Control and Observation of Mixing and Fluid Flow

Northeastern University, Boston MA

Investigators

Abstract

The objective of the proposed research is to develop generic methods for active feedback control of complex, non-equilibrium fluid flow. While active control of fluid flow has been studied, the use of feedback in non-equilibrium flows is largely a new territory. A main hindrance to applying off-the-shelf control methods is the absence of appropriate models. Existing models tend to either be simplistic steady models or, on the other extreme, complex computational fluid dynamics (CFD) simulation models, whose mere size and the lack of an invariant concept of state space are prohibitive in feedback design. The modeling challenge goes hand in hand with the development of practical design tools, tailored to the needs of fluid flow applications, and utilizing their ``redeeming factors". Such factors include the formation of few, large coherent structures, periodicity of some reference orbits, and useful concepts of Hamiltonian energy. A focus on periodic characteristics of coherent structures, such as the period itself, extrema of relevant indices over a period, and, indeed, leading Fourier coefficients (phasors), reduces the model to manageable size and incorporates intrinsic filtering. That filtering (both spatially and temporally) is expected to reduce effects of chaotic and stochastic dynamics, that feasible control methods are likely to be unable to address. Under typical, periodic and low gain actuation, periodic characteristics of both the controlled structure and sensor signals are expected to be slowly varying. In its simplest form, an observer model would be that of fixed period and phasors. Identified algebraic and / or (slow) dynamic relationships between periodic characteristics of the sensor signal, the actuation signal and those of the controlled structure, together will comprise the control-oriented system model and will be used for control design. That is, feedback control will translate observed slow variations in the periodic characteristics of the system into slow variations in the periodic characteristics of the actuation signal. Energy storage expressions for the lumped model can be used for feasible control design, such as in regulating the total stored energy, or the periodic energy exchange between relevant Hamiltonians.