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一类不确定线性周期离散时间系统的分析与控制 总被引:1,自引:0,他引:1
讨论具有参数区间不确定性的线性周期离散时间系统的反馈控制问题,首先进行系统的鲁棒稳定性分析和镇定研究,分别给出了基于线性矩阵不等式的系统渐近稳定和状态反馈镇定的条件.接着研究系统的增益分析和控制综合问题,对于增益分析问题,得到一个基于线性矩阵不等式的条件,在该条件下,具有参数不确定性的线性周期自治系统渐近稳定,且有小于γ的增益,对于控制综合问题,导出基于线性不等式的条件,由该条件可以得到一个状态反馈器,使得闭环系统渐近稳定.且有小于γ的增益,所有这些条件都是充分必要的. 相似文献
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针对一类不确定上界未知的非线性时滞系统,基于松散稳定性条件,讨论了系统的模糊自适应控制问题 .通过在Lyapunov泛函中引入参数,得到带调节因子的时滞相关稳定性条件.设计出基于观测器的自适应模糊控制器,观测增益矩阵和反馈增益矩阵可以通过求解线性矩阵不等式得到 .当调节因子取不同值时,观测增益矩阵和反馈增益矩阵也是不同的,因此,闭环系统的动态性能可以通过选取合适的调节因子来优化.最后通过一个实例验证了所给结论的有效性. 相似文献
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采用压电材料研究了参数激励非线性梁结构的运动稳定性及其主动控制,通过速度反馈控制算法获得主动阻尼,利用Hamilton原理建立含阻尼的立方非线性运动方程,采用多尺度方法求解运动方程获得稳定性区域.通过数值算例,分析了控制增益、外激振力幅值等因素对稳定性区域和幅频曲线特性的影响.分析表明:控制增益增大,结构所能承受的轴向力也增大,在一定范围内结构的主动阻尼比也增加;随着控制增益的增大,响应幅值逐渐降低,但所需的控制电压存在峰值点. 相似文献
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考虑边界反馈时,一维热弹性系统的衰减速度.证明了闭环系统的谱确定增长条件成立,且反馈增益常数可任意改变高本征频谱.最后谱方法给出了数值模拟结果. 相似文献
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静水压力下压电弹性圆柱振动的主动控制 总被引:3,自引:0,他引:3
对静水压力下压电弹性层合壳的振动控制进行了研究。首先利用Hamiltion原理推导出压电弹性层合壳的非线性动力基本方程,进一步得到了静水压力作用下封闭压电弹性层合壳的动力方程。对两端简支条件下的压电弹性圆柱壳的振动问题进行了求解,并基于速度反馈控制法得到了带压电感测层/激励层的层合圆柱壳的主动控制模型,相应的数值结果表明在载荷的情况下,压电层上施加合适大小,方向的电压可以改变圆柱壳的静变形。对于系统的动力响应问题,速度反馈的增益越大,越能抑制系统在共振区的振动,验证了该控制模型抑制结构振动的有效性。 相似文献
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本文研究了Lorenz系统的控制与同步问题.利用负状态反馈的方法和Lyapunov稳定性理论,得到了能保证系统渐近稳定和同步的有关反馈增益的一些充分条件.最后,数值实验证实了理论分析的结果. 相似文献
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研究了Duffing-Van der Pol振子的主参数共振响应及其时滞反馈控制问题.依平均法和对时滞反馈控制项Taylor展开的截断得到的平均方程表明,除参数激励的幅值和频率外,零解的稳定性只与原方程中线性项的系数和线性反馈有关,但周期解的稳定性还与原方程中非线性项的系数和非线性反馈有关.通过调整反馈增益和时滞,可以使不稳定的零解变得稳定.非零周期解可能通过鞍结分岔和Hopf分岔失去稳定性,但选择合适的反馈增益和时滞,可以避免鞍结分岔和Hopf分岔的发生.数值仿真的结果验证了理论分析的正确性. 相似文献
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In this paper, we consider a variable-coefficient wave equation with memory type acoustic boundary conditions and a constant time delay in the boundary feedback. Using the Riemannian geometry method, we prove the exponential decay of the system with memory type acoustic boundary conditions and a constant time delay under some suitable assumptions. 相似文献
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This paper presents the thickness-shear (TSh) vibration modes of an infinite circular AT-cut quartz resonator with ring electrodes. By application of 2D scalar differential equations derived by Tiersten and Smythe, we obtain the resonant frequencies and vibration amplitude distributions of thickness-shear modes in the resonator. The theoretical results have been verified in commercial FEM software COMSOL. Through numerical examples, we illustrate that the distribution of displacement fields in the center part of the ring electrode is adjustable. Furthermore, we optimize the size of the electrodes and the mass ratio of the electrode to the plate, in order to achieve a nearly uniform displacement distribution and mass sensitivity of the resonator. These results can be a theoretical guidance for design and optimization of sensors based on quartz resonators. 相似文献
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The relations connecting perturbations specific for acoustic and entropy modes in an accelerated fluid or in a fluid affected by constant mass force, are derived. They allow to decompose the total vector of perturbations and the overall energy into acoustic and non-acoustic parts uniquely at any instant. In order to do this, three quantities are required, for example total perturbations in entropy, pressure and velocity. The evaluations are made in regard to the content of acoustic and non-acoustic parts of the total energy excluding its kinetic part. In some cases, exact relations may be derived. 相似文献
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《Finite Elements in Analysis and Design》2009,45(1):13-24
Shell type components and structures are very common in many mechanical and structural systems. In smart structural applications, piezolaminated plates and shells are commonly used. In this paper a finite element formulation is presented to model the static and dynamic response of laminated composite shells containing integrated piezoelectric sensors and actuators subjected to electrical, mechanical and thermal loadings. The formulation is based on the first order shear deformation theory and Hamilton's principle. In this formulation, the mass and stiffness of the piezo-layers have been taken into account. A nine-noded degenerated shell element is implemented for the analysis. The model is validated by comparing with existing results documented in the literature. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The influence of the stacking sequence and position of sensors/actuators on the response of the laminated cylindrical shell is evaluated. Numerical results show that piezoelectric sensors/actuators can be used to control the shape and vibration of laminated composite cylindrical shell. 相似文献
