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Optimal Boundary Control Method for a Flow Recirculation System Nhan Nguyen ∗ (2004)
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@MISC{Ardema04optimalboundary,
author = {Mark Ardema},
title = {Optimal Boundary Control Method for a Flow Recirculation System Nhan Nguyen ∗},
year = {2004}
}
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Abstract
This paper is concerned with the optimal control of a class of distributed systems described by first order, quasilinear hyperbolic partial differential equations. In particular, this paper investigates 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 prescribing flow controls for the wind tunnel via a compressor performance model. The boundary control variables are further constrained by a set of ordinary differential equations representing dynamics of a lumped-parameter system that models a drive compressor speed regulation dynamics. Thus, the control variables of the lumped-parameter system influence the boundary control variables, which in turn influence the state variables of the distributed system. Necessary conditions for optimality are derived using variational principles. To illustrate the theory, we consider linear-quadratic optimal control for a linear hyperbolic partial differential equation with boundary control. Future work will apply these results to obtain a numerical solution of an optimal wind tunnel flow recirculation problem.
Keyphrases
optimal boundary control method flow recirculation system nhan nguyen distributed system boundary control variable drive compressor speed regulation dynamic future work quasilinear hyperbolic partial differential equation flow recirculation optimal control problem linear-quadratic optimal control compressor performance model numerical solution flow control necessary condition first order wind tunnel boundary control state variable flow recirculation system boundary condition lumped-parameter system ordinary differential equation lumped-parameter system influence turn influence linear hyperbolic partial differential equation control variable closed-circuit wind tunnel euler equation variational principle optimal control
