Frequency selection by feedback control in a turbulent shear flow

Abstract

Many previous studies have shown that the turbulent mixing layer under periodic forcing tends to adopt a lock-on state, where the major portion of the fluctuations in the flow are synchronized at the forcing frequency. The goal of this experimental study is to apply closed-loop control in order to provoke the lock-on state, using information from the flow itself. We aim to determine the range of frequencies for which the closed-loop control can establish the lock-on, and what mechanisms are contributing to the selection of a feedback frequency. In order to expand the solution space for optimal closed-loop control laws, we use the genetic programming control (GPC) framework. The best closed-loop control laws obtained by GPC are analysed along with the associated physical mechanisms in the mixing layer flow. The resulting closed-loop control significantly outperforms open-loop forcing in terms of robustness to changes in the free-stream velocities. In addition, the selection of feedback frequencies is not locked to the most amplified local mode, but rather a range of frequencies around it.

Drag reduction of a car model by linear genetic programming control

“…Sensor-based feedback has been shown to outperform periodic forcing for drag reduction of a D-shaped body (Pastoor et al 2008). A very general method for sensor-based feedback is provided by genetic programming control (GPC) (Gautier et al 2015;Debien et al 2016;Parezanović et al 2016). Yet, the advantages of filtering out noise has hardly been explored in GPC ).…”

“…In addition, there is no a priori reason why sensor-based feedback should be better than optimized forcing. In fact, a mixing layer control study (Parezanović et al 2016) shows that optimized periodic forcing may be better or worse than sensor-feedback depending on the location of the sensors and the definition of the cost functional. However, closed-loop control laws may be formulated in a manner to include the optimal open-loop control.…”

“…The regression problem is solved with symbolic genetic programming using the plant (experiment) to evolve the control law. This model-free control strategy can detect and exploit nonlinear actuation mechanisms in an unsupervised manner as evidenced in several shear flow control experiments (Gautier et al 2015;Debien et al 2016;Parezanović et al 2016).…”

Sliding mode control applied to a square-back Ahmed body

“…Unsupervised generic methodology based on machine learning which can exploit arbitrary nonlinearities in complex systems has recently gain traction on the past years in the fluid mechanics community to, literarily, learn a control law. As a pioneer work, Noack and co-authors used genetic programming to achieve both structure and parameters identification of control laws in the context of various turbulence flow control problems even at high Reynolds numbers [46,29,20,18]. One of the obstacles of using machine learning, such as introduced in Duriez et al [20], is that a large number of experiments are required to fulfill the criterion of statistical convergence.…”

Synchronization control of oscillator networks using symbolic regression

“…Previous attempts to use symbolic regression for the control of dynamical systems were mostly restricted to experiments [1,24,25] without multiobjectivity and without the optimization of constants involved in the equations. In contrast, here we use a multi-objective formulation of GP, which allows learning much sparser, as well as multiple Pareto (or non-dominated) solutions [20,21,22].…”