Abstract
The conventional linear parameter varying (LPV) modeling for turbofan engines is performed at a set of equilibrium points, which may result in inaccurate description of dynamics of engines when the engine accelerates/decelerates in a broad range and operates away from the equilibria. Meanwhile, to ensure stable operation of turbofan engines, the engine pressure ratio (EPR) needs to be regulated when turning on afterburner. According to this complex multi-input multi-output (MIMO) problem mixed with disturbances, this paper proposes a hybrid robust control framework based on off-equilibrium linearization. We first establish an off-equilibrium linearization based polynomial LPV model for the MIMO turbofan engine, and then design an robust controller by solving sum-of-squares (SOS) programing. The simulation results show that the controller can simultaneously achieve fast dual command tracking and disturbance suppression when turning on afterburner. Furthermore, this control framework is superior to the equilibrium linearization-based controller in many aspects, which further proves the accuracy of the off-equilibrium based LPV model.
Issue Section:
Research Papers
References
1.
Reberga
,
L.
,
Henrion
,
D.
,
Bernussou
,
J.
, and
Vary
,
F.
, 2005
, “
LPV Modeling of a Turbofan Engine
,” IFAC Proc. Vol.
,
38
(1
), pp. 526
–531
.10.3182/20050703-6-CZ-1902.004882.
Lv
,
C.
,
Chang
,
J.
,
Bao
,
W.
, and
Yu
,
D.
, 2022
, “
Recent Research Progress on Airbreathing Aero-Engine Control Algorithm
,” Propul. Power Res.
,
11
(1
), pp. 1
–57
.10.1016/j.jppr.2022.02.0033.
Montazeri-Gh
,
M.
,
Rasti
,
A.
,
Jafari
,
A.
, and
Ehteshami
,
M.
, 2019
, “
Design and Implementation of MPC for Turbofan Engine Control System
,” Aerosp. Sci. Technol.
,
92
(September
), pp. 99
–113
.10.1016/j.ast.2019.05.0614.
Yu
,
B.
,
Li
,
Z.
,
Ke
,
H.
, and
Zhang
,
T.
, 2022
, “
Wide-Range Model Predictive Control for Aero-Engine Transient State
,” Chin. J. Aeronaut.
,
35
(7
), pp. 246
–260
.10.1016/j.cja.2021.10.0155.
Liu
,
X.
,
Zhang
,
L.
, and
Luo
,
C.
, 2023
, “
Model Reference Adaptive Control for Aero-Engine Based on System Equilibrium Manifold Expansion Model
,” Int. J. Control
,
96
(4
), pp. 884
–899
.10.1080/00207179.2021.20169796.
Liu
,
J.
,
X.
, Wang
,
M.
, Zhu
., and
K.
, Miao
, 2021
, “
Multivariable Adaptive Control Method for Turbofan Engine With Dynamic and Input Uncertainties
,” ASME J. Eng. Gas Turbines Power
,
143
(7
), p. 071027
.10.1115/1.40492967.
Yang
,
S.
,
Wang
,
X.
, and
Yang
,
B.
, 2018
, “
Adaptive Sliding Mode Control for Limit Protection of Aircraft Engines
,” Chin. J. Aeronaut.
,
31
(7
), pp. 1480
–1488
.10.1016/j.cja.2018.05.0118.
Liu
,
S.
,
Bai
,
J.
,
Wang
,
Q.
, and
Wang
,
W.
, 2019
, “
Tracking Controller Design for Aero-Engine Based on Improved Multi-Power Reaching Law of Sliding Mode Control
,” Int. J. Aeronaut. Space Sci.
,
20
(3
), pp. 722
–731
.10.1007/s42405-019-00159-49.
Bruzelius
,
F.
,
Breitholtz
,
C.
, and
Pettersson
,
S.
, 2023
, “
LPV-Based Gain Scheduling Technique Applied to a Turbo Fan Engine Model
,” Proceedings of the International Conference on Control Applications
, Glasgow, UK
, Sept. 18–20
, pp. 713
–718
.10.1109/CCA.2002.103868810.
