Abstract:
Control systems, driven by a discontinuous unit feedback in a Hilbert space, are studied. The equation which describes a system motion, taking place in the discontinuity ...Show MoreMetadata
Abstract:
Control systems, driven by a discontinuous unit feedback in a Hilbert space, are studied. The equation which describes a system motion, taking place in the discontinuity manifold and further referred to as a sliding mode, is derived by means of a special regularization technique. Based on the sliding mode equation, the procedure of synthesis of a discontinuous unit control signal is developed. Restricted to a class of infinite-dimensional systems with finite-dimensional unstable part, this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed-loop system with respect to matched disturbances. As an illustration of the capabilities of the procedure proposed, a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators.
Published in: IEEE Transactions on Automatic Control ( Volume: 45, Issue: 5, May 2000)
DOI: 10.1109/9.855545
References is not available for this document.
Select All
1.
A. M. Breger, A. G. Butkovskii, V. A. Kubyshkin and V. I. Utkin, "Sliding modes for control of distributed parameter entities subjected to a mobile multicycle signal", Automation and Remote Contr., vol. 41, pp. 346-355, 1980.
2.
C. I. Byrnes and A. Isidori, "Asymptotic stabilization of minimum phase nonlinear systems", IEEE Trans. Automat. Contr., vol. 10, pp. 1122-1137, 1991.
3.
R. F. Curtain and A. J. Pritchard, Infinite-Dimensional Linear Systems Theory, Berlin:Springer-Verlag, 1978.
4.
J. C. Doyle, K. Glover, P. P. Khargonekar and B. A. Francis, " State-space solutions to standard H \$_{2}\$ and H \$_{infty}\$ control problems ", IEEE Trans. Automat. Contr., vol. 34, pp. 831-847, 1989.
5.
N. Dunford and J. T. Schwartz, Linear Operators, New York:Wiley, 1958.
6.
C. Foias, H. Özbay (Ozbay) and A. Tannenbaum, Robust Control of Infinite Dimensional Systems: Frequency Domain Methods, U.K., London:Springer-Verlag, 1996.
7.
A. Friedman, Partial Differential Equations, New York:Holt, Reinhart, and Winston, 1969.
8.
S. Gutman, "Uncertain dynamic systems̵