四维超Jerk系统的分岔特性及同步控制研究

研究具有双翼混沌吸引子的四维超Jerk系统的分岔特性和混沌路径,并设计有效的自适应反馈控制器实现该系统的全局指数同步.通过相图、Poincaré映射图、分岔图和Lyapunov指数谱等揭示系统的混沌特性,并得到系统进入混沌的主要路径是逆倍周期分岔和大幅度的周期振荡.将高维分岔理论和扰动方法应用于该系统的动力学分析中,建立分岔点处参数之间的精确关系,进一步得出产生的周期轨道的稳定性及其近似解表达式.基于自适应同步理论,提出一种实现混沌系统完全同步的方案.数值模拟结果表明所提出机制的可行性和有效性.本文可为此类系统在混沌加密领域内的实际应用提供理论参考.     

慢变参数激励Duffing系统中的延迟分岔现象及其诱发的簇发振荡

研究了慢变参数激励下Duffing系统的动力学行为.由于慢变参数激励可以周期性地穿越叉型分岔点,周期性的延迟分岔行为可能会发生.探讨了延迟分岔的动力学特性,尤其是基于此产生的簇发振荡.指出了延迟分岔现象所形成的稳定慢流形之间的滞后环是系统中可以观测到簇发振荡主要原因.此外,还分析了初始时间对延迟行为的延迟时间的影响.研究表明,首次延迟行为依赖于系统的初值.但是,随后发生的延迟现象与系统初值无关.     

梁的强迫振动问题Green函数解及应用研究综述

针对一类周期激励下的广义离散Duffing系统,运用快慢分析方法,对系统状态进行数值模拟,通过分岔图和时间历程图对系统进行分析,得到不同参数下系统所表现出的新型簇发振荡模式,并探讨其与连续Duffing系统之间的联系.系统的簇发振荡模式被分为两类,一类是当慢变量穿过Fold分岔点或混沌激变点,吸引子发生转迁所诱发的各种对称式簇发振荡,另一类则是当慢变量无法穿过Fold分岔点或混沌激变点,由延迟Flip分岔所诱发的各种非对称式簇发振荡.     

周期激励下四维非线性系统的簇发共存现象

在一个周期激励的四维非自治系统中,当激励的频率远小于系统的固有频率时,系统表现出了两时间尺度的动力学行为.将激励项定义为慢变参数,激励系统可以转化为广义自治系统.分析了广义自治系统平衡点的稳定性及其分岔条件.应用快慢分析法和转换相图,探讨了系统对应于不同初始条件的簇发现象及其产生机制,并对其中多种簇发共存的形成机理进行了讨论.同时,由于慢过效应的存在,簇发振荡的激发态和沉寂态的连接点和理论分析中的分岔点相比存在一定的滞后现象.     

化学振荡反应的频域特征

本文应用自行研制的化学振荡反应计算机数据采集与处理系统，收集了苯胺－溴酸钾－硫酸非催化化学振荡反应体系的时间序列信号数据及其功率谱图，探讨了电极信号处于非平衡定态，周期，拟周期等状态时的功率谱特征。     

非线性电路的簇发现象及分岔机制

通过在立方非线性Hartley模型中引入交变的电流源,并选定适当的参数和激励频率,建立了具有快慢行为的两时间尺度周期激励电路系统．由Hopf分岔的产生条件,推导了对应自治系统Hopf分岔的第一Lyapunov系数解析表达式,并在数值计算中得到了验证．结合该系数,重点分析了系统中的快慢行为,给出了典型的周期簇发现象及其相应的分岔模式,并利用自治系统和转换相图从分岔角度指出了该种簇发现象的产生机理．     

基于分岔理论的永磁同步电机有限时间混沌控制

永磁同步电机运行系统具有不稳定的分岔特性,随着系统参数的变化,系统会在平衡点处发生分岔行为.首先,基于分岔理论构建了永磁同步电机的混沌模型.其次,通过研究系统的分岔参数,分析了系统在平衡点处的分岔特性,发现系统在零平衡点处会产生静态分岔并出现新的平衡点,随着参数的继续变化,系统在新的平衡点处发生连续的Hopf分岔,而连...     

一类分段线性神经元系统的动力学行为分析

针对一类平面上三分段连续线性神经元模型,研究了边界平衡点的持续性分岔(persistence)、非光滑折分岔(non-smooth fold)的存在条件及一类跨边界周期解.最后,通过施加缓慢变化的周期外激励研究其对边界分岔和系统周期放电的影响.     

