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1.
The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed. 相似文献
2.
E. H. Boutyour H. Zahrouni M. Potier‐Ferry M. Boudi 《International journal for numerical methods in engineering》2004,60(12):1987-2012
The aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches. It is based upon the asymptotic numerical method (ANM) and Padé approximants. The bifurcation point is detected by analysing the poles of Padé approximants or by evaluating, along the computed solution branch, a bifurcation indicator well adapted to ANM. Several examples are presented to assess the effectiveness of the proposed method, that emanate from buckling problems of thin elastic shells. Especially problems involving large rotations are discussed. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
The motion equations governing the dynamical behavior of a viscoelasticTimoshenko beam with finite deformation are derived and simplified byGalerkin method. The viscoelastic material is assumed to obey thethree-dimensional fractional derivative constitutive relation. Thedynamical behaviors of the simplified systems with order 1 and order 2are numerically computed and compared by using the computational methodpresented by the authors. The dynamical behaviors of the systems areuniform qualitatively, but there is a little deviation quantitatively.And the truncated system with order 1 is safer than the one of order 2.It is also shown that the lower order system is reasonable. Theinfluences of the load parameter and the fractional derivative parameter(material parameter) on the deflection of the beam are consideredrespectively. The numerical methods in nonlinear dynamics, such as phasediagram, and Poincaré section, are applied to reveal dynamical behaviorsof the nonlinear viscoelastic Timoshenko beam. There are plenty ofdynamical behaviors, such as periodicity, bifurcation, quasi-periodicityand chaos in the dynamical system. 相似文献
4.
5.
Jianlong Zou Xikui Ma Chi K. Tse Dong Dai 《International Journal of Circuit Theory and Applications》2006,34(3):251-264
In this paper, we derive the discrete‐time model for the power‐factor‐correction (PFC) buck‐boost converter in terms of a stroboscopic switching map. Fast‐scale instability is analysed through a fold diagram, which exposes the periodicity of the operation as well as the locations of the critical phase angles of the line voltage at which instability begins to occur along a half‐line cycle. The asymmetrical locations of the critical phase angles along a half‐line cycle is explained in terms of ‘under‐developed’ bifurcation. Border collision bifurcations are observed and analysed in detail. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
6.
固定化酵母粒子中生产乙醇的定态分岔行为研究 总被引:4,自引:0,他引:4
运用变分原理和打靶法将分布参数系统的非线性边值问题转化为集总参数系统的初值问题,基于延拓算法,研究了固定床中球形固定化酵母粒子表面乙醇和葡萄糖浓度随参数的变化关系,得出了单颗粒固定化酵母生产乙醇的多定态特性。结果表明:随系统尺度三的变化,方程出现分岔点;方程的解与液相主体浓度有关。在某些条件下酵母粒子表面浓度有三个定态:在多定态区域,随三的增加,方程一个解支的乙醇浓度迅速增加,从而可以在固定床中通过控制粒径而使反应器达到较高的产率。研究结果为固定床反应器的开工及控制提供了重要的理论依据。 相似文献
7.
参数强迫激励下非线性振子尖点型奇点的分叉 总被引:2,自引:0,他引:2
本文首先研究了不具有Z_2—对称性时的规范形理论和退化向量场的普适开折理论。然后利用这些理论研究了参数激励与强迫激励联合作用下非线性振动系统的尖点型奇点的余维2退化分叉。 相似文献
8.
We establish a numerically feasible algorithm to find a simplicial approximation A to a certain part
of the boundary of the set
of stable (or Hurwitz) polynomials of degree 4. Moreover, we have that
. Using this, we build an algorithm to find a piecewise-linear approximation to the intersection curve of a given surface contained in
4 with
. We have also devised an efficient computer program to perform all these operations. The main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2-parametric Hopf bifurcation problem of dimension 4. 相似文献
9.
10.
提出膛口系统是一种准耗散结构,并分析了符合耗散结构的条件,在分析分歧解线性稳定性的基础上,使用高维定态投影解定态分歧解,分歧解与实验结果吻合较好。 相似文献