Reduced-order energy shaping control of large-scale linear port-Hamiltonian systems

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-09-25 DOI:10.1016/j.automatica.2024.111934

Cristobal Ponce , Hector Ramirez , Yann Le Gorrec

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引用次数: 0

Abstract

This paper is concerned with reduced-order control design for a class of high dimensional linear port-Hamiltonian systems stemming from the modeling of large-scale systems networks or from the discretization of distributed parameter systems. A class of dynamic controllers synthesized from low-dimensional and reduced-order models of the system are proposed. First, the controller structure and the criteria for asymptotic stability are established for a controller based on the full-order model. Then, using structural invariants, two design methods are proposed and compared: one based on a low-dimensional model of the system and the other on a reduced-order model based on modal truncation. With applications in shape control in mind, the system’s equilibrium points are parametrized using the controller parameters. It allows to establish an optimal criterion to minimize the norm of the error between the intended and achievable closed-loop equilibrium configurations. An asymptotic stability margin in terms of the full and low/reduced order models stiffness matrices is provided and related with the closed-loop transient performances. Mindlin plate with specific inputs is used to show how dynamic shape control can be achieved using the proposed approach.

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大规模线性端口-哈密尔顿系统的降阶能量整形控制

本文主要研究大规模系统网络建模或分布式参数系统离散化过程中产生的一类高维线性端口-哈密尔顿系统的降阶控制设计。本文提出了一类由低维和降阶系统模型合成的动态控制器。首先，为基于全阶模型的控制器建立了控制器结构和渐近稳定性标准。然后，利用结构不变式，提出并比较了两种设计方法：一种是基于系统的低维模型，另一种是基于模态截断的降阶模型。考虑到形状控制中的应用，使用控制器参数对系统的平衡点进行了参数化。这样就可以建立一个最优标准，最大限度地减小预期闭环平衡配置与可实现闭环平衡配置之间的误差。提供了全阶和低阶/降阶模型刚度矩阵的渐近稳定性裕度，并将其与闭环瞬态性能联系起来。使用带有特定输入的 Mindlin 板来展示如何利用所提出的方法实现动态形状控制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.