Abstract
Achieving stability is the essential issue in the control system design. In this paper, four approaches that can be used to calculate the stability margin of the interval plant family are summarized and compared. The μ approach gives the bounds of the stability margin, and good estimation can be obtained with the numerical method. The eigenvalue approach yields accurate value, and the MATLAB’s function robuststab sometimes provides wrong results. Since the eigenvalue approach is both accurate and computationally efficient, it is recommended for the calculation of the stability margin, while utilization of the function robuststab should be avoided due to the unreliable results it gives.
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References
H. Chapellat, S. P. Bhattacharyya. A generalization of Kharitonov’s theorem: robust stability of interval plants[J]. IEEE Transactions on Automatic Control, 1989, 34(3): 306–311.
B. R. Barmish, C. V. Hollot, F. J. Kraus, et al. Extreme point results for robust stabilization of interval plants with first order compensators[J]. IEEE Transactions on Automatic Control, 1992, 37(6): 707–714.
S. Skogestad, I. Postlethwaite. Multivariable Feedback Control Analysis and Design[M]. New York: John Wiley & Sons, 2005.
Q. Wu. On the stability radius of control systems with interval plants and first order controllers[J]. International Journal of Robust and Nonlinear Control, 2000, 10(10): 763–777.
Q. Wu. Robust stability analysis of control systems with interval plants[J]. International Journal of Control, 2001, 74(9): 921–937.
G. Balas, R. Chiang, A. Packard, et al. Robust Control Toolbox: User’s Guide[M]. Natick: The Math Works, 2007.
B. R. Barmish. New Tools for Robustness of Linear Systems[M]. New York: Macmillan Publishing Company, 1994.
Q. Wu, B. Lü, L. XU. A parameter optimization approach to robust PI-controller design for systems with interval plants[J]. Journal of Control Theory and Applications, 2008, 6(4): 435–441.
Q. Wu. Stabilizability may be sufficient for robustly stabilizing an interval plant[J]. Acta Automatica Sinica, 2007, 33(10): 1084–1087.
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This work was supported by the National Natural Science Foundation of China (No.69574003, 69904003) and the Research Fund for the Doctoral Program of the Higher Education (RFDP) (No.1999000701), and was partly supported by the Advanced Weapons Research Supporting Fund (No.YJ0267016).
Bin LÜ received the Ph.D. degree from the Beijing Institute of Technology in 2009. He is currently a research associate in Akita Prefectural University. His research interest covers robust control system designing and optimization.
Qinghe WU received the Ph.D. degree from the Eidgenossische Technische Hochschule Zürich in 1990. He is currently a professor at the Department of Automatic Control in Beijing Institute of Technology. His research interest mainly covers robust control theory.
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Lü, B., Wu, Q. Stability margin of uncertain control systems. J. Control Theory Appl. 7, 427–432 (2009). https://doi.org/10.1007/s11768-009-8071-9
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DOI: https://doi.org/10.1007/s11768-009-8071-9