细胞钙振荡模型的Hopf分岔与计算机仿真

利用中心流形定理和分岔理论,研究了Borghans-Dupont模型平衡点分岔现象,揭示了钙振荡现象发生机理。通过对系统分岔现象的理论分析,不仅证明了Hopf分岔的存在,而且也说明了振荡现象产生和消失的主要原因来源于两个分别为超临界和亚临界的Hopf分岔。利用计算机仿真,绘制了系统平衡点分岔图、相图与时序图,验证了理论分析的正确性。     

时滞诱发的忆阻型Hopfield神经网络的复杂动力学

本文研究含时滞的忆阻型环状Hopfield神经网络的稳定性、Hopf分岔以及复杂振荡模式.根据特征方程根分布情况,获得了系统全时滞稳定条件和与时滞相关的稳定条件.通过数值计算揭示了丰富的动力学现象,如多种周期运动和混沌吸引子等,并给出了Poincaré截面上的分岔图.设计了电路实验平台,取得了与理论分析和数值计算高度吻合的实验结果.     

A robust control scheme for nonlinear non-isothermal uncertain jacketed continuous stirred tank reactor

A Non-isothermal Jacketed Continuous Stirred Tank Reactor (CSTR) is extensively used in chemical as well as in other process industries to manufacture different products. The dynamics of non-isothermal CSTR are highly nonlinear and open-loop unstable in nature. Moreover, it may have parametric uncertainties, disturbances and un-modeled side reactions which may cause the reactor temperature to deviate from the reference value. This deviation may degrade quality of the product because the chemical reaction inside the CSTR depends on reactor temperature. For such a nonlinear, unstable and uncertain process, designing a control scheme with the ability to reject the effects of disturbances along with a good reference tracking capability is a challenging control engineering problem. In this work, a novel robust sliding mode control technique named as Improved Integral Sliding Mode Control (IISMC) has been presented for uncertain non-isothermal jacketed CSTR process. Moreover, a variety of recently developed sliding mode control techniques such as Classical Integral Sliding Mode Control (CISMC) and Super Twisted Algorithm based Sliding Mode Control (STA-SMC) have also been devised and compared with the proposed approach in order to investigate the effectiveness of the proposed scheme. A Lyapunov based analysis has also been provided to assure the robust stability of the closed loop process. Furthermore, in order to extend the state feedback approach to the output feedback scheme, two robust observers; High Gain Observer (HGO) and Extended High Gain Observer (EHGO), are also designed for the very process. They have also been compared with each other and have been investigated for robust stability using Lyapunov based approach. Finally, an output feedback control scheme using IISMC and EHGO has been presented and its performance has been examined and compared with the IISMC based state feedback approach. The simulation results show that the proposed control scheme effectively rejects the uncertainties and disturbances without leading the process to instability and offers good reference tracking capabilities.     

蛇管与夹套冷却CSTR温度双重控制

连续搅拌釜式化学反应器(CSTR)是重要的化工设备。对蛇管与夹套双冷却CSTR单回路温度控制方案只利用一种操纵变量,无法兼顾动态性能与静态性能的不足进行了深入分析后,提出了CSTR温度双重控制系统方案。通过双重系统的协调控制,在温度出现偏差时由蛇管冷却器快速消除温度偏差,使温度迅速返回设定值;然后由冷却效率高的夹套冷却器逐步取代蛇管冷却器所承担的冷却负荷变化——即在动态过程,由动态性能好的操作变量(蛇管冷却器)进行控制,过渡过程短,动态偏差小;在平稳生产过程,CSTR冷却负荷主要由静态性能好的操作变量(夹套冷却器)承担,冷却效率高,冷却水用量少。CSTR温度双重控制充分发挥了CSTR蛇管与夹套冷却器各自的优势,使CSTR温度控制的动态性能与静态性能都达到较为理想水平。最后,通过半实物仿真实验验证了CSTR温度双重控制在动态性能和节能降耗二方面的优越性。该双重控制方案可应用于具有类似结构特征的其他生产系统。     

Critical evaluation of non-linear filter configurations for the state estimation of Continuous Stirred Tank Reactor

A systematic approach has been attempted to design a non-linear observer to estimate the states of a non-linear system. The neural network based state filtering algorithm proposed by A.G. Parlos et al. has been used to estimate the state variables, concentration and temperature in the Continuous Stirred Tank Reactor (CSTR) process. (CSTR) is a typical chemical reactor system with complex nonlinear dynamics characteristics. The variables which characterize the quality of the final product in CSTR are often difficult to measure in real-time and cannot be directly measured using the feedback configuration. In this work, the comparison of the performances of an extended Kalman filter (EKF), unscented Kalman filter (UKF) and neural network (NN) based state filter for CSTR that rely solely on concentration estimation of CSTR via measured reactor temperature has been done. The performances of these three filters are analyzed in simulation with Gaussian noise source under various operating conditions and model uncertainties.     

