Stabilization of the fluidic pinball with gradient-enriched machine learning control

TL;DR

This paper demonstrates how gradient-enriched machine learning algorithms can effectively stabilize flow past a cluster of cylinders, with optimized control laws improving flow stability through asymmetric forcing and feedback control.

Contribution

It introduces gradient-enriched machine learning control (gMLC) for flow stabilization, outperforming genetic programming control in speed and effectiveness.

Findings

Optimal control includes asymmetric forcing.

Best performance achieved with phasor control and asymmetric steady forcing.

gMLC learns control laws faster than previous methods.

Abstract

We stabilize the flow past a cluster of three rotating cylinders, the fluidic pinball, with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open- and closed-loop manner. These laws are optimized with respect to the average distance from the target steady solution in three successively richer search spaces. First, stabilization is pursued with steady symmetric forcing. Second, we allow for asymmetric steady forcing. And third, we determine an optimal feedback controller employing nine velocity probes downstream. As expected, the control performance increases with every generalization of the search space. Surprisingly, both open- and closed-loop optimal controllers include an asymmetric forcing, which surpasses symmetric forcing. Intriguingly, the best performance is achieved by a combination of phasor control and asymmetric steady forcing. We hypothesize that asymmetric forcing is typical for pitchfork bifurcated dynamics of nominally symmetric configurations. Key enablers are automated machine learning algorithms augmented with gradient search: explorative gradient method for the open-loop parameter optimization and a gradient-enriched machine learning control (gMLC) for the feedback optimization. gMLC learns the control law significantly faster than previously employed genetic programming control. The gMLC source code is freely available online.