A new modeling method for a nonlinear system by using equilibrium manifold (EM) and its expansion model (EME model) was presented. The property of the EME model was discussed, and the effect of mapping design to the model has been discussed. This paper also has researched the adaptivity analysis to the EME model. Then an approximate nonlinear model for an aircraft engine is applied, followed by an identification procedure for an aircraft engine. Simulations showed good precision of this model in capturing the nonlinear behavior of nonlinearities and had the simpler structure.

References

References
1.
Ljung
,
L.
,
2010
, “
Perspectives on System Identification
,”
Ann. Rev. Control
,
34
(
1
), pp.
1
12
.10.1016/j.arcontrol.2009.12.001
2.
Tanizaki
,
H.
,
1996
,
Nonlinear Filters: Estimation and Applications
,
Berlin, Germany
:
Springer
.
3.
Gan
,
Q.
, and
Harris
,
C. J.
,
1999
, “
Fuzzy Local Linearization and Local Basis Function Expansion in Nonlinear System Modeling
,”
Syst. Man Cybernet B Cybernet
,
29
(
4
), pp.
559
565
.10.1109/3477.775275
4.
Kailath
,
T.
,
1980
,
Linear Systems
,
Prentice Hall
,
Englewood Cliffs, NJ
.
5.
Zhao
,
Q.
, and
Bohn
,
C. A.
,
2013
, “
Linearization Free Recursive Prediction Error Method for Combined State and Parameter Estimation for Nonlinear Systems
,”
American Control Conference (ACC)
, IEEE, pp.
899
904
.
6.
Pashchenko
,
A. F.
, and
Pashchenko
,
F. F.
,
2012
, “
Application of the Method of Statistical Linearization in Problems of Identification of Nonlinear Systems
,”
7th IEEE Conference on Industrial Electronics and Applications (ICIEA)
, pp.
1529
1532
.
7.
Dosthosseini
,
R.
,
Sheikholeslam
,
F.
, and
Kouzani
,
A. Z.
,
2010
, “
Identification of Nonlinear Systems Using Hybrid Functions
,”
8th IEEE International Conference on Control and Automation (ICCA)
, IEEE, pp.
1994
1998
.
8.
Zhang
,
J.
,
Zhang
,
Y.
, and
Ali
,
W.
,
2011
, “
Linearization Modeling for Non-Smooth Dynamical Systems With Approximated Scalar Sign Function
,”
50th IEEE Conference on Decision and Control and European Control Conference (CDC–ECC)
, IEEE, pp.
5205
5210
.
9.
Mowery
,
O. V.
,
1965
, “
Least Squares Recursive Differential-Correction Estimation in Nonlinear Problems
,”
IEEE Trans. Auto. Contr.
,
10
(
4
), pp.
399
407
.10.1109/TAC.1965.1098194
10.
Neal
,
S. R.
,
1968
, “
Nonlinear Estimation Techniques
,”
IEEE Trans. Auto Contr.
,
13
(
6
), pp.
705
708
.10.1109/TAC.1968.1099070
11.
Diop
,
S.
,
Grizzle
,
J. W.
, and
Chaplais
,
F.
,
2000
, “
On Numerical Differentiation Algorithms for Nonlinear Estimation
,”
Proceedings of 39th IEEE Conference on Decision and Control
,
2
, pp.
1133
1138
.
12.
Kreysig
,
E.
,
1999
,
Advanced Engineering Mathematics
,
John Wiley & Sons, Inc.
,
New York
.
13.
Ghosh
,
S.
,
Ray
,
A.
,
Yadav
D.
, and
Karan
B. M.
,
2011
, “
A Genetic Algorithm Based Clustering Approach for Piecewise Linearization of Nonlinear Functions
,” Devices and Communications (ICDeCom), 2011 International Conference on. IEEE, pp.
1
4
.
14.
Zhang
,
Y.
,
Sankaranarayanan
,
S.
, and
Somenzi
,
F.
,
2012
, “
Piecewise Linear Modeling of Nonlinear Devices for Formal Verification of Analog Circuits
,”
Proceedings of the 12th Conference on Formal Methods in Computer-Aided Design
, pp.
196
203
.
15.
Shamma
,
J.
, and
Athans
,
M.
,
1992
, “
Gain Scheduling: Potential Hazards and Possible Remedies
”,
IEEE Contr. Syst. Mag.
,
12
(
3
), pp.
101
107
.10.1109/37.165527
16.
Leith
,
D. J.
, and
Leithead
,
W. E.
,
2000
, “
On Formulating Nonlinear Dynamics in LPV Form
,”
IEEE Conference On Decision & Control
, pp.
3526
3527
.
17.
Sommer
,
S.
, and
Korn
,
U.
,
2000
, “
Modeling a Class of Nonlinear Plants as LPV-Systems via Nonlinear State-Transformation
,”
3rd IMACS symposium on Mathematical Modeling
, pp.
795
798
.
18.
Packard
,
A.
, and
Kantner
,
M.
,
1996
, “
Gain Scheduling the LPV Way
,”
IEEE Conference on Decision & Control
, pp.
3938
3941
.
19.
Bruzelius
,
F.
, and
Breitholtz
,
C.
,
2001
, “
Gain Scheduling via Affine Linear Parameter-Varying Systems and H∞ Synthesis
,”
IEEE Conference on Decision & Control
, pp.
2386
2391
.
20.
Ibrir
,
S.
,
1009
, “
LPV Approach to Continuous and Discrete Nonlinear Observer Design
,”
Proceedings of the 48th IEEE Conference on Decision and Control, 2009/2009 28th Chinese Control Conference, IEEE
, pp.
8206
8211
.
21.
Preitl
,
Z.
,
Kulcsar
,
B.
, and
Bokor
,
J.
,
2008
, “
Piecewise Linear Parameter Varying Mathematical Model of a Hybrid Solar Vehicle
,”
Intelligent Vehicles Symposium, 2008 IEEE
, pp.
895
900
.
22.
Fujimori
,
A.
, and
Ljung
,
L.
,
2006
, “
Model Identification of Linear Parameter Varying Aircraft Systems
,”
Proc. IMechE G J. Aerosp. Eng.
,
220
(
4
), pp.
337
346
.10.1243/09544100JAERO28
23.
Krantz
,
S. G.
, and
Parks
,
H. R.
,
2002
,
The Implicit Function Theorem: History, Theory, and Applications
,
Birkhauser, Boston, MA
.
24.
Zhao
,
H.
,
Liu
,
J. F.
, and
Yu
,
D. R.
,
2011
, “
Approximate Nonlinear Modeling and Feedback Linearization Control for Aeroengines
,”
ASME J. Eng. Gas Turb. Power
,
13
(
11
), pp.
111601
111610
.10.1115/1.4003642
25.
Jaw
,
L. C.
, and
Mattingly
,
J. D.
,
2009
,
Aircraft Engine Controls: Design, System Analysis, and Health Monitoring
,
AIAA, Inc.
,
Reston, VA
.
You do not currently have access to this content.