CLOSED-LOOP ADAPTIVE MODEL PREDICTIVE CONTROL OF A BLUFF BODY WAKE AND ANALYSIS OF MECHANISMS LEADING TO OPTIMAL SYSTEM STATES

Abstract

A machine learning methodology is outlined to achieve robust closed-loop feedback control of a bluff body turbulent wake. A Long Short-Term Memory (LSTM) Neural Network is implemented with Model Predictive Control (MPC) to achieve closed-loop flow control. The LSTM model is trained using actuation and pressure sensor data to forecast future pressure states. The candidate system is a square cross-sectional cylinder with two modulated moving surface actuators embedded in the windward face leading corners. The controller performance is tested experimentally for three objective functions: recovery of mean-base pressure set-point after perturbation; and minimization of drag or wake fluctuation intensity. An adaptive learning strategy is implemented to adjust the model to new Reynolds number (Re) conditions without user intervention, thereby extending the controller performance and achieving more robust control. A key objective of this study is to understand how the black-box controller found these optimum solutions and address their limitations by investigating how the controller and actuators affect wake dynamics, with these findings discussed later in the thesis to guide improvements in controller design, as well as actuator and sensor placement. A practical application of this research is reducing the drag on high speed vehicles. Minimum drag (MD) and minimum wake fluctuation (MWF) cases are discovered from closed-loop control optimization. To characterize the modifications to the wake, pressure data and velocity field data are obtained using Particle Image Velocimetry (PIV) for unactuated and optimized actuation cases. A Proper Orthogonal Decomposition (POD) analysis shows that most of the change in total kinetic energy (TKE) is due to significant reduction in the intensity of shed vortices. In the actuated cases, high frequency POD modes show small scale vortical structures shedding from the upper and lower surfaces of the square cylinder. The shear layer flapping interacts with these vortical structures reaching a maximum contribution to the total TKE in the MD case. These high frequency structures prevent the shear layer from rolling up, resulting in vortex shedding energy significantly decreasing. In the MD case, vortex shedding POD modes contain the lowest TKE, while the high frequency vortical structures POD modes are at their maximum TKE. In the MWF case, leeward face pressure RMS is locally minimized which corresponds to lower fluctuations right at the surface of the obstacle, however globally, vortex shedding POD modes have increased energy, and the wake fluctuations are higher compared to the MD case. This observation highlighted a major limitation of black-box controllers: while they can achieve optimal system states based on local sensor feedback, if the local quantity being optimized ceases to accurately estimate the global wake state, the black-box controller cannot determine a true global optimum.