论文标题

机械Frenkel-Kontorova模型边界控制的实验平台

Experimental Platform for Boundary Control of Mechanical Frenkel-Kontorova Model

论文作者

Do, Loi, Pučejdl, Krištof, Hurák, Zdeněk

论文摘要

在本文中,我们提出了一个实验室机电平台,用于实验验证和证明Frenkel-Kontorova(FK)模型所表现出的各种动力学和控制系统现象,这是一个正弦 - 戈登方程的空间分散版本。该平台由围绕单个轴旋转的一系列扭转耦合摆组成,该轴可以通过电动机以边界进行控制,而所有角度都是电子读取的。我们首先介绍和描述平台,提供其机电设计和软件体系结构的详细信息。所有文件均通过公共存储库以开源许可与研究社区自由共享。这种共享的动机是帮助可重复性或研究 - 该平台对于其他人来说是对此类动态系统的控制算法的测试床,例如,分布式控制或对灵活结构的控制。然后,在本文的第二部分中,我们使用针对FK模型量身定制的两个控制问题公式展示了该平台 - 我们讨论了研究这些问题的实际动机,提出了(某些)解决这些问题的方法,并使用实验证明了它们的功能。特别是,在从另一个边界发出的干扰的情况下,第一个控制配方涉及通过阵列一个边界对单个摆的非聚解控制/调节;第二个控制问题包括同步摆的角速度。肯定可以使用所提出的平台来制定,解决和证明其他一些动机问题。

In this paper, we present a laboratory mechatronic platform for experimental verification and demonstration of various dynamical and control system phenomena exhibited by the Frenkel-Kontorova (FK) model -- a spatially discretized version of the sine-Gordon equation. The platform consists of an array of torsionally coupled pendulums pivoting around a single shaft that can be controlled through the motors at boundaries while all angles are read electronically. We first introduce and describe the platform, providing details of its mechatronic design and software architecture. All the files are freely shared with the research community under an open-source license through a public repository. The motivation for this sharing is to help reproducibility or research -- the platform can be useful for others as a testbed for control algorithms for this class of dynamical systems, for instance, distributed control or control of flexible structures. In the second part of the paper, we then showcase the platform using two control problem formulations tailored to the FK model -- we discuss the practical motivation for studying these problems, propose (some) methods for solving them and demonstrate the functionality using experiments. In particular, the first control formulation deals with non-collocated control/regulation of a single pendulum through one boundary of the array in the presence of a disturbance sent from the other boundary; the second control problem consists in synchronizing pendulums' angular speeds. Some other motivated problems can certainly be formulated, solved, and demonstrated using the proposed platform.

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