Optimal Boundary Control Method for a Flow Recirculation System

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. ∗Aerospace Engineer, NASA Ames Research Center, Moffett Field, CA 94035 †Professor, AIAA Associate Fellow, Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053 1