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Research Papers: Gas Turbines: Aircraft Engine

Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

[+] Author and Article Information
Mehrdad Pakmehr

Postdoctoral Fellow
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: mehrdad.pakmehr@gatech.edu

Nathan Fitzgerald

Propulsion Development Engineer
Aurora Flight Sciences Corporation,
Manassas, VA 20110
e-mail: nfitz@alum.mit.edu

Eric M. Feron

Professor
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: feron@gatech.edu

Jeff S. Shamma

Professor
School of Electrical and Computer Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: shamma@gatech.edu

Alireza Behbahani

Senior Aerospace Engineer
Air Force Research Laboratory,
Wright-Patterson Air Force Base, OH 45433
e-mail: alireza.behbahani@wpafb.af.mil

1Corresponding author.

Contributed by the Aircraft Engine Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 29, 2013; final manuscript received September 30, 2013; published online November 14, 2013. Editor: David Wisler.This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Eng. Gas Turbines Power 136(3), 031201 (Nov 14, 2013) (15 pages) Paper No: GTP-13-1332; doi: 10.1115/1.4025637 History: Received August 29, 2013; Revised September 30, 2013

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

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Figures

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Fig. 1

Schematic of the output dependent gain scheduled control system

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Fig. 2

Schematic of the output dependent gain scheduled control system with saturation

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Fig. 3

Controller interpolation schematic

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Fig. 4

Schematic of the stability region and the equilibrium manifold

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Fig. 5

JetCat SPT5 turboshaft engine setup on the test stand

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Fig. 6

Ap(α(t)) components as functions of scheduling parameter α(t)

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Fig. 7

Bp(α(t)) components as functions of scheduling parameter α(t)

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Fig. 8

xep(α(t)) and ue(α(t)) as functions of scheduling parameter α(t)

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Fig. 9

Engine equilibrium manifold in 3D space of spool speeds and fuel control input

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Fig. 10

Kp(α(t)) components as functions of scheduling parameter α(t)

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Fig. 11

Ki(α(t)) components as functions of scheduling parameter α(t)

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Fig. 12

JetCat SPT5 engine compressor map with data points used to compute P

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Fig. 13

History of the optimization error (eopt(t))

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Fig. 14

History of the coefficients βi,i=1,...,40

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Fig. 15

History of the states (xp(t)) for the nonlinear system and the linear parameter dependent model

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Fig. 16

History of the rate of states (x·p(t)) for the nonlinear system and the linear parameter dependent model

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Fig. 17

Norm of the closed-loop system matrices (‖Acl(t)‖), and (‖Bcl(t)‖)

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Fig. 18

Closed-loop system eigenvalues (λ[Acl(α(t))])

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Fig. 19

Scheduling parameter (α(t) = ‖xp(t)‖) and its rate of change (α·(t)=(xp(t)Tx·p(t)/‖xp(t)‖))

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Fig. 20

High and low pressure spool speeds versus high and low pressure spool accelerations

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Fig. 26

Control inputs to the augmented system (v(t))

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Fig. 27

Rate of change for fuel flow and prop pitch angle control inputs (u·(t))

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Fig. 28

Fuel and prop pitch angle control inputs (u(t))

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Fig. 29

Controllers integral gain matrix (Ki(α(t))) elements histories

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Fig. 30

Controllers proportional gain matrix (Kp(α(t))) elements histories

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Fig. 31

Turbine temperature, TSFC, compressor overall pressure ratio, and air flow rate histories

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Fig. 21

Plant states: high and low pressure spool speeds (xp(t))

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Fig. 22

Controller states (xc(t))

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Fig. 23

Output: high pressure spool speed and its reference signal

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Fig. 24

Output: low pressure spool speed and its reference signal

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Fig. 25

Thrust and its reference signal

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