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Research Papers

Nonlinear System Modeling and Application Based on System Equilibrium Manifold and Expansion Model

[+] Author and Article Information
Xiaofeng Liu

School of Transportation
Science and Engineering,
Beijing University of
Aeronautics and Astronautics,
Beijing 100191, China
e-mail: liuxf@buaa.edu.cn

Ye Yuan

School of Power and Engineering,
Beijing University of
Aeronautics and Astronautics,
Beijing 100191, China
e-mail: desertdeagle@163.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 25, 2013; final manuscript received August 29, 2013; published online October 30, 2013. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 9(2), 021013 (Oct 30, 2013) (17 pages) Paper No: CND-13-1158; doi: 10.1115/1.4025478 History: Received June 25, 2013; Revised August 29, 2013

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.

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Figures

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Fig. 1

Feasible mappings to build an EME model

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Fig. 2

EM of this example

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Fig. 3

Comparison of simulations with different expansion methods (a) x1 (b) x2

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Fig. 4

Frame of expansion model based on EM

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Fig. 5

Comparison of simulation with different models under deterministic input signal (a) Simulation input (b) System output under different models (c) Error of system output (d) Relative error of system output

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Fig. 6

Comparison of simulation with different models under random input signal (a) Simulation input (b) System output under different models (c) Error of system output (d) Relative error of system output

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Fig. 7

Comparison of simulation with parameter perturbation under unit step input (a) x1 (b) x2

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Fig. 8

Comparisons of simulation with parameter perturbation under tri-wave signal input (a) System input (b) x1 (c) x2

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Fig. 9

Comparisons of simulation with parameter perturbation under random signal input (a) System input (b) x1 (c) x2 (d) Error of x1 (e) Error of x2

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Fig. 10

Schematic configuration of the two-spool turbofan engine

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Fig. 12

Deviation items (a) Fuel input (b) Deviation responding of nL to command signal (c) Deviation responding of wf to command signal

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Fig. 13

Fitting results of the EME model partial items by nHe (a) a12 (b) a22 (c) b1 (d) b2 (e) c2 (f) d

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Fig. 14

Identified EME model compared with NCL model at H = 0 and Ma = 0 (a) nH (b) Relative error of nH (c) nL (d) Relative error of nL (e) SMC (f) Relative error of SMC

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Fig. 15

Identified EME model compared with NCL model at H = 8 km and Ma = 0.6 (a) nH (b) Relative error of nH (c) SMC (d) Relative error of SMC

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Fig. 16

Degradation EM compared with normal model

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Fig. 17

Identified EME model compared with NCL model at H = 8 km and Ma = 0.6 (a) nH (b) SMC

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Fig. 18

Comparison with NCL, EME, and LPV models (a) nH (b) SMC

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