时滞反馈控制的若干问题

近几十年来, 时滞系统动力学的研究得到了众多学者的大量关注, 研究者在时滞系统的稳定性、非线性、辨识、时滞消除与利用技术等方面做了大量研究, 取得了许多成果. 本文主要介绍作者十多年来在时滞系统动力学方面的研究成果, 包括时滞辨识、两种基于时滞方程的控制律的设计方法、时滞鲁棒控制律的设计、时滞正反馈控制技术、非线性结构时滞控制律的设计、时滞实验等内容.     

时滞耦合系统非线性动力学的研究进展

随着对自然界客观规律的深入认识,工程系统设计的精细化和复杂性要求也与日剧增.在许多耦合的动态系统设计过程中要考虑由耦合过程的时滞所引发的动力学行为,该时滞来自于与传感系统、作动系统和控制系统耦合的过程.耦合时滞也广泛存在于交通、系统生物学、电子通讯、神经和信息网络等技术中.本文首先从耦合时滞出发,在以时滞为中心的耦合系统复杂动力学机制、时滞镇定耦合系统的实验基础和实现、快慢变时滞耦合系统动力学和时滞神经网络同步和去同步4个方面,对耦合时滞诱发的动力学研究进展进行综述.着重介绍了时滞耦合系统中耦合时滞诱发的高余维分岔奇异性及新的定量分析方法、中立型时滞微分方程的规范型计算、具有耦合时滞的非线性系统中耦合时滞和非线性参数的辨识方法与实验实现、快慢变时滞耦合系统的张弛振荡、耦合时滞诱发的网络系统的同步模式切换等问题的研究进展;然后在应用方面重点介绍了车床磨削加工过程中耦合时滞诱发的颤振及其机理、具有惯性项和耦合时滞的神经网络系统中耦合时滞诱发的高余维分岔和复杂动力学、时滞动力吸振器与隔振装置的设计与实验实现.最后,从耦合时滞系统的一般性理论和工程应用两个方面展望了近期值得关注的一些问题.     

时滞对于参数激励系统周期运动的影响

本文以结构物承受周期激励地震波和具有时滞的弹性地基为背景，研究时滞对于结构物振动响应的影响规律。问胚的数学模型是一个非线性参数激励时滞系统，采用中心流形和平均法得到Hopf分岔方程，研究结果表明时滞量对结构物的地震响应有重要影响，它可使响应振幅增大，意味着结构物遭破坏的危险性增大，同时，结果也表明可以通过阻尼控制器克服时滞引起的危险性。最后，对于不同的时滞量，比较理论分析与数值模拟结果基本吻合，说明了本文结果的可靠性。     

Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay

We prove the existence of a stationary random solution to a delay random ordinary differential system, which attracts all other solutions in both pullback and forwards senses. The equation contains a one-sided dissipative Lipschitz term without delay, while the random delay appears in a globally Lipschitz one. The delay function only needs to be continuous in time. Moreover, we also prove that the split implicit Euler scheme associated to the random delay differential system generates a discrete time random dynamical system, which also possesses a stochastic stationary solution with the same attracting property, and which converges to the stationary solution of the delay random differential equation pathwise as the stepsize goes to zero.     

Active control for a flexible beam with nonlinear hysteresis and time delay

A new active control method is presented to attenuate vibrations of a flexible beam with nonlinear hysteresis and time delay. The nonlinear and hysteretic behavior of the system is illustrated by the Bouc—Wen model. By specific transformation and augmentation of state parameters, we can convert the motion equation of the system with explicit time delay to the standard state space representation without any explicit time delay. Then the instantaneous optimal control method and Runge—Kutta method in fourth-order are applied to the controller design with time delay. Finally, in order to verify the effectivity of the time-delay controller proposed, numerical simulations are implemented. It is indicated by the simulation results that the control performance will deteriorate if neglect the time delay in process of the controller design and proposed time delay controller works well with both small and large time delay problems.     

气相爆轰波胞格尺度与点火延迟时间关系研究

讨论点火延迟时间和爆轰波胞格尺度的内在关系,将点火延迟时间作为特征参量来模拟胞格尺度. 分别对两个总包单步化学反应模型和一个基元反应模型的点火延迟时间进行了数值模拟研究. 对于满足当量比的氢气/空气混合气体,分析了不同初始压力下点火延迟时间随初始温度的变化关系. 研究表明:总包单步反应模型的点火延迟时间不随压力变化,且与初始温度呈线性关系. 基元反应模型的点火延迟时间随压力变化,而且存在理论上的S 型曲线,但是在拐点区域和低温区域与CHEMKIN 计算的结果相差1~3 个量级. 现有模型模拟的胞格尺度普遍偏小,其相应的点火延迟时间也偏小,胞格尺度与点火延迟时间具有正相关性. 入射激波后的气体的点火延迟时间与三波点的运动周期一致,是定量化模拟胞格的关键因素.      

