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Research Papers

Modeling of Atmospheric Turbulence as Disturbances for Control Design and Evaluation of High Speed Propulsion Systems

[+] Author and Article Information
George Kopasakis

 National Aeronautics and Space Administration Glenn Research Center, Cleveland, OH 44135 e-mail: gkopasakis@nasa.gov

J. Dyn. Sys., Meas., Control 134(2), 021009 (Dec 30, 2011) (12 pages) doi:10.1115/1.4005368 History: Received July 08, 2010; Revised June 21, 2011; Published December 30, 2011; Online December 30, 2011

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying integrated couplings between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms. Then a generalized formulation is developed in frequency domain for these scale models that approximates the fractional order with the products of first order transfer functions. Given the parameters describing the conditions of atmospheric disturbances and utilizing the derived formulations, the objective is to directly compute the transfer functions that describe these disturbances for acoustic velocity, temperature, pressure, and density. Utilizing these computed transfer functions and choosing the disturbance frequencies of interest, time domain simulations of these representative atmospheric turbulences can be developed. These disturbance representations are then used to first develop considerations for disturbance rejection specifications for the design of the propulsion control system and then to evaluate the closed-loop performance.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Wind and potential temperature spectra as reported by Nastrom and Gage [1]. Note: for clarity, the meridional wind and temperature spectra have been shifted one and two decades to the right, respectively.

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Figure 2

Acoustic wave velocity spectral comparisons for the Kolmogorov and von Karman spectral

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Figure 3

Longitudinal acoustic wave velocity spectral comparisons for different integral length scales

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Figure 4

Longitudinal acoustic wave velocity spectral comparisons for different eddy dissipation rates

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Figure 5

Equivalent TF of atmospheric disturbance

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Figure 6

Longitudinal von Karman spectral, final adjusted TF fit

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Figure 7

Transverse von Karman spectral, final adjusted TF fit

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Figure 8

Temperature von Karman spectral and its TF fit

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Figure 9

von Karman acoustic wave velocity spectral due to temperature gust and its TF fits for different eddy dissipation rates

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Figure 10

von Karman acoustic wave velocity spectral due to temperature gust and its TF fits for different integral scale lengths

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Figure 11

Pressure von Karman spectral and its TF fit

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Figure 12

von Karman longitudinal acoustic wave velocity spectral and its TF fits due to different values of eddy dissipation rates and integral length scales

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Figure 13

Feedback control diagram of inlet shock position system via bypass door actuation

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Figure 14

Atmospheric disturbances of Eqs. 30, 32,33,34, with unit amplitude input sinusoids

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Figure 15

Shock disturbance, control command, valve position, and shock position response due to atmospheric disturbances

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Figure 16

Combined atmospheric wind gust for disturbance frequencies 0.2–30 Hz, with ɛ = 8.6 × 10−5

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Figure 17

Shock disturbance for disturbance frequencies 0.2–30 Hz, with ɛ = 8.6 × 10− 5

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Figure 18

Shock control response for disturbance frequencies 0.2–30 Hz, with ɛ = 8.6 × 10− 5

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Figure 19

Combined atmospheric wind gust for disturbance frequencies 5–30 Hz, with ɛ = 1.7 × 10− 3

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Figure 20

Shock disturbance for disturbance frequencies 5–30 Hz, with ɛ = 1.7 × 10− 3

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Figure 21

Shock control response for disturbance frequencies 5–30 Hz, with ɛ = 1.7 × 10− 3

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