正弦函数作用下的Martin过程

为了弥补单纯Martin过程在描述天气、石油和股市行情等变化过程方面的不足，首先通过对正弦函数作用下的Martin过程进行相图分析，发现该系统状态随着参数的变化而变化，同时经过稳定焦点、倍周期分岔，可将其收缩到混沌吸引子上，且这个状态变化过程会重复出现；然后进一步通过计算机从理论上计算了该系统的最大Lyapunov指数，并通过绘制了分岔图定量地说明了该系统具有混沌行为。     

Passivity-based nonlinear control of CSTR via asymptotic observers

This work makes use of a passivity-based approach (PBA) and tools from Lyapunov theory to design a nonlinear controller for the asymptotic stabilization of a class of nonisothermal Continuous Stirred Tank Reactors (CSTR) around any desired stationary point. The convergence and stability proofs are derived in the port Hamiltonian framework. Asymptotic observers that do not require knowledge of reaction kinetics are also proposed for a system with incomplete state measurement. Numerical simulations are given to illustrate the application of the theoretical results to a CSTR with multiple steady states.     

MPCE实验装置连续反应过程控制策略研究与实现

以多功能过程和实验系统（NIPCE）中的连续反应过程（CSTR）为对象,对整个CSTR系统进行了控制策略研究。系统融合了PID控制、模糊控制、串级控制、分程控制等多种控制算法,实现了对系统的开车顺序控制、反应过程控制和安全控制。利用S7—300PLC对系统进行设计与实现。最终的运行结果表明系统对CSTR有较好的控制效果,同时控制系统具有较强的鲁棒性、实用性及可行性。     

Process design in SISO systems with input multiplicity using bifurcation analysis and optimisation

This paper presents an approach using continuation and optimisation methods for modifying a process design to avoid control difficulties caused by input multiplicity. The approach assumes an initial design, with a preassigned SISO control structure, has been obtained and is useful where there is an input multiplicity in the operating region. The condition for input multiplicity is obtained by inflating the state space model with a state representing the locus of the point of zero gain. The multiplicity condition is determined using the bifurcation analysis package, AUTO, which allows the study of the influence of operating conditions and parameters on input multiplicity behaviour to obtain an expression for the point of zero gain as a function of the design and disturbance variables. A process modification problem is formulated within an optimisation framework and solved to determine the minimal design parameter changes necessary to avoid input multiplicity given an assumed maximal disturbance. Results are presented for the application of the algorithm to a CSTR system demonstrating that small changes in some design variables can avoid input multiplicity problems in this case, and that the method can determine the changes necessary.     

Bifurcation phenomenon in the wake of a 3-D cylinder

Numerical simulations are carried out for a long slender rigid circular cylinder in a cross flow to investigate the effect of end-plates on the bifurcation phenomenon in the near wake. A multiple relaxation time lattice Boltzmann method (MRT-LBM) is used for the solution of three-dimensional unsteady flow. At the Reynolds number of 200, there exists shedding frequency bifurcation along the span which is resulted from the shedding phase oscillation.     

一类脉冲动力系统的状态反馈控制

对一类具有状态反馈控制的脉冲动力系统的动力学性质进行了研究．由周期解的扰动解得到了一个Poincare映射，利用Poincare映射讨论了系统周期解的分岔，并得到了半平凡周期解和正周期-1解存在和稳定的充分条件．定性分析和数学模拟表明，半平凡周期解通过fold分岔分钻出正周期-1解，正周期-1解通过flip分岔分岔出正周期-2解，再通过一系列flip分岔通向混沌，此外，讨论了脉冲状态反馈控制的效果．     

连续搅拌反应釜系统的自抗扰控制

针对连续搅拌反应釜系统(CSTR)大滞后,大惯性以及动态特性随工况不确定性变化的特点,通过设计参数可调的跟踪微分器和扩张状态观测器,改进经典PID算法的固有缺陷,提出不依赖于精确CSTR模型的离散自抗扰控制方案,采用西门子新一代工业可编程控制器-SIMATIC PCS7在多功能过程与控制系统的CSTR实验仿真对象上实现...