Model Reduction and Controller Design for a Nonlinear Heat Conduction Problem Using Finite Element Method

作     者：Paramita Guha Mashuq Un Nabi 

作者机构：Department of Electrical EngineeringIndian Institute of Technology 

出 版 物：《International Journal of Automation and computing》 (国际自动化与计算杂志（英文版）)

年 卷 期：2012年第9卷第5期

页      码：474-479页

摘      要：The mathematical models for dynamic distributed parameter systems are given by systems of partial differential equations. With nonlinear material properties, the corresponding finite element (FE) models are large systems of nonlinear ordinary differential equations. However, in most cases, the actual dynamics of interest involve only a few of the variables, for which model reduction strategies based on system theoretical concepts can be immensely useful. This paper considers the problem of controlling a three dimensional profile on nontrivial geometries. Dynamic model is obtained by discretizing the domain using FE method. A nonlinear control law is proposed which transfers any arbitrary initial temperature profile to another arbitrary desired one. The large dynamic model is reduced using proper orthogonal decomposition (POD). Finally, the stability of the control law is proved through Lyapunov analysis. Results of numerical implementation are presented and possible further extensions are identified.

主 题 词：Thermal systems partial differential equations finite element (FE) models model reduction techniques proper orthogonal decomposition (POD) nonlinear control Lyapunov stability 

学科分类：07[理学] 070102[070102] 0701[理学-数学类] 0702[理学-物理学类] 

核心收录：

D　O　I：10.1007/s11633-012-0669-6

馆 藏 号：203840706...