Abstract
A sliding mode control (SMC) design method is proposed for a class of point-delayed systems. A linear transformation is applied to convert the delayed system to delay-free system whose spectra embed all the unstable poles of the original system with given stability margin. It is proved that the delayed system is asymptotically stable with SMC based on the delay-free system. The method is applied to internal combustion (IC) engine idle speed control, not for stabilization, but for compensation with the effects of the time delay in the system states.
Preview
Unable to display preview. Download preview PDF.
References
S. V. Drakunov and V. I. Utkin, “Sliding mode control in dynamic systems,” Int. J. Control, Vol.55, pp. 1029–1037, 1992.
R. El-Khazali, “Variable structure robust control of uncertain time-delay systems,” Automatica, Vol.34, pp. 327–332, 1998.
Y. A. Fiagbedzi and A. E. Pearson, “Feedback stabilization of linear autonomous time lag systems,” IEEE Trans. Auto. Control, AC-31, pp. 847–855, 1986.
Y. A. Fiagbedzi and A. E. Pearson, “A multistage reduction technique for feedback stabilizing distributed time-lag systems,” Automatica, Vol.23, pp. 311–326, 1987.
D. Hrovat and J. Sun, “Models and control methodologies for IC engine idle speed control design,” Proc. 13th IFAC World Congress, pp. 243–248, 1996.
K. J. Hu, V. R. Basker and O. D. Crisalle, “Sliding mode control of uncertain input-delay systems,” Proc. American Control Conference, pp. 564–568, 1998.
E. M. Jafarov, “Analysis and synthesis of multidimensional SVS with delays in sliding-modes,” Proc. 11th IFAC World Congress, pp. 46–49, 1990.
A. W. Olbrot, “Stabilizability, detectability and spectrum assignment for linear autonomous systems with general time delays,” IEEE Trans. Auto. Control, AC-23, pp. 887–890, 1978.
A. S. C. Sinha, M. El-Sharkawy and M. Rizkalla, “Sliding mode control of uncertain delay differential systems,” Nonlinear Analysis, Theory, Methods & Applications, Vol. 30, pp. 1075–1086, 1997.
W. C. Su, S. V. Drakunov and U. Ozguner, “Constructing discontinuity surfaces for variable structure systems: A Lyapunov approach,” Automatica, Vol 32, pp. 925–928, 1996.
V. I. Utkin, Sliding modes in control and optimization, Springer, 1992.
J. Wills, S. Yurkovich and G. Rizzoni, “Direct fuzzy control of idle speed in an internal combustion engine,” IFAC Workshop: Advances in Automotive Control, Mohican State Park, Oh, Feb. 1998.
S. Yurkovich and M. Simpson, “Comparative analysis for idle speed control: A crank-angle domain viewpoint,” Proc. American Control Conference, pp. 278–283, 1997.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this chapter
Cite this chapter
Li, X., Yurkovich, S. (1999). Sliding mode control of systems with delayed states and controls. In: Young, K., Özgüner, Ü. (eds) Variable structure systems, sliding mode and nonlinear control. Lecture Notes in Control and Information Sciences, vol 247. Springer, London. https://doi.org/10.1007/BFb0109972
Download citation
DOI: https://doi.org/10.1007/BFb0109972
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-197-9
Online ISBN: 978-1-84628-540-0
eBook Packages: Springer Book Archive