Lu
,
S.
,
Pan
,
M.
, and
Chen
,
Y.-H.
, 2022
, “
Robust Control of Uncertain Nonlinear Systems With Input Saturation and Aero-Engine Application
,” 2022 International Conference on Advanced Robotics and Mechatronics (ICARM
), Guilin, China
, July 9–11
, pp. 996
–1001
.10.1109/ICARM54641.2022.995940711.
Chen
,
C.
, and
Zhao
,
J.
, 2018
, “
Switching Control of Acceleration and Safety Protection for Turbo Fan Aero-Engines Based on Equilibrium Manifold Expansion Model
,” Asian J. Control
,
20
(5
), pp. 1689
–1700
.10.1002/asjc.174512.
Sui
,
Y.
, and
Daren
,
Y.
, 2007
, “
Identification of Expansion Model Based on Equilibrium Manifold of Turbojet Engine
,” Acta Aeronaut.
,
28
(3
), pp. 531
–534
. https://www.semanticscholar.org/paper/Identificationof-Expansion-Model-Based-on-Manifold-Daren/650f1fb604b0bd1ef4e8ca544e533285193bf78b13.
Yu
,
D.
,
Zhao
,
H.
,
Xu
,
Z.
,
Sui
,
Y.
, and
Liu
,
J.
, 2011
, “
An Approximate Non-Linear Model for Aeroengine Control
,” Proc. Inst. Mech. Eng., Part G
,
225
(12
), pp. 1366
–1381
.10.1177/095441001140095914.
Zhao
,
H.
,
Liu
,
J.
, and
Yu
,
D.
, 2011
, “
Approximate Nonlinear Modeling and Feedback Linearization Control for Aeroengines
,” ASME J. Eng. Gas Turbines Power
,
133
(11
), p. 011601
.10.1115/1.400364215.
Lu
,
F.
,
Qian
,
J.
,
Huang
,
J.
, and
Qiu
,
X.
, 2017
, “
In-Flight Adaptive Modeling Using Polynomial LPV Approach for Turbofan Engine Dynamic Behavior
,” Aerosp. Sci. Technol.
,
64
(May
), pp. 223
–236
.10.1016/j.ast.2017.02.00316.
Chen
,
Q.
,
Huang
,
J.
,
Pan
,
M.
, and
Lu
,
F.
, 2019
, “
A Novel Real-Time Mechanism Modeling Approach for Turbofan Engine
,” Energies
,
12
(19
), p. 3791
.10.3390/en1219379117.
Shi
,
Y.
,
Zhao
,
J.
, and
Liu
,
Y.
, 2017
, “
Switching Control for Aero-Engines Based on Switched Equilibrium Manifold Expansion Model
,” IEEE Trans. Ind. Electron.
,
64
(4
), pp. 3156
–3165
.10.1109/TIE.2016.263347018.
Chung
,
G.-Y.
,
Prasad
,
J. V. R.
,
Dhingra
,
M.
, and
Meisner
,
R.
, 2014
, “
Real Time Analytical Linearization of Turbofan Engine Model
,” ASME J. Eng. Gas Turbines Power
,
136
(1
), p. 011201
.10.1115/1.402531019.
Johansen
,
T. A.
,
Hunt
,
K. J.
,
Gawthrop
,
P. J.
, and
Fritz
,
H.
, 1998
, “
Off-Equilibrium Linearisation and Design of Gain-Scheduled Control With Application to Vehicle Speed Control
,” Control Eng. Pract.
,
6
(2
), pp. 167
–180
.10.1016/S0967-0661(98)00015-X20.
Korba
,
P.
, and
Werner
,
H.
, “
Counter-Example to Ad-Hoc Off-Equilibrium Linearisation Methods in Gain-Scheduling
,” Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No. 01CH37228
), Orlando, FL
, Dec. 4–7
, pp. 1342
–1347
.10.1109/CDC.2001.98107621.
