Abstract
It is well known that a problem formulation containing only matched uncertainty can be forced to attain a sliding mode and exhibit the precise nominal dynamic which is defined by the choice of switching surface. This paper has formulated a nonlinear control strategy which will prescribe bounded motion about an ideal sliding mode dynamic for an uncertainty set including both matched and unmatched uncertainty which can be readily applied to engineering problems. A tracking requirement has been successfully incorporated into the methodology. The results have been illustrated by considering the design of a temperature controller for an industrial furnace.
Preview
Unable to display preview. Download preview PDF.
References
Barmish, B.R. 1983, Stabilization of uncertain systems via linear control. IEEE Transactions on Automatic Control 28, 848–850
Bühler, H. 1991, Sliding mode control with switching command devices. in Deterministic Control of Uncertain Systems, ed. Zinober, A.S.I., Peter Peregrinus, London, 27–51
Burton, J.A., Zinober, A.S.I. 1986, Continuous approximation of variable structure control. International Journal of Systems Science 17, 875–885
Dorling, C.M., Zinober, A.S.I. 1990, Hyperplane design and CAD of variable structure control systems. in Deterministic Control of Uncertain Systems, ed. Zinober, A.S.I., Peter Peregrinus London, 52–79
Edwards, C., Spurgeon, S.K. 1993, On the development of discontinuous observers. International Journal of Control, to appear
Kautsky, J., Nichols, N.K., Van Dooren, P. 1985, Robust pole assignment in linear state feedback. International Journal of Control 41, 1129–1155
Khargonekar, P.P., Petersen, R., Zhou, K. 1990, Robust stabilization of uncertain linear systems: Quadratic stabilizability and H ∞ control theory. IEEE Transactions on Automatic Control 35, 356–361
Rhine, J.M., Tucker, R.J. 1991, Modelling of gas fired furnaces and boiler and other industrial heating processes, McGraw-Hill, New York, Chapters 13 and 14
Ryan, E.P., Corless, M. 1984, Ultimate boundedness and asymptotic stability of a class of uncertain dynamical systems via continuous and discontinuous feedback control. IMA Journal of Mathematics and Control Information 1, 223–242
Slotine, J.J. 1984, Sliding controller design for nonlinear systems. International Journal of Control 53, 163–179
Spurgeon, S.K., Davies, R. 1993, A nonlinear control strategy for robust sliding mode performance in the presence of unmatched uncertainty. International Journal of Control 57, 1107–1123
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag London Limited
About this chapter
Cite this chapter
Davies, R., Edwards, C., Spurgeon, S.K. (1994). Robust tracking with a sliding mode. In: Zinober, A.S.I. (eds) Variable Structure and Lyapunov Control. Lecture Notes in Control and Information Sciences, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033678
Download citation
DOI: https://doi.org/10.1007/BFb0033678
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19869-7
Online ISBN: 978-3-540-39325-2
eBook Packages: Springer Book Archive