Using dominant modes for optimal feedback control of aerodynamic forces

作者：Akhtar Imran^*; Naqvi Muntazir; Borggaard Jeff; Burns John A

来源：Proceedings of the Institution of Mechanical Engineers - Part G: Journal of Aerospace Engineering , 2013, 227(12): 1859-1869.

DOI：10.1177/0954410012466348

• Proper orthogonal decomposition
• reduced-order model
• linear quadratic regulator control
• Navier-Stokes equations
• aerodynamic forces

The problem of active feedback control of fluid flows falls into a class of problems in the area of distributed parameter control, typically defined by partial-differential equations. Physical processes modeled by partial-differential equations are infinite-dimensional systems and are often simulated by numerical methods. However, for complex flows, the degrees of freedom may still be of the order of millions and are not practical for direct use in control design and optimization of fluid flow systems. Consequently, reduce-then-control%26apos; strategy is often employed for flow control of many engineering and industrial applications. In this study, we develop a linear quadratic regulator control to suppress fluctuating forces on a circular cylinder using a proper orthogonal decomposition based low-dimensional model. We numerically simulate the flow past a circular cylinder by solving the incompressible Navier-Stokes equations, and record the flow field data over one vortex shedding cycle. Using the data ensemble, we compute the proper orthogonal decomposition basis functions (modes) of the divergence-free velocity and pressure fields. We project the Navier-Stokes equations onto these proper orthogonal decomposition modes to develop a reduced-order model. Later, we modify the model by applying suction on the cylinder surface and adding a control function in the velocity expansion. The nonlinear dynamical system thus developed is linearly unstable due to negative damping in the system. We linearize the system about the mean velocity and apply optimal control. We seek to minimize the fluctuating forces on the cylinder using a reasonable amount of control effort. The novelty in this control strategy lies in feeding back only the dominant mode to suppress the fluctuating forces. On the contrary, feedback of higher modes fails to control and destabilizes the system.

• 出版日期2013-12
• 单位美国弗吉尼亚理工大学(Virginia Tech)