Interpolatory Model Reduction for the Control of Fluids

流体控制的插值模型简化

基本信息

项目摘要

Fluid flow control problems are ubiquitous. They arise in important applications such as drag reduction (with the benefits of saving fuel or improving range/speed), enhancing mixing (for more efficient combustion), reducing structural fatigue, improved solidification and die casting, and efficient cooling in large indoor-air environments. However, the ever-increasing need for improved accuracy and complexity of the underlying flow problems lead to very large-scale dynamical systems whose simulations and control make overwhelming and unmanageable demands on computational resources. This research project aims to develop novel computational techniques and a new rigorous mathematical framework to solve large-scale flow control problems very efficiently. In addition, the project will develop a year-long graduate course on Model Reduction and Flow Control and will provide students with valuable interdisciplinary education.The current state-of-the-art is to solve flow control problems by using reduced models constructed using the proper orthogonal decomposition. However, these models are limited in that they are only guaranteed to be accurate for a pre-selected range of inputs. This project will provide significantly improved tools for the efficient analysis and approximation of large-scale dynamical systems. It will also have direct application to model reduction for problems with bilinear and quadratic nonlinearities. Bilinear models arise in control problems for heat exchangers, and nonlinear partial differential equations with quadratic nonlinearities include the Korteweg-de Vries (shallow waves), the Kuramoto-Sivashinsky (turbulent flames), and the Landau-Lifshitz (magnetic fields in solid state physics) equations. Using rational interpolation, this research will lead to new algorithms to systematically perform high-fidelity, in most cases optimal, model reduction for linear and nonlinear systems associated with (discretized) flow equations. These reduced models will be used to design optimal feedback laws. The new framework will offer major advantages: First, unlike current approaches, the proposed control design will not require expensive full-order, time-accurate simulations for specific input trajectories or solutions of large dense matrix equations; the computational efforts lie in computing a steady-state solution and solving a modest number of sparse linear systems. Second, the reduced models will be uniformly accurate for a wide range of input profiles and will not depend on specific input trajectories. Third, the methodology will naturally create reduced models that respect the stability properties of the original flow.
流体流动控制问题是普遍存在的。它们出现在重要的应用中,如减少阻力(节省燃料或提高范围/速度的好处),加强混合(更有效的燃烧),减少结构疲劳,改善凝固和压铸,以及在大型室内空气环境中的有效冷却。然而,对潜在流动问题的精度和复杂性的不断提高的需求导致了非常大规模的动力系统,其模拟和控制对计算资源提出了压倒性的和难以管理的要求。本研究项目旨在开发新的计算技术和新的严格的数学框架,以非常有效地解决大规模流动控制问题。此外,该项目将开设为期一年的模型简化和流量控制研究生课程,为学生提供有价值的跨学科教育。目前的发展趋势是利用适当的正交分解构造的简化模型来解决流量控制问题。然而,这些模型是有限的,因为它们只能保证在预先选择的输入范围内是准确的。该项目将为大规模动力系统的有效分析和近似提供显著改进的工具。它也将直接应用于双线性和二次非线性问题的模型简化。双线性模型出现在热交换器的控制问题中,具有二次非线性的非线性偏微分方程包括Korteweg-de Vries(浅波),Kuramoto-Sivashinsky(湍流火焰)和Landau-Lifshitz(固态物理中的磁场)方程。利用合理插值,本研究将产生新的算法,系统地执行高保真度,在大多数情况下是最优的,与(离散)流动方程相关的线性和非线性系统的模型简化。这些简化模型将用于设计最优反馈律。新框架将提供主要优势:首先,与目前的方法不同,所提出的控制设计将不需要昂贵的全阶,时间精确的模拟特定的输入轨迹或大型密集矩阵方程的解;计算的努力在于计算一个稳态解和求解有限数量的稀疏线性系统。其次,简化后的模型对于大范围的输入曲线是一致准确的,并且不依赖于特定的输入轨迹。第三,该方法将自然地创建尊重原始流的稳定性特性的简化模型。

项目成果

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Serkan Gugercin其他文献

Interpolatory weighted-H2H2 model reduction
插值加权 H2H2 模型简化
  • DOI:
    10.1016/j.automatica.2013.01.040
  • 发表时间:
    2013
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Branimir Anić;Christopher A. Beattie;Serkan Gugercin;Athanasios C. Antoulas
  • 通讯作者:
    Athanasios C. Antoulas
The AAA framework for modeling linear dynamical systems with quadratic output
用于对具有二次输出的线性动力系统进行建模的 AAA 框架
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
  • DOI:
    10.1016/j.automatica.2012.05.052
  • 发表时间:
    2012-09-01
  • 期刊:
  • 影响因子:
  • 作者:
    Serkan Gugercin;Rostyslav V. Polyuga;Christopher Beattie;Arjan van der Schaft
  • 通讯作者:
    Arjan van der Schaft

Serkan Gugercin的其他文献

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{{ truncateString('Serkan Gugercin', 18)}}的其他基金

Collaborative Research: Nonlinear Balancing: Reduced Models and Control
合作研究:非线性平衡:简化模型和控制
  • 批准号:
    2130695
  • 财政年份:
    2022
  • 资助金额:
    $ 31.99万
  • 项目类别:
    Standard Grant
AMPS: Model Reduction for Analysis, Identification, and Optimal Design of Power Networks
AMPS:用于电力网络分析、识别和优化设计的模型简化
  • 批准号:
    1923221
  • 财政年份:
    2019
  • 资助金额:
    $ 31.99万
  • 项目类别:
    Standard Grant
Efficient Algorithms for Optimal Control of Time-Periodic and Nonlinear Systems
时间周期和非线性系统最优控制的高效算法
  • 批准号:
    1819110
  • 财政年份:
    2018
  • 资助金额:
    $ 31.99万
  • 项目类别:
    Standard Grant
CAREER: Reduced-order Modeling and Controller Design for Large-scale Dynamical Systems via Rational Krylov Methods
职业:通过 Rational Krylov 方法对大型动力系统进行降阶建模和控制器设计
  • 批准号:
    0645347
  • 财政年份:
    2007
  • 资助金额:
    $ 31.99万
  • 项目类别:
    Standard Grant

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