STUDY ON THE RELATIONSHIP BETWEEN IGNITION DELAY TIME AND GASEOUS DETONATION CELL SIZE

讨论点火延迟时间和爆轰波胞格尺度的内在关系,将点火延迟时间作为特征参量来模拟胞格尺度. 分别对两个总包单步化学反应模型和一个基元反应模型的点火延迟时间进行了数值模拟研究. 对于满足当量比的氢气/空气混合气体,分析了不同初始压力下点火延迟时间随初始温度的变化关系. 研究表明:总包单步反应模型的点火延迟时间不随压力变化,且与初始温度呈线性关系. 基元反应模型的点火延迟时间随压力变化,而且存在理论上的S 型曲线,但是在拐点区域和低温区域与CHEMKIN 计算的结果相差1~3 个量级. 现有模型模拟的胞格尺度普遍偏小,其相应的点火延迟时间也偏小,胞格尺度与点火延迟时间具有正相关性. 入射激波后的气体的点火延迟时间与三波点的运动周期一致,是定量化模拟胞格的关键因素.     

The delay in the build-up of halogen-quenched counters

Summary It is shown experimentally that the so-called delay in halogen-quenched counters is only an apparent delay. There is no real delay but only a very slow multiplication giving the impression of a delay. The secondary mechanism is assumed to be ionization of halogen molecules by metastable rare gas atoms, the latter being formed by resonance radiation. The counters used were quenched with iodine and bromine.     

State-dependent delay in regenerative turning processes

Stability of a two degrees of freedom model of the turning process is considered. An accurate modeling of the surface regeneration shows that the regenerative delay, determined by the combination of the workpiece rotation and the tool vibrations, is in fact state-dependent. For that reason, the mathematical model considered in this paper is a delay-differential equation with state-dependent time delay. In order to study linearized stability of stationary cutting processes, an associated linear system, corresponding to the state-dependent delay equation, is derived. Stability analysis of this linear system is performed analytically. A comparison between the state-dependent delay model and the previously used constant or time-periodic delay models shows that the incorporation of the state-dependent delay into the model slightly affects the linear stability properties of the system in certain parameter domains.     

点火延迟时间对铝粉爆炸特性参数的影响

为了研究装置点火延迟时间对不同浓度粉尘爆炸压力和压力上升速率的影响,以铝粉为介质在5L圆柱形爆炸装置中进行系列爆炸实验。结果表明:装置点火延迟时间对铝粉爆炸压力和压力上升速率有十分显著的影响,且存在一个最佳点火延迟时间,此时最大爆炸压力最大;随着铝粉浓度的增加,最佳点火延迟时间先增加后保持不变。最佳点火延迟时间下的最大爆炸压力和最大压力上升速率明显高于点火延迟时间固定为60s时的。相对粉尘不同浓度均采用固定点火延迟时间,不同浓度时采用最佳点火延迟时间,所测得的粉尘最大爆炸压力和最大压力上升速率明显符合实际。     

Generalized macroscopic traffic model with time delay

The effect of delay or reaction time on traffic flow dynamics has been investigated widely in the literature using microscopic traffic models. Recent studies using second-order Payne-type models have shown analytically that, on a macroscopic scale, time delay does not contribute to whether traffic instabilities occur. This paper will attempt to show that it all depends on the (macroscopic) model used for the analysis that delay does have effect on traffic instabilities or not. To this end, we will formulate a generalized (linear) stability condition for a second-order macroscopic model with delay and investigate analytically the effect of such delay on traffic instabilities in some specific macroscopic models. It is found that the choice of the equilibrium speed function in a (second order) macroscopic model will determine how delay affects such (linear) stability condition     

Further results on memory control of nonlinear discrete-time networked control systems with random input delay

This paper is concerned with the problem of memory state feedback stabilization for a class of nonlinear discrete-time networked control systems with partly known probability distribution of input delay. Different from the common assumptions on the delay in the existing literatures, it is assumed that the probabilities of the delay taking values in a finite set are partly known or fully known in advance. In terms of the information about the occurrence probabilities of the delay taking values in the two finite sets, a new stochastic delay model is proposed, where the probability information of the delay is included in the parameter matrices of the transformed system. Based on the new model, a delay-dependent stabilization criterion is derived using a combination of the Lyapunov functional method, convexity of matrix inequalities, and linear matrix inequality technique. Finally, three illustrative examples are provided to show the effectiveness and applicability of the developed theoretical results.     

