教学研究

物理中的控制理论教学:端口哈密顿系统

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  • 1. 上海交通大学船舶海洋与建筑工程学院,上海200240; 2. 约翰霍普金斯大学怀挺工程学院,美国巴尔的摩21218
刘畅( 1995 —) ,男,江苏南京人,约翰霍普金斯大学博士研究生,主要从事控制理论在湍流中的应用.

收稿日期: 2018-12-19

  修回日期: 2019-04-02

  网络出版日期: 2019-11-14

Teaching control theory in physics: the port-Hamiltonian framework

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  • 1. School of Naval Architecture,Ocean & Civil Engineering,Shanghai Jiao Tong University,Shanghai200240,China; 2. Whiting School of Engineering,Johns Hopkins University,Baltimore21218,U.S.A

Received date: 2018-12-19

  Revised date: 2019-04-02

  Online published: 2019-11-14

摘要

控制理论具有广泛的应用,在物理课堂中教学控制理论具有重要意义. 基于哈密顿力学的端口哈密顿系统提供了一种基于物理的控制策略. 该方法为物理学科中的控制理论教学提供了重要的手段. 本文使用端口哈密顿系统描述若干经典物理系统并介绍了基于物理的控制策略,包括配置能量、耗散以及系统结构. 闭环哈密顿量是系统的李雅普诺夫函数,从而保证系统的( 渐近) 稳定性. 本文使用杜芬振子和洛伦兹系统来说明基于物理的控制策略. 最后,使用端口哈密顿系统描述了天体力学中的两个例子供读者参考.

本文引用格式

刘畅 . 物理中的控制理论教学:端口哈密顿系统[J]. 大学物理, 2019 , 38(10) : 1 . DOI: 10.16854 /j.cnki.1000-0712.180691

Abstract

The control theory has wide application and is also important in physics teaching. Based on the formalism of Hamiltonian mechanics,the port-Hamiltonian framework provides a physics-based control strategy. This framework is also promising in teaching control theory in physics. In this paper,we employ the port - Hamiltonian framework to reformulate some classical physics systems and introduce the resulting physics - based control strategies,including the energy,dissipation and structure assignments. The closed-loop Hamiltonian is thus a candidate of Lyapunov function,which achieves the ( asymptotic) stability. The introduced physics-based control strategies are demonstrated using the Duffing oscillator and the Lorenz system. We also provide port-Hamiltonian descriptions for two examples in celestial mechanics.
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