Optimal Control of Flow Recirculation in a Wind Tunnel

Abstract

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This paper is concerned with a new model-based control approach using first order, quasilinear hyperbolic partial differential equations to investigate an optimal control problem of a flow recirculation system; namely, a closed-circuit wind tunnel. The flow recirculation is modeled by the Euler equations with boundary conditions that prescribe control variables for the wind tunnel flow via a compressor performance model. The compressor control variables at the system boundaries are further constrained by a set of ordinary differential equations that describe lumped-parameter system dynamics of drive motors and an inlet guide vane actuation system. Thus, the distributed PDE system and the lumped-parameter ODE system are coupled together such that PDE control variables at the boundary become the state variables for the ODE system. Necessary conditions for optimality are derived using variational principles. We apply theoretical results to investigate optimal trajectories of the compressor control variables for a wind tunnel.