Using dominant modes for optimal feedback control of 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’ strategy is often employed for flow control of many engineering and industrial applications. In this study, the authors develop a linear quadratic regulator control to suppress fluctuating forces on a circular cylinder using a proper orthogonal decomposition based low-dimensional model. They 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, they compute the proper orthogonal decomposition basis functions (modes) of the divergence-free velocity and pressure fields. The authors project the Navier–Stokes equations onto these proper orthogonal decomposition modes to develop a reduced-order model. Later, they 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. They linearize the system about the mean velocity and apply optimal control. The authors 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.


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  • Accession Number: 01498964
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Nov 12 2013 9:17AM