Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm

Abstract

We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid–structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.

A realizable data-driven approach to delay bypass transition with control theory

“…The control problem alone needs only the portion of the system that is observable and controllable. The practice of model reduction in flow control was treated in Bagheri et al (2009), Semeraro et al (2011), Poussot-Vassal & Sipp (2015 and Yao & Jaiman (2017). The approach was shown to be successful in the sense that the solution to the control problem was nearly unaffected by the use of a ROM.…”

An Efficient Deep Learning Technique for the Navier-Stokes Equations: Application to Unsteady Wake Flow Dynamics

“…Finally, we demonstrated that the trained CNN can be used to predict many different geometries. The efficient prediction of force coefficients using the present data-driven method has a great value for the iterative engineering design and the feedback flow control[34]. We hope that this work will help to expand the use of deep neural networks in a wider range of CFD applications.D and t, τ ≥ 0 can be expressed as: Lψ(x, t) = ∆p 2µ ψ(x, t), (B.1) LG(x, t; ξ, τ ) = δ(x − ξ)δ(t − τ ), (B.2) where D is the fluid domain of interest and ξ and τ are the dummy variables.…”

Resolvent-based approach for H2-optimal estimation and control: an application to the cylinder flow

“…The work of Rowley [49] further extended balanced truncation to high-dimensional systems where approximate balanced truncation can be achieved using a snapshot-based algorithm named balanced proper orthogonal decomposition (BPOD). The ERA is a system identification method that is equivalent to BPOD and allows direct application to flow systems using only DNS or experimental data [7,32,25,56,57] without requiring simulations of the adjoint system. These methods were originally designed for stable systems of large dimension and were subsequently extended to unstable systems either by a state-projection method [1] or by limiting the sampling time [25].…”

Stability analysis of passive suppression for vortex-induced vibration

“…Mathematically equivalent to the balanced POD (Ma, Ahuja & Rowley 2011), the ROM resulting from the ERA is a linear projection of the original system on the set of modes possessing the most observable and controllable flow structures. Recently, the ERA-based ROM has been used for stability analysis and flow control problems by the fluid mechanics community in various instances (Ma et al 2011;Flinois, Morgans & Schmid 2015;Flinois & Morgans 2016;Yao & Jaiman 2017a). The work presented by Yao & Jaiman (2017b) attempts to construct a unified description of frequency lock-in for elastically mounted cylinders.…”

Model-based estimation of vortex shedding in unsteady cylinder wakes

“…Physics-driven approaches derive models based on the Navier-Stokes equations, including the Galerkin-POD method [7] and a recently developed resolvent-based method [8][9][10]. Alternatively, models can be built via data-driven approaches, including Dynamic Mode Decomposition (DMD) [11], Artificial Neural Networks (ANN) [12], Sparse Identification of Nonlinear Dynamics (SINDy) [13], and the Eigensystem Realization Algorithm (ERA) [14,15].…”