Clusterbased control of a separating flow over a

Authors: Eurika Kaiser Bernd R Noack Andreas Spohn Louis N Cattafesta Marek Morzyński

Publish Date: 2017/01/17

Volume: 31, Issue: 5-6, Pages: 579-593

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Abstract

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications The proposed closedloop control framework addresses a key issue of modelbased control The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model Hence we employ a probabilistic approach based on a clusterbased discretization of the Liouville equation for the evolution of the probability distribution The proposed methodology frames highdimensional nonlinear dynamics into lowdimensional probabilistic linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms The datadriven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters The temporal evolution of the probability distribution on this set of clusters is then described by a controldependent Markov model This Markov model can be used as predictor for the ergodic probability distribution for a particular control law This probability distribution approximates the longterm behavior of the original system on which basis the optimal control law is determined We examine how the approach can be used to improve the openloop actuation in a separating flow dominated by Kelvin–Helmholtz shedding For this purpose the feature space in which the model is learned and the admissible control inputs are tailored to strongly oscillatory flows

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