Black-Box Modeling and Optimal Control of a Two-Phase Flow Using Level Set Methods

An approach for optimal control of the interface between water and ferrofluid in a 2-D two-phase flow is proposed in the presence of a magnetic field generated by a matrix of driving electromagnets. First, a model combining Navier–Stokes equations and level set methods is developed. Since it is very computationally demanding, an approximate black-box model based on neural networks replacing the original model is constructed for the purpose of control design. In particular, one-hidden-layer feedforward neural networks with a different number of neurons are trained to predict the water–ferrofluid behavior with accuracy. Then, optimal control based on such black-box models is addressed by selecting the currents flowing in the electromagnets that minimize a cost function given by the symmetric difference between the desired shape and the actual interface separating water and ferrofluid. Numerical results based on both simulation and experimental data collected on the field showcase the effectiveness of the proposed approach.