms for estimating the effective nuclear parameters involved. This approach has the advantage of allowing the periodic re-estimation of the effective parameter values pertaining to each reactor on the basis of its recent history. By so doing, other effects, such as the burn up, are automatically taken into account.