Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application

[+] Author and Article Information
Nhan Nguyen

 NASA Ames Research Center, Mail Stop 269-1, Moffett Field, CA 94035

Mark Ardema

 Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053

J. Dyn. Sys., Meas., Control 128(4), 946-959 (Apr 26, 2006) (14 pages) doi:10.1115/1.2362814 History: Received November 18, 2004; Revised April 26, 2006

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

NASA Ames 11 by 11ft Transonic Wind Tunnel

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Figure 2

NASA Ames 11 by 11ft Transonic Wind Tunnel Mach number envelope

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Figure 3

Distributed parameter control block diagram

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Figure 4

Mach number transition

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Figure 5

Test model induced friction factor perturbation

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Figure 6

Solution surface of a(x,t)

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Figure 7

Optimal control input perturbations to rive motors and IGV system

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Figure 8

Solution surface of total pressure perturbation

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Figure 9

Test section Mach number response

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Figure 10

Compressor speed response

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Figure 11

IGV flap position response




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