Leith
,
D. J.
, and
Leithead
,
W. E.
, 1998
, “
Gain-Scheduled and Nonlinear Systems: Dynamic Analysis by Velocity-Based Linearization Families
,” Int. J. Control
,
70
(2
), pp. 289
–317
.10.1080/00207179822241522.
Tang
,
Y.
,
Li
,
Y.
,
Cui
,
T.
, and
Zheng
,
Y.
, 2020
, “
Off-Equilibrium Linearisation-Based Nonlinear Control of Turbojet Enginese With Sum-of-Squares Programming
,” Aeronaut. J.
,
124
(1282
), pp. 1879
–1895
.10.1017/aer.2020.8823.
Jaw
,
L. C.
, 2009
, Aircraft Engine Controls: Design, System Analysis, and Health Monitoring
,
American Institute of Aeronautics & Astronautics
,
Reston, VA
.24.
Löfberg
,
J.
, 2008
, “
Modeling and Solving Uncertain Optimization Problems in YALMIP
,” IFAC Proc. Vol.
,
41
(2
), pp. 1337
–1341
.10.3182/20080706-5-KR-1001.0022925.
MOSEK ApS
., 2019
, “
MOSEK Optimization Toolbox for Matlab
, User's Guide and Reference Manual, Version 4(1),” Taylor & Francis, Oxfordshire, UK.26.
Sturm
,
J. F.
, 1999
, “
Using SeDuMi 1.02, a Matlab Toolbox for Optimization Over Symmetric Cones
,” Optim. Methods Software
,
11
(1–4
), pp. 625
–653
.10.1080/1055678990880576627.
Parrilo
,
P. A.
, 2000
, Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
,
California Institute of Technology
, Pasadena, CA.28.
Wu
,
F.
, and
Prajna
,
S.
, 2005
, “
SOS-Based Solution Approach to Polynomial LPV System Analysis and Synthesis Problems
,” Int. J. Control
,
78
(8
), pp. 600
–611
.10.1080/0020717050011486529.
Anderson
,
J.
, and
Papachristodoulou
,
A.
, 2013
, “
Robust Nonlinear Stability and Performance Analysis of an F/A-18 Aircraft Model Using Sum of Squares Programming
,” Int. J. Robust Nonlinear Control
,
23
(10
), pp. 1099
–1114
.10.1002/rnc.292830.
Chapman
,
J. W.
,
Lavelle
,
T. M.
,
May
,
R. D.
,
Litt
,
J. S.
, and
Guo
,
T. H.
, 2014
, “
Toolbox for the Modeling and Analysis of Thermodynamic Systems
(T-MATS
) User's Guide,” NASA, Washington, DC.https://ntrs.nasa.gov/api/citations/20140012486/downloads/20140012486.pdf31.
Xie
,
W.
, 2008
, “
An Equivalent LMI Representation of Bounded Real Lemma for Continuous-Time Systems
,” J. Inequalities Appl.
,
2008
(1
), p. 672905
.10.1155/2008/67290532.
Yu
,
L.
, 2002
, Robust Control-Linear Matrix Inequalities Approach
,
Tsinghua University Press
,
Beijing, China
.33.
Topcu
,
U.
,
Packard
,
A.
,
Seiler
,
P.
, and
Wheeler
,
T.
, 2007
, “
Stability Region Analysis Using Simulations and Sum-of-Squares Programming
,” 2007 American Control Conference
, New York
, July 9–13
, pp. 6009
–6014
.10.1109/ACC.2007.428301334.
Mattingly
,
J. D.
,
Boyer
,
K. M.
,
Haven
,
B. A.
,
Heiser
,
W. H.
, and
Pratt
,
D. T.
, 2018
, Aircraft Engine Design
,
Virginia American Institute of Aeronautics and Astronautics, Inc
.,
Reston
.35.
Vinnicombe
,
G.
, 2000
, Uncertainty and Feedback. H∞ Loop-Shaping and the ν-Gap Metric
,
Imperial College Press
, London, UK.Copyright © 2023 by ASME
You do not currently have access to this content.
