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.
Issue Section:
Research Papers
Topics:
Design,
Engines,
Equilibrium (Physics),
Manifolds,
Modeling,
Nonlinear systems,
Simulation,
Surges,
Errors,
Signals,
Turbofans
References
1.
Ljung
, L.
, 2010
, “Perspectives on System Identification
,” Ann. Rev. Control
, 34
(1
), pp. 1
–12
.10.1016/j.arcontrol.2009.12.0012.
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
.10.1109/3477.7752754.
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.1965.109819410.
Neal
, S. R.
, 1968
, “Nonlinear Estimation Techniques
,” IEEE Trans. Auto Contr.
, 13
(6
), pp. 705
–708
.10.1109/TAC.1968.109907011.
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
.10.1109/37.16552716.
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
.10.1243/09544100JAERO2823.
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
.10.1115/1.400364225.
Jaw
, L. C.
, and Mattingly
, J. D.
, 2009
, Aircraft Engine Controls: Design, System Analysis, and Health Monitoring
, AIAA, Inc.
, Reston, VA
.Copyright © 2014 by ASME
You do not currently have access to this content.