Flow disturbance is the main cause which leads to the instability occurred in aero-engines, and it is an infinite-dimensional quantity that is impossible for a direct online measurement in reality. The unstable flow not only results in a drastic pressure reduction but also can damage to engine's components during the compressor operations. In this paper, we construct a local state observer which can deliver the full information of the flow disturbance by only sensing on an arbitrarily small area at the duct entrance in terms of averaging the flow disturbance, which provides a practical approach for real applications. The proposed observer makes possible in applications by using a feedback control to stabilize the system. The convergent gain is obtained through the approach of operator spectrum theory. Numerical simulations are provided to illustrate the effectiveness of the proposed observer by showing typical types of flow situations for aero-engine compressors.

References

1.
Chung
,
Y.
, and
Titi
,
E. S.
,
2003
, “
Inertial Manifolds and Gevrey Regularity for the Moore–Greitzer Model of an Axial-Flow Compressor
,”
J. Nonlinear Sci.
,
13
(
1
), pp.
1
25
.10.1007/s00332-002-0516-y
2.
Day
, I
. J.
,
Greitzer
,
E. M.
, and
Cumpsty
,
N. A.
,
1978
, “
Prediction of Compressor Performance in Rotating Stall
,”
J. Eng. Power
,
100
(
1
), pp.
1
12
.10.1115/1.3446318
3.
McCaughan
,
F. E.
,
1990
, “
Bifurcation Analysis of Axial Flow Compressor Stability
,”
SIAM J. Appl. Math.
,
50
(
5
), pp.
1232
1253
.10.1137/0150075
4.
Moore
,
F. K.
, and
Greitzer
,
E. M.
,
1986
, “
A Theory of Post-Stall Transients in Axial Compression Systems: Part I—Development of Equations
,”
ASME J. Eng. Gas Turbines Power
,
108
(
1
), pp.
68
76
.10.1115/1.3239887
5.
Xiao
,
M.
, and
Başar
,
T.
,
2000
, “
Center Manifold of the Viscous Moore–Greitzer PDE Model
,”
SIAM J. Appl. Math.
,
61
(
3
), pp.
855
869
.10.1137/S0036139999354261
6.
Xiao
,
M.
,
2006
, “
Characterization of Critical Eigenvalues of Axial Flow Engine Compressor PDE Model
,”
Appl. Anal.
,
85
(
9
), pp.
1123
1142
.10.1080/00036810600835201
7.
Xiao
,
M.
,
2008
, “
Quantitative Characteristic of Rotating Stall and Surge for Moore–Greitzer PDE Model of an Axial Flow Compressor
,”
SIAM J. Appl. Dyn. Syst.
,
7
(
1
), pp.
39
62
.10.1137/060658254
8.
Moore
,
F. K.
, and
Greitzer
,
E. M.
,
1986
, “
A Theory of Post-Stall Transients in Axial Compression Systems: Part II—Application
,”
ASME J. Eng. Gas Turbines Power
,
108
(
2
), pp.
231
239
.10.1115/1.3239887
9.
Gu
,
G.
,
Chen
,
X.
,
Sparks
,
A.
, and
Banda
,
S.
,
1999
, “
Bifurcation Stabilization With Local Output Feedback
,”
SIAM J. Control Optim.
,
37
(
3
), pp.
934
956
.10.1137/S0363012997320924
10.
Humbert
,
J. S.
, and
Krener
,
A. J.
,
1998
, “
Dynamics and Control of Entrained Solutions in Multi-Mode Moore–Greitzer Compressor Models
,”
Internat. J. Control
,
71
(
5
), pp.
807
821
.10.1080/002071798221588
11.
Liaw
,
D.-C.
, and
Abed
,
E. H.
,
1996
, “
Active Control of Compressor Stall Inception: A Bifurcation-Theoretic Approach
,”
Automatica
,
32
(
1
), pp.
109
115
.10.1016/0005-1098(95)00096-8
12.
