Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

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.     

STATIONARY TANGENT: THE DISCRETE AND NON-SMOOTH CASE

Abstract. In Keich (2000 ),we define a stationary tangent process, or a locally optimal stationary approximation, to a real non-stationary smooth Gaussian process. This paper extends the idea by constructing a discrete tangent – a `locally' optimal stationary approximation – for a discrete time, real Gaussian process. Analogously to the smooth case, our construction relies on a generalization of the recursion formula for the orthogonal polynomials of the spectral distribution function. More precisely, we use a generalization of the Schur parameters to identify the stationary tangent. By way of discretizing, we later demonstrate how this tangent can be used to obtain `good' local stationary approximations to non-smooth continuous time, real Gaussian processes. Further, we demonstrate how, analogously to the curvatures in the smooth case, the Schur parameters can be used to determine the order of stationarity of a non-smooth process.     

Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants

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.     

Efficient and accurate approach for powder compaction problems

 In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations. Received: 20 March 2002 / Accepted: 15 October 2002 The partial financial support of the Ministerio de Ciencia y Tecnología (grant number DPI 2001-2204) is gratefully acknowledged.     

Application of Galerkin Method to Dynamical Behavior of Viscoelastic Timoshenko Beam with Finite Deformation

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.     

含损伤软化材料层合板承压时的分叉分析

本文讨论了由纤维和树脂-损伤应变软化材料组成的层合板在面内受压时的压缩分叉。用有限变开理论和半解析有限元法建立了相应的分叉方程,并进行数值模拟。计算结果表明,分叉将在损伤材料的应变软化阶段发生,为剪切带形分叉,损伤材料骨有剪应变集中,而且在纤维和树脂的界面附近有较大的剪应变突变等现象。     

Dynamic-mechanical properties of polybutadiene rubbers

The dynamic properties of high-cis (98%) and cis-trans (42% cis) polybutadienes, crosslinked with 0.1 to 1.0% of crosslinking agent, have been studied using a torsion pendulum method over the temperature range ?170 to +20°C. For the high-cis rubber plots of damping factor (tan δ) against temperature showed the expected peak in the glass-transition region with an additional peak in the neighbourhood of 0°C attributable to crystallization. The cis-trans rubber showed two damping maxima in the transition region, separated by 30 to 40°C (depending on the degree of crosslinking), suggesting incipient phase separation of the component structures. The rebound resilience of the high-cis rubber at room temperature exceeded that of the cis-trans, reaching 92% at the highest crosslink density. Plots of resilience versus temperature for both rubbers showed a single minimum in the glass transition region.     

Fast‐scale bifurcation in power‐factor‐correction buck‐boost converters and effects of incompatible periodicities

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.     

带有给定切线多边形的保形有理三次B样条曲线

本文给出了带有给定切线多边形的保形有理三次Ｂ样条曲线，其部分权因子可通过选取切点的位置来确定，由此方法还导出了保形有理三次Ｂ样条插值曲线，最后，给出了两个例子。     

固定化酵母粒子中生产乙醇的定态分岔行为研究

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。