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On solitary *** 2 A unified perturbation theory for higher-order waves

Acta Mechanica Sinica 2005年第6期21卷 515-530页

作者： Theodore Yaotsu Wu Xinlong Wang Wendong Qu California Institute of Technology Pasadena CA 91125 U.S.A. Fellow Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China State Key Laboratory of Modern Acoustics and Institute of Acoustics Nanjing University Nanjing 210093 China California Institute of Technology Pasadena CA 91125 U.S.A PIMCO Newport Beach CA 92660 U.S.A.

A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n）（the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.

关键词： Solitary waves on water Unified perturbation theory base functions base parameters Asymptotic representation

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Predictive functional control （PFC） and its application in chlorinated polyethylene process

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Journal of Zhejiang University Science 2003年第3期4卷 300-304页

作者：李鸿亮苏宏业刘军褚健 NationalKeyLaboratoryofIndustrialControlTechnology InstituteofAdvancedProcessControl MaterialandChemicalengineeringInstitute ZhejiangUniversityHongzhou310027China）

The main principle and the characteristic of Predictive Functional Control (PFC) strategy are presented in this paper and the corresponding control system aid design software APC-PFC is also introduced. For a chlorinated polyethylene (CPE) process, a design scheme of cascade predictive functional control system is described and the control performance is improved obviously.

关键词： Predictive control Predictive functional control (PFC) base functions Chlorinated Polyethylene (CPE)

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