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We consider a model for the time evolution of a piezoelectric cantilever with tip mass. With appropriately shaped actuator and sensor electrodes, boundary control is applied and a passivity based feedback controller is designed to include damping into the system. Assuming that the cantilever can be modeled by the Euler-Bernoulli beam equation, we obtain a coupled PDE-ODE system. First we discuss its dissipativity, and its asymptotic but non-exponential stability. Next we derive a FEM using piecewise cubic Hermitian shape functions that is still dissipative. This is illustrated on a numerical simulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The paper treats the question of robust control of chaos in Chua’s circuit based on the internal model principle. The Chua’s diode has polynomial non-linearity and it is assumed that the parameters of the circuit are not known. A robust control law for the asymptotic regulation of the output (node voltage) along constant and sinusoidal reference trajectories is derived. For the derivation of the control law, the non-linear regulator equations are solved to obtain a manifold in the state space on which the output error is zero and an internal model of the k-fold exosystem (k = 3 here) is constructed. Then a feedback control law using the optimal control theory or pole placement technique for the stabilization of the augmented system including the Chua’s circuit and the internal model is derived. In the closed-loop system, robust output node voltage trajectory tracking of sinusoidal and constant reference trajectories are accomplished and in the steady state, the remaining state variables converge to periodic and constant trajectories, respectively. Simulation results are presented which show that in the closed-loop system, asymptotic trajectory control, disturbance rejection and suppression of chaotic motion in spite of uncertainties in the system are accomplished. 相似文献
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Harry Yserentant 《Numerische Mathematik》2001,88(3):581-601
Summary. The propagation of sound in compressible fluids is described by the acoustic equations that result from the linearization
of the Euler equations around a state of constant mass density and velocity zero. In this article, it is shown that a stable
and convergent discretization of the acoustic wave equation for the velocity field can be recovered from the particle model
of compressible fluids recently developed by the author in [Numer. Math. (1997) 76: 111–142] by linearizing the equations
of motion for the particles. For particles of proper shape, this discretization is second order accurate, and with an obvious
modification of the basic particle model, one can even reach an arbitrarily high order of convergence.
Received January 24, 2000 / Published online November 8, 2000 相似文献
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L. Meirovitch 《Journal of Optimization Theory and Applications》1987,54(1):1-21
Control of structures can be carried out conveniently by modal control, whereby the structure is controlled by controlling its modes. Modal control requires the estimation of the modal states for feedback, which can present a problem. One approach that does not require modal state estimation is direct feedback control, which implies collocated sensors and actuators. This paper examines some problems encountered in direct feedback control of distributed structures in conjunction with pole placement. A perturbation technique permits the computation of control gains for multi-input systems. The paper demonstrates that the difficulties experienced in using direct feedback in conjunction with pole placement are endemic to the approach.This research was sponsored by the Air Force Office of Scientific Research Grant No. AFOSR-83-0017, monitored by Dr. A. K. Amos, whose support is fully appreciated. This paper was presented at the Meeting on Optimal Control and Calculus of Variations, Oberwolfach, West Germany, June 15–21, 1986. 相似文献
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Due to the coupling of mechanical and electrical quantities in a piezoceramic material, it is possible to transform a harmonic input voltage to a harmonic output voltage by using a piezoceramic transformer. The advantage of such a transformer is the avoidance of magnetic fields and the very simple assembly. The piezoelectric transformer considered here consists of several parts. Three brass and two piezoceramic rods, that are glued together. The purpose of the system is to transform a determined input voltage to a determined ouput voltage with a high efficiency. Therefore, one of the piezoceramics is excited harmonically with a frequency close to a resonance frequency of the system. According to the electromechanical coupling in piezoceramics, the transformer oscillates with the excitation frequency. Due to the piezoelectric effect an electric displacement or an electric voltage is generated between the electrodes of the second piezoceramic. The amplitude of the output voltage depends on the geometry and the load connected between the electrodes of the second piezoceramic. In this paper a theoretical model to determine the gain and input impedance for such a transformer is derived and the results are compared with experiments. 相似文献