Sum-of-squares approach to feedback control of laminar wake flows
Sum-of-squares approach to feedback control of laminar wake flows
复制标题
层流尾流反馈控制的平方和方法
DOI：
10.1017/jfm.2016.688
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发表时间：
2016-04
影响因子：
3.7
通讯作者：
Chernyshenko Sergei
中科院分区：
文献类型：
--
作者：
Lasagna Davide;Huang Deqing;Tutty Owen R;Chernyshenko Sergei
本文提出了一种针对不可压缩流体流动的非线性反馈控制设计方法，旨在优化流量的长时间平均值。它适用于流体流动的降阶有限维模型，表示为一组一阶非线性常微分方程，右边是状态变量和控制中的多项式函数。Chernyshenko等人首先讨论了这一关键思想。反式。r . Soc。Lond。A, vol. 372, 2014, 20130350)，是通过使用这些平均值的上/下界作为目标函数来放松处理和优化成本的长期平均值的困难。在这种情况下，控制设计简化为找到一个优化边界的反馈控制器，受制于涉及成本函数、非线性系统、控制器本身和可调多项式函数的多项式不等式约束。提出了一种基于平方和技术和半定规划的数值上易于处理和有效的方法来解决这类优化问题。为了展示该方法，通过控制表面的角运动，对层流状态下圆柱后非定常尾迹在Re=100时的波动动能的减缓进行了数值研究。首先利用适当的正交分解和伽辽金投影导出了一个紧凑的降阶模型，该模型解决了流体流动的长期行为和驱动的影响。在全信息设置中，反馈控制器被设计用于减少与极限环相关的解析动能的长时间平均值。然后将这些控制器直接应用于被驱动流量的数值模拟。详细分析了控制性能、总能源效率和确定的物理控制机制。最后讨论了方法的关键要素、影响和未来的工作。
In this paper a novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. (Phil. Trans. R. Soc. Lond. A, vol. 372, 2014, 20130350), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by using the upper/lower bounds of such averages as the objective function. In this setting, control design reduces to finding a feedback controller that optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller itself and a tunable polynomial function. A numerically tractable and efficient approach to the solution of such optimisation problems, based on sum-of-squares techniques and semidefinite programming, is proposed. To showcase the methodology, the mitigation of the fluctuation kinetic energy in the unsteady wake behind a circular cylinder in the laminar regime at $Re=100$ , via controlled angular motions of the surface, is numerically investigated. A compact reduced-order model that resolves the long-term behaviour of the fluid flow and the effects of actuation, is first derived using proper orthogonal decomposition and Galerkin projection. In a full-information setting, feedback controllers are then designed to reduce the long-time average of the resolved kinetic energy associated with the limit cycle. These controllers are then implemented in direct numerical simulations of the actuated flow. Control performance, total energy efficiency and the physical control mechanisms identified are analysed in detail. Key elements of the methodology, implications and future work are finally discussed.
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影响因子：
4.6
作者：
Shao-jie Tang;N. Aubry
通讯作者：
Shao-jie Tang;N. Aubry
DOI：
10.1098/rsta.2010.0367
发表时间：
2011-04
期刊：
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
影响因子：
--
作者：
G. Tadmor;O. Lehmann;B. R. Noack;L. Cordier;J. Delville;J. Bonnet;M. Morzynski
通讯作者：
G. Tadmor;O. Lehmann;B. R. Noack;L. Cordier;J. Delville;J. Bonnet;M. Morzynski
影响因子：
2.6
作者：
M. Amaouche
通讯作者：
M. Amaouche
影响因子：
3.9
作者：
Dan Zhao;Jianliang Wang
通讯作者：
Dan Zhao;Jianliang Wang
影响因子：
3.7
作者：
B. Galletti;C. Bruneau;L. Zannetti;A. Iollo
通讯作者：
B. Galletti;C. Bruneau;L. Zannetti;A. Iollo