Small Delay Inertial Manifolds Under Numerics: A Numerical Structural Stability Result

In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C ¹-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.     

Noether symmetries and conserved quantities for Birkhoffian systems with time delay

The Noether symmetries and conserved quantities for Birkhoffian systems with time delay are proposed and studied. First, the Pfaff–Birkhoff principle with time delay is proposed, and Birkhoff’s equations with time delay are obtained. Second, based on the invariance of the Pfaff action with time delay under a group of infinitesimal transformations, the Noether symmetric transformations and the Noether quasisymmetric transformations of the system are defined, and the criteria of the Noether symmetries are established. Finally, the relationship between the symmetries and the conserved quantities are studied, and the Noether theorems for Birkhoffian systems with time delay are established. Some examples are given to illustrate the application of the results.     

Sufficient Stability Conditions for Systems with Delay

Nonlinear systems with delay consisting of subsystems, also with delay, are studied. The theory of Lyapunov stability for systems with delay is developed on the basis of matrix-valued functionals. A large-scale system is used to illustrate the applicability of the technique proposed     

The sufficient and necessary conditions of unconditional stability and the delay bound of the third-order neutral delay differential equation

In this paper,the sufficient and necessary conditions of the unconditional stability.andthe delay bound of the third-order neutral delay differential equation with real constantcoefficients are given.The conditions are brief and practical algebraic criterions.Furthermore,we get the delay bound     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated.A new stability condition is presented based on the Lyapunov-Krasovskii method,which is dependent on the amount of delay.A result is given in the form ofa linear matrix inequdlity,and the admitted upper bound of the delay can be easily obtained.The time delay dependent and independent results can be obtained,which include flome previously published resultS.A numerical example is given to show the effectiveness of the main results.     

Bursting-like motion induced by time-varying delay in an internet congestion control model

Time delay is an important parameter in the problem of internet congestion control. According to some researches, time delay is not always constant and can be viewed as a periodic function of time for some cases. In this work, an internet congestion control model is considered to study the time-varying delay induced bursting-like motion, which consists of a rapid oscillation burst and quiescent steady state. Then, for the system with periodic delay of small amplitude and low frequency, the method of multiple scales is employed to obtain the amplitude of the oscillation. Based on the expression of the asymptotic solution, it can be found that the relative length of the steady state increases with amplitude of the variation of time delay and decreases with frequency of the variation of time delay. Finally, an effective method to control the bursting-like motion is proposed by introducing a periodic gain parameter with appropriate amplitude. Theoretical results are in agreement with that from numerical method.     

时滞效应对弹性地基上梁主共振响应影响分析

本文研究了弹性地基上梁主共振响应的时滞效应．基于Hamilton原理,建立了时滞影响下弹性地基上梁的非线性运动微分方程,采用多尺度法,求得了时滞效应下主共振响应调制方程以及稳定性条件．通过数值算例,分析了时滞和调谐参数影响下主共振响应的峰值及幅频响应特性．结果表明,地基反力中的时滞效应对主共振响应影响较大,会导致共振域偏移,在一定区间内,响应幅值随时滞变化先减小再增大,呈现出周期性,并导致幅频曲线弯曲程度增大．     

Study of mixed-mode oscillations in a parametrically excited van der Pol system

This paper investigates the effects of slowly varying parametric excitation on the dynamics of van der Pol system. Periodic bifurcation delay behaviors are exhibited when the parametric excitation slowly passes through Hopf bifurcation value of the controlled van der Pol system. The first bifurcation delay behavior relies on initial conditions, while the bifurcation delay behaviors that follow the first one are immune to initial conditions. These bifurcation delay behaviors result in a hysteresis loop between the spiking attractor and the rest state, which is responsible for the generation of mixed-mode oscillations. Then an approximate calculation for the number of spikes in each cluster of repetitive spiking of mixed-mode oscillations is explored based on bifurcation delay behaviors. Theoretical results agree well with numerical simulations.