Xiao
,
M.
, and
Başar
,
T.
,
1999
, “
Analysis and Control of Multi-Mode Axial Flow Compression System Models
,”
J. Dyn. Sys., Meas., Control
,
122
(
3
), pp.
393
401
.10.1115/1.1286432
13.
Banaszuk
,
A.
,
Hauksson
,
H. A.
, and
Mezić
,
I.
,
1999
, “
A Backstepping Controller for a Nonlinear Partial Differential Equation Model of Compression System Instabilities
,”
SIAM J. Control Optim.
,
37
(
5
), pp.
1503
1537
.10.1137/S0363012997317876
14.
Birnir
,
B.
, and
Hauksson
,
H. A.
,
1999
, “
A Finite-Dimensional Attractor of the Moore-Greitzer PDE Model
,”
SIAM J. Appl. Math.
,
59
(
2
), pp.
636
650
.10.1137/S0036139997325527
15.
Birnir
,
B.
, and
Hauksson
,
H. A.
,
2000
, “
Basic Control for the Viscous Moore-Greitzer Partial Differential Equation
,”
SIAM J. Control Optim.
,
38
(
5
), pp.
1554
1580
.10.1137/S0363012998345184
16.
Xiao
,
M.
,
1998
, “
Stabilization of the Full Model Compression System
,”
Proceeding of 37th IEEE Conference on Decision and Control
,
Tampa, FL
, Dec. 16–18, Vol.
3
, pp.
2575
2580
.
17.
Xiao
,
M.
, and
Başar
,
T.
,
1999
, “
Rotating Stall Control of MG3 Compressor Models Governed by Partial Differential Equations
,”
Proc. of the 14th IFAC World Congress, Vol. E
, pp.
183
188
.
18.
Wen
,
J.
,
Xiao
,
M.
, and
Xu
,
J.
,
2012
, “
Control of Hopf Bifurcations of Nonlinear Infinite-Dimensional Systems: Application to Axial Flow Engine Compressor
,”
Appl. Anal.
,
91
(
11
), pp.
1959
1980
.10.1080/00036811.2011.577742
19.
Yahya
,
S. M.
,
2011
,
Turbines Compressors and Fans
,
Tata McGraw-Hill
,
New York
.
20.
Chen
,
G.
,
Hsu
,
S.-B.
,
Zhou
,
J.
,
Chen
,
G.
, and
Crosta
,
G.
,
1998
, “
Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition, Part I: Controlled Hysteresis
,”
Trans. Am. Math. Soc.
,
350
(
11
), pp.
4265
4311
.10.1090/S0002-9947-98-02022-4
21.
Chen
,
G.
,
Hsu
,
S.-B.
, and
Zhou
,
J.
,
1998
, “
Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition, Part II: Energy Injection, Period Doubling and Homoclinic Orbits
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
,
8
(
3
), pp.
423
445
.10.1142/S0218127498000280
22.
Chen
,
G.
,
Hsu
,
S.-B.
, and
Zhou
,
J.
,
1998
, “
Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition, Part III: Natural Hysteresis Memory Effects
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
,
8
(
3
), pp.
447
470
.10.1142/S0218127498000292
23.
Chen
,
G.
,
Hsu
,
S.-B.
, and
Zhou
,
J.
,
2003
,
Chaotic Vibration of the Wave Equation With Nonlinear Feedback Boundary Control: Progress and Open Questions (Lecture Notes in Control and Information Science)
, Vol. 292, Springer, Berlin, Germany, pp.
25
50
.
24.
Curtain
,
R. F.
, and
Zwart
,
H.
,
1995
,
An Introduction to Infinite-Dimensional Linear Systems Theory (Texts in Applied Mathematics)
, Vol.
21
,
Springer
,
New York.
25.
Pazy
,
A.
,
1983
,
Semigroups of Linear Operators and Applications to Partial Differential Equations (Applied Mathematical Sciences)
, Vol.
44
,
Springer
,
New York
.
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