Sine-Gordon方程的动态边界反馈镇定

考虑一端固定,控制输入在另一端的Sine-Gordon方程的动态边界反馈镇定问题.我们给出闭环系统的适定性,并利用乘子方法得到在动态边界反馈控制下闭环系统的多项式衰减率.     

梁振动边界反馈的最优反馈增益的数值解

本用Legendre谱方法估计一端固定,一端加弯矩耗散线性反馈的梁振动的闭环系统使能量最快衰减的最优反馈增益,我们给出了数值产生的图形结果,通过比较发现另一种非耗散的线性反馈在最优反馈增益下比相应的耗散线性反馈有更好的衰减率。     

基于边界位移量测的一维波方程的稳定性

本文考虑一类非同位波方程的控制问题,提出了一个新的基于观测边界位移的时滞反馈控制器.通过算子半群理论和Riesz基逼近的方法,证明了相关闭环系统的适定性和稳定性,并给出系统指数稳定时的条件.数字模拟进一步验证了结论的成立.     

一维薛定谔方程的自适应误差反馈输出调节

针对具有一般谐波干扰和输出均与控制非同位的一维薛定谔方程,研究了基于误差反馈的控制输出调节问题.首先,构造了一个辅助系统,将测量误差变为输出.紧接着,基于测量误差,设计了一个自适应观测器估计辅助系统的状态和未知参数.然后,建立了新的辅助系统,将干扰与控制变为同位,有助于设置自适应控制器,使得测量误差满足e(t)∈ L2...     

带有时滞控制的一维热传导方程的参数化控制器设计与稳定性研究

研究具有Dirichlet边界条件和内部时滞控制的热方程的镇定问题.文章的目标是设计一个状态反馈控制器,使得闭环系统以指定的衰减率λ指数衰减.与早期的控制器设计方法不同,文章探索一种新的控制器设计方法——对偏微分方程的参数化控制器设计.首先,将带有时滞的控制系统转换成由传输方程和热方程构成的串联系统.然后,构建一个具有指数稳定性并且与文章所研究的系统具有类似结构的目标系统.最后,选择合适的核函数,使其构成的有界线性变换可以将闭环系统映到目标系统.通过选择不同的核函数,可以得到由目标系统到闭环系统的逆变换.     

一个复合系统边界反馈的Riesz基性质

该文考虑一端固定 ,一端具负荷的梁的振动问题 .证明了线性反馈的闭环系统是一个 Riesz谱系统 ,即系统存在一列广义本征函数列构成状态空间的 Riesz基 .从而系统的谱确定增长条件成立 .在此过程中 ,简单的导出了系统本征值的渐近展开式 .并因此推论出系统的指数稳定性的条件     

正则型控制系统的全局反馈镇定

在对非线性控制系统全局镇定的研究中 ,Byrness,Isidori讨论了光滑非线性系统的光滑反馈与全局正则型的等价条件 ;Kokotovic,Sussmann则在讨论了全局镇定的正实条件后 ,得到了一个判定系统为全局光滑可镇定的重要条件 .本文则考察一类正则型控制系统 ,通过变换系统和构造全局反馈镇定律的方法 ,得到全局光滑镇定     

广义Hamilton弹性梁控制系统的几何结构与数值解

基于广义Hamilton控制系统的几何结构,给出了适用于点测量,点控制计算与模拟的Euler- Bernoulli梁方程的广义Hamilton典则方程,并且对于一端加剪切力反馈的受控Euler-Bernoulli梁方程在周期初始条件下运用Euler中点公式进行了数值模拟.     

