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TECHNICAL PAPERS

Analysis and Control of Multi-Mode Axial Flow Compression System Models

[+] Author and Article Information
MingQing Xiao

Institute of Theoretical Dynamics, University of California at Davis, Davis, CA 95616e-mail: xiao@math.ucdavis.edu

Tamer Başar

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801e-mail: tbasar@decision.csl.uiuc.edu

J. Dyn. Sys., Meas., Control 122(3), 393-401 (Jun 22, 1999) (9 pages) doi:10.1115/1.1286432 History: Received June 22, 1999
Copyright © 2000 by ASME
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References

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, pp. 68–76.
McCaughan,  F., 1990, “Bifurcation analysis of axial flow compressor stability,” SIAM J. Appl. Math., 50, pp. 109–115.
Liaw,  D., and Abed,  E., 1996, “Active control of compressor stall inception: a bifurcation theoretic approach,” Automatica, 32, pp. 109–115.
Chen,  X., Gu,  G., Martin,  P., and Zhou,  K., 1998, “Rotating stall control via bifurcation stabilization,” Automatica, 4, pp. 437–443.
Humbert,  J. S., and Krener,  A. J., 1998, “Dynamics and control of entrained solutions in multi-mode Moore-Greitzer compressor models,” Int. J. Control, 71, pp. 807–821.
Leonessa, A., Chellaboina, V., and Haddad, W., 1997, Globally stabilizing controllers for multi-mode axial flow compressors via equilibria-dependent Lyapunov functions, Proc. American Control Conference, pp. 993–997.
Henderson, E., and Sparks, A., 1997, “On the suitability of bifurcation stabilization control laws for high order Moore-Greitzer compressor models,” Proc. American Control Conf., Albuquerque, NM, June 1997, pp. 801–805.
Crandall,  M., and Rabinowitz,  P., 1973, “Bifurcation, perturbation of simple eigenvalues and linearized stability,” Arch. Ration. Mech. Anal., 53, pp. 161–181.
Crandall, M., and Rabinowitz, P., 1980, “Mathematical theory of bifurcation,” Bifurcation Phenomena in Mathematical Physics and Related Topics, Bardos C., and Bessis D., eds., Reidel, Dordrecht.
Xiao, M., 1998, “Stabilization of the full model compression system,” Proc. of 37th IEEE Decision and Control Conference, pp. 2575–2580.
Xiao, M., and T. Başar, 1999, “Rotating stall control of MG3 compressor models governed by partial differential equations,” Proc. of the 14th World Congress, IFAC, July 5–9, 1999, Beijing, P. R. China.

Figures

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Axial flow compression system
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Compressor characteristic and throttle characteristic
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States of axisymmetric steady flow
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Axisymmetric flow trajectory projection on the ΦΨ-plane with a parabolic throttle characteristic and B=0.1, for the MG6 model
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State response of nonaxisymmetric flow with B=0.1
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Nonaxisymmetric flow trajectory projection on the ΦΨ-plane with a parabolic throttle characteristic and B=0.1, for the MG6 model
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State response of the system with B=2
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Flow trajectory projection on the ΦΨ-plane with a parabolic throttle characteristic and B=2 for the MG6 model
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State response under controller (6.1) with B=0.1
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Trajectory projection on the ΦΨ-plane under controller (6.1) and with B=0.1, for the MG6 model
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State response under controller (6.1) with B=2
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Trajectory projection on the ΦΨ-plane under controller (6.1) and with B=2, for the MG6 model

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