一类平面Hamilton系统的大范围非线性化近似方法

在非线性动力系统的研究已经进入了占主导地位的时期,对其提出大范围的非线性化近似方法具有特别重要的意义。在本文中,我们主要对于一类典型的Hamilton系统,根据等势线有两个,或者三个交点的不同情形,给出7种不同的大范围最低次非线性化近似系统,并通过积分近似系统给出近似解(轨道)。结果表明,近似椭圆周期轨道可通过线性化近似系统得到,而同(异)宿轨道则可通过2、3次非线性化近似系统得到。最后,将近似方法应用于一个具体Hamilton系统的分析。

一维动力系统的大范围非线性化近似方法及其在一个商品定价模型中的应用

因为分析含有多个平衡点，或者超越函数的一维动力系统的可积性和稳定性通常是困难的，所以对一维动力系统进行简化是一个很有意义的问题．对含有2-3个平衡点的一维动力系统，根据系统右端函数的7种情况，利用Lagrange和Hermite插值多项式的方法，提出了相应的7类大范围最低次非线性化近似系统，通过积分近似系统得出部分近似解，通过稳定性分析得出平衡点的稳定性保持结果．最后，将一种近似方法应用于一个商品定价模型的具体分析，得到了定价模型的平衡价格的稳定性和动态价格的近似表达式．

LQR控制策略在旋转机架模型中的应用

以加拿大Quanser公司生产的2自由度起重机机架模型———旋转机架系统为研究对象,首先基于拉格朗日方程建立了系统的数学模型,然后对模型进行了线性化处理得到了其状态空间表达式,在此基础之上设计出了线性二次型最优控制器(LQR)。借助Matlab/Simulink和Wincon控制平台,进行了仿真与实时控制实验。结果表明,LQR控制策略具有良好的效果。

Effects of Pressure Stress Work and Viscous Dissipation in Mixed Convection Flow Along a Vertical Flat Plate

The Effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical fiat plate have been investigated. The results are obtained by transforming the governing system of boundary layer equations into a system of non-dimensional equations and by applying implicit finite difference method together with Newton＇s linearization approximation. Numerical results for different values of pressure stress work parameter, viscous dissipation parameter and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction co-efficient and the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters.

A Method to Obtain Complex Transfer Functions of Four Order DC-DC Converters

Two TFs （transfer functions） are needed to analyze switching DC-DC converters in control-voltage mode： the duty-cycle to output-voltage （control to output） and the input-voltage to output-voltage （line to output）. To obtain these TFs a small-signal analysis is required. The CCM （continuous conduction mode） and the DCM （discontinuous conduction mode） analysis are different. When a circuit includes the loss resistances of the components, the number of parameters increases considerably, making manual nodal-loop circuit analysis techniques impractical to obtain the TFs. Moreover, these circuits are bilinear （non-linear） and it is necessary to linearize the equations at a DC operating-point （approximate linearization）. Vorp6rian describes a PWM （pulse-width-modulated） switch model that includes all non-linear parts of the DC-DC switching converters. This model can be linearized and replaced on the switching converter schematic leading to a linear circuit. At this point it is possible to use symbolic analysis programs to obtain these TFs or to simply apply numerical values for either the Bode diagrams or the calculation of poles and zeros. Here we describe an application of Ekrem Cangeici＇s method on X DC-DC converter to obtain control to output and line to output TFs in CCM and DCM including loss resistances. The method presented in this paper is optimized to use in the online publishing platform OctaveRS. Also the control to output TF for PCC （peak current controlled） in CCM is obtained.

STABILIZATION OF A KIND OF PREY-PREDATOR MODEL WITH HOLLING FUNCTIONAL RESPONSE

The stabilization problem of a kind of prey-predator model with Holling fimctional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closed- loop system is obtained. On the other hand, by exact linearization approach, a suitable change of coordinates in the state space and a feedback control law render the complex nonlinear system to be a linear controllable one such that the positive equilibrium point of the closed-loop system is globally asymptotically stable.