Euler-Bernoulli梁边界反馈控制系统的Riesz基生成问题

本文用基扰动的方法,证明了由速度和角速度组成的边界反馈Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ梁振动系统的广义本征元生成状态空间Ｈ的Ｒｉｅｓｚ基,从而给出了振动系统最优指数衰减率的计算公式,     

广义控制系统状态观测器的结构

在广义控制系统的设计中,经常会遇到状态反馈问题.如极点配置和二次性能指标的最优控制都是状态反馈.可是在实际系统中,直接量测的是输出,而状态通常不能直接量测.从而知道状态反馈是物理上不能实现的.已知在正常系统中,解决这一问题的方法是重构状态——即通过一个被称为状态观测器的动态系统来实现它.因此对广义系统亦可期望通过状态观测器来获得状态反馈中的状态.文献[1]曾为广义系统具体设计了     

动态控制下Euler-Bernoulli梁的多项式镇定

考虑动态输出反馈控制下Euler-Bernoulli梁的振动抑制问题,证明了系统算子生成的C0-半群,不指数稳定但渐近稳定.且当初值充分光滑时,利用Riesz基方法估计出系统能量多项式衰减.     

具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.     

Effects of time delays on the stability of collocated and noncollocated point control of discrete dynamic structural systems

The effects of time delays on collocated as well as noncollocated point control of discrete dynamic systems have been examined. Controllers of proportional-integral-derivative (PID) type have been considered. Analytical estimates of time delays to maintain/obtain stability for small gains have been given. Several new results dealing with the effect of time delays on collocated and noncollocated control designs are obtained. It is shown that undamped structural systems cannot be stabilized with pure velocity (or integral) feedback without time delays while using a controller which is not collocated with the sensor when the mass matrix is diagonal. However, with the appropriate choice of time delays for certain classes of commonly occurring structural systems, stable noncollocated control can be achieved. Analytical results providing the upper bound on the controller's gain necessary for stability have been presented. The theoretical results obtained are illustrated and verified with numerical examples.     

Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls

In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.     

Stabilization of a hybrid system of elasticity by feedback boundary damping

Summary A hybrid control system is presented as consisting of an elastic beam linked to a rigid body, and the system is asymptotically stabilized through feedback boundary damping. Solutions of the hybrid system are constructed that decay towards zero at nonexponential, even arbitrarily slow, decay rates. This feedback control analysis complements the authors' earlier report on the open-loop controllability of this same hybrid system, which is a simplified model of a space-structure.This research was partially supported by NSF Grant DMS 86-07687 and AFOSR-ISSA-860088, and the second author also received support from SERC.     

Stabilization of the uniform Timoshenko beam by one locally distributed feedback

In this article, we study the energy decay rate for an elastic Timoshenko system. This system consists of two coupled wave equations. Only the equation about the rotation angle is damped by one locally distributed feedback at the neighbourhood of the boundary. The equation for the transverse displacement of the beam is only indirectly damped through the coupling. First, we establish an exponential energy decay rate in the case of the same speed of propagation. Next, when the wave speeds are different, a polynomial-type decay rate is obtained. These results are proved by verifying the frequency domain conditions.     

STABILIZATION OF VIBRATING BEAM BY VELOCITY FEEDBACK CONTROL

1IntroductionInrecentyearstherehasbeenmuchinterestintopicofcontrolandstabilizationofflexiblevibratingsystemdescribedbyaEuler-Bernoullibeamequationasfollowing(See[1]-[8]).Thequestionofstabilizationofsystem(1.O)hasbeenstudiedbymanyauthors.Forexample,seeLagnese[1],Chen.et.al[2],R.b.,b.,l3]forstabilization,Lagllese[5]forconcentratedS/A'sstabilization.Letusmentionthatthesepapersstudyasymptoticoruniformdecayforthecollsideredsystem,butnotprovetheoptimalityofthedecayrate.C..,.d[8]studytheoptimali…     

具有局部非线性反馈的非均质Timoshenko梁的能量衰减估计

该文考虑具有局部非线性反馈的非均质Timoshenko梁的能量衰减估计.由非线性算子半群理论得到系统的适定性;应用乘子方法,给出了系统的能量衰减估计.