Systematic experimental exploration of nonlinear structures with control-based continuation

基于控制延拓的非线性结构的系统实验探索

• 批准号: EP/K032739/1
• 负责人: David Barton
• 金额: $ 11.9万
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK032739%2F1
• 关键词: Systematic; experimental; exploration; nonlinear; structures

In numerous research areas across engineering and the applied sciences there are nonlinear structures or systems for which there are inadequate or multiple competing mathematical models. This is often caused by a poor understanding of the physics at the appropriate scale. Two examples of this are the study of shimmy oscillations in aircraft landing gear, and the onset of chatter during high-speed machining. In these areas experimental investigations are of fundamental importance in order to resolve the details that the models cannot.However, systematically investigating nonlinear dynamics in an experiment is fraught with difficulties due to the potential for sudden changes in the dynamics as system parameters are varied; moreover, the changes may be qualitative as well as quantitative. For example, for particular choice of parameters a system may have a single stable steady-state whereas for another choice it may become bistable. Of particular interest are the boundaries between different types of qualitative behaviour (so-called bifurcations). This proposal seeks to make the determination of these boundaries in a physical experiment a normal and routine task by leveraging ideas from control theory and dynamical systems, and so reveal previously unseen dynamical phenomena.Control-based continuation is a new method, developed in Bristol in 2008, for systematically characterising the qualitative behaviour of a physical nonlinear experiment. Its potential has been recognised by experimenters in other institutions, who are now applying it to their own systems. The key idea is that dynamical features of the system, such as stability changes or the onset of mixed-mode oscillations, can be found and tracked directly in a physical experiment using a combination of feedback control and numerical path following techniques. Thus a `map' or bifurcation diagram showing different regions of qualitative behaviour can be traced out.To enable the widespread uptake of control-based continuation three key objectives must be satisfied. (1) It must be possible to determine the local linearisation of a steady-state, thus providing additional dynamical information and a means to perform on-line controller design/adaptation. (2) The underpinning numerical methods must be made fast and robust. (3) The scalability of control-based continuation to multi-degree-of-freedom systems must be demonstrated. This proposal seeks to address all three points.

在工程和应用科学的许多研究领域中，存在非线性结构或系统，对于这些非线性结构或系统，存在不足或多个竞争的数学模型。这通常是由于在适当的尺度上对物理学的理解不足造成的。这方面的两个例子是飞机起落架摆振振荡的研究，以及高速加工过程中颤振的发生。在这些领域中，实验研究对于解决模型无法解决的细节问题至关重要。然而，在实验中系统地研究非线性动力学充满了困难，因为当系统参数发生变化时，动力学可能会发生突然的变化，而且这种变化可能是定性的，也可能是定量的。例如，对于参数的特定选择，系统可能具有单一稳定的稳态，而对于另一种选择，它可能变得不稳定。特别令人感兴趣的是不同类型的定性行为（所谓的分叉）之间的界限。该建议旨在通过利用控制理论和动力系统的思想来确定物理实验中的这些边界，从而揭示以前看不见的动力学现象。基于控制的延续是一种新方法，于2008年在布里斯托开发，用于系统地表征物理非线性实验的定性行为。它的潜力已经被其他机构的实验人员所认识，他们现在正在将其应用到自己的系统中。其关键思想是，系统的动态特性，如稳定性的变化或混合模式振荡的发生，可以发现和跟踪直接在物理实验中使用的反馈控制和数值路径跟踪技术相结合。因此，一个“地图”或分叉图显示不同区域的定性行为可以追溯出来。为了使控制为基础的连续性的广泛吸收，三个关键目标必须得到满足。(1)它必须是可能的，以确定一个稳定状态的局部线性化，从而提供额外的动态信息和一种手段来执行在线控制器的设计/适应。(2)托换数值方法必须快速和鲁棒。(3)必须证明基于控制的连续多自由度系统的可扩展性。这项建议旨在解决所有三个问题。

项目成果

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

• DOI: 10.1142/s0218127417300026
• 发表时间: 2017-02
• 期刊: Int. J. Bifurc. Chaos
• 作者: L. Renson;D. Barton;S. Neild

Identifying the significance of nonlinear normal modes.

• DOI: 10.1098/rspa.2016.0789
• 发表时间: 2017-03
• 期刊: Proceedings. Mathematical, physical, and engineering sciences
• 作者: Hill TL;Cammarano A;Neild SA;Barton DAW
• 通讯作者: Barton DAW

Force appropriation of nonlinear structures.

• DOI: 10.1098/rspa.2017.0880
• 发表时间: 2018-06
• 期刊: Proceedings. Mathematical, physical, and engineering sciences
• 作者: Renson L;Hill TL;Ehrhardt DA;Barton DAW;Neild SA
• 通讯作者: Neild SA

Control-based continuation: Bifurcation and stability analysis for physical experiments

• DOI: 10.1016/j.ymssp.2015.12.039
• 发表时间: 2017-02-01
• 期刊: MECHANICAL SYSTEMS AND SIGNAL PROCESSING
• 影响因子: 8.4
• 作者: Barton, David A. W.

Nonlinear Dynamics, Volume 1

非线性动力学，第 1 卷

• DOI: 10.1007/978-3-319-29739-2_3
• 发表时间: 2016
• 作者: Renson L