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Research Papers: Gas Turbines: Aircraft Engine

Real Time Analytical Linearization of Turbofan Engine Model

[+] Author and Article Information
Gi-Yun Chung

e-mail: giyun.chung@gatech.edu

J. V. R. Prasad

e-mail: jvr.prasad@aerospace.gatech.edu
School of Aerospace Engineering,
Georgia Institute of Technology,
270 Ferst Drive,
Atlanta, GA 30332

Manuj Dhingra

e-mail: manuj.dhingra@pw.utc.com

Richard Meisner

e-mail: richard.meisner1@pw.utc.com
Pratt & Whitney,
400 Main Street,
East Hartford, CT 06108

1Corresponding author.

Contributed by the Aircraft Engine Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 9, 2013; final manuscript received August 19, 2013; published online October 22, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(1), 011201 (Oct 22, 2013) (13 pages) Paper No: GTP-13-1250; doi: 10.1115/1.4025310 History: Received July 09, 2013; Revised August 19, 2013

This paper presents a methodology for developing a control oriented analytical linear model of a turbofan engine at both equilibrium and nonequilibrium conditions. This scheme provides improved accuracy over the commonly used linearization method based on numerical perturbation and piecewise linear interpolation. Linear coefficients are obtained by evaluating at current conditions analytical expressions, which result from differentiation of simplified nonlinear expressions. Residualization of the fast dynamics states are utilized since the fast dynamics are outside of the primary control bandwidth. Analytical expressions based on the physics of the aerothermodynamic processes of a gas turbine engine facilitate a systematic approach to the analysis and synthesis of model based controllers. In addition, the use of analytical expressions reduces the computational effort, enabling linearization in real time at both equilibrium and nonequilibrium conditions to enable more accurate capture of system dynamics during aggressive transient maneuvers. The methodology is formulated and applied to a separate flow twin spool turbofan engine model in the numerical propulsion system simulation (NPSS) platform. The derived linear model is validated against the full nonlinear engine model.

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References

Figures

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Fig. 1

(a) On-equilibrium linearization [15] and (b) off-equilibrium linearization

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Fig. 2

Separate flow twin spool turbofan model

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Fig. 3

Engine dynamics residualization

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Fig. 4

Compressor block diagram

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Fig. 6

Burner block diagram

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Fig. 7

Turbine block diagram

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Fig. 8

Nozzle block diagram

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Fig. 9

Linearization about arbitrary point

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Fig. 10

System-level linearization

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Fig. 11

(a) Power lever angle as function of time during Bodie maneuver and (b) fuel input during Bodie maneuver

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Fig. 12

Bodie trajectory on HPC map (scaled)

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Fig. 13

Closed loop model uncertainty [23,24]

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Fig. 14

Change in temperature at different stations during Bodie maneuver at sea-level static

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Fig. 15

Change in pressure at different stations during Bodie maneuver at sea-level static

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Fig. 16

Shaft dynamics during Bodie maneuver at sea-level static

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Fig. 17

Comparison of additive uncertainty using different linearization schemes at sea-level static

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Fig. 18

Comparison of the ν-gap metric using different linearization schemes at sea-level static

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Fig. 19

Model inversion control block diagram

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Fig. 20

Model inversion control for tracking N1

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