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Research Papers

Observer Design for Axial Flow Compressor

[+] Author and Article Information
Xuejun Gao

Faculty of Applied Mathematics,
Guangdong University of Technology,
Guangzhou 510006, China
e-mail: gaoxxj@163.com

Tingwen Huang

Department of Mathematics,
Texas A&M University at Qatar,
Doha 23874, Qatar
e-mail: tingwen.huang@qatar.tamu.edu

Yu Huang

Department of Mathematics,
Zhongshan (Sun Yat-Sen) University,
Guangzhou 510275, China
e-mail: stshyu@mail.sysu.edu.cn

Jun Liu

Department of Mathematics,
Southern Illinois University,
Carbondale, IL 62901
e-mail: junliu2010@siu.edu

MingQing Xiao

Department of Mathematics,
Southern Illinois University,
Carbondale, IL 62901
e-mail: mxiao@siu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 4, 2012; final manuscript received April 23, 2014; published online July 9, 2014. Assoc. Editor: Nariman Sepehri.

J. Dyn. Sys., Meas., Control 136(5), 051017 (Jul 09, 2014) (12 pages) Paper No: DS-12-1360; doi: 10.1115/1.4027525 History: Received November 04, 2012; Revised April 23, 2014

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.

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References

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. [CrossRef]
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. [CrossRef]
McCaughan, F. E., 1990, “Bifurcation Analysis of Axial Flow Compressor Stability,” SIAM J. Appl. Math., 50(5), pp. 1232–1253. [CrossRef]
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. [CrossRef]
Xiao, M., and Başar, T., 2000, “Center Manifold of the Viscous Moore–Greitzer PDE Model,” SIAM J. Appl. Math., 61(3), pp. 855–869. [CrossRef]
Xiao, M., 2006, “Characterization of Critical Eigenvalues of Axial Flow Engine Compressor PDE Model,” Appl. Anal., 85(9), pp. 1123–1142. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Liaw, D.-C., and Abed, E. H., 1996, “Active Control of Compressor Stall Inception: A Bifurcation-Theoretic Approach,” Automatica, 32(1), pp. 109–115. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
Yahya, S. M., 2011, Turbines Compressors and Fans, Tata McGraw-Hill, New York.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Curtain, R. F., and Zwart, H., 1995, An Introduction to Infinite-Dimensional Linear Systems Theory (Texts in Applied Mathematics), Vol. 21, Springer, New York.
Pazy, A., 1983, Semigroups of Linear Operators and Applications to Partial Differential Equations (Applied Mathematical Sciences), Vol. 44, Springer, New York.

Figures

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Fig. 1

An outline of a compression system

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Fig. 2

Compressor geometry

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Fig. 3

Notation used in definition of compressor characteristic with w = 0.5 and H = ψc0 = 2

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Fig. 4

The dynamics of the flow coefficient and the pressure rise coefficient for B = 0.5 and μ = 0.565 (rotating stall case)

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Fig. 5

System states (solid line) and estimations (dotted line) for B = 0.5 and μ = 0.565

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Fig. 6

Error dynamics (log ei) for B = 0.5 and μ = 0.565

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Fig. 7

The dynamics of the flow coefficient and the pressure rise coefficient for B = 2 and μ = 0.6 (surge case)

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Fig. 8

System states (solid line) and estimations (dotted line) for B = 2 and μ = 0.6

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Fig. 9

Error dynamics (log ei) for B = 2 and μ = 0.6

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Fig. 10

The dynamics of the flow coefficient and the pressure rise coefficient for B = 0.72058 and μ = 0.572 (combination of rotating stall and surge)

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Fig. 11

System states (solid line) and estimations (dotted line) for B = 0.72058 and μ = 0.572

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Fig. 12

Error dynamics (log ei) for B = 0.72058 and μ = 0.572

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