Feedback control has been pursued to address the rotating stall problem in axial flow compressors in order to extend the stable operating range and to improve engine performance. These controllers guarantee the stability of the bifurcated operating solution near the stall point. In this paper, an analytic approach is developed to characterize the robustness of some stabilizing controllers for rotating stall in axial-flow compressors. The numerical examples show that the size of the admissible uncertainty set changes for stabilizing controllers with different feedback gains. It is also proved that a nonlinear stabilizing control is not necessarily superior to a linear one.

1.
McCaughan
,
F. E.
,
1990
, “
Bifurcation analysis of axial flow compressor stability
,”
SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
,
20
, pp.
1232
1253
.
2.
Behnken, R. L., D’Andrea, R., and Murray, R. M., 1995, “Control of rotating stall in a low-speed axial flow compressor using pulsed air injection: Modeling, simulations, and experimental validation,” Proc. of 34th IEEE Conf. Dec. and Contr., 3056–3061.
3.
Chen
,
X.
,
Gu
,
G.
,
Martin
,
P.
, and
Zhou
,
K.
,
1998
, “
Rotating stall control via bifurcation stabilization
,”
Automatica
,
34
, 4, pp.
437
443
.
4.
Gu
,
G.
,
Chen
,
X.
,
Sparks
,
A. G.
, and
Banda
,
S. S.
,
1999
, “
Bifurcation stabilization with local output feedback
,”
SIAM J. Control Optim.
,
37
, No.
3
, pp.
934
956
.
5.
Gravdahl, Jan T., and Egeland, O., Compressor surge and rotating stall: modeling and control, Springer, New York, 1999.
6.
Xiao
,
MingQing
, and
Basar
,
Tamer
,
2000
, “
Analysis and control of multi-mode axial flow compression system models
,”
ASME J. Dyn. Syst., Meas., Control
,
122
, pp.
393
393
.
7.
Wang, H. O., Adomaitis, R. A. and Abed, E. H., 1994, “Nonlinear analysis and control of rotating stall in axial flow compressors,” in American Control Conference, 2317–2321.
8.
Chen
,
X.
,
Sparks
,
A. G.
,
Zhou
,
K.
, and
Gu
,
G.
,
2001
, “
Local robustness of stationary bifurcation control
,”
Latin American Applied Research
,
31
, No.
3
, pp.
163
170
.
9.
Moore
,
F. K.
, and
Greitzer
,
E. M.
,
1986
, “
A theory of post-stall transients in axial compressors: Part I-development of the equations
,”
ASME J. Eng. Gas Turbines Power
,
108
, pp.
68
76
.
10.
Abed
,
E. H.
, and
Fu
,
Jyun-Horng
,
1986
, “
Local feedback stabilization and bifurcation control, II. Stationary bifurcation
,”
Syst. Control Lett.
,
8
, pp.
467
473
.
11.
Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, NY, 1990.
12.
Kailath, T., Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
13.
Liaw
,
D.-C.
, and
Abed
,
E. H.
,
1996
, “
Active control of compressor stall inception: A bifurcation theoretical approach
,”
Automatica
,
32
, pp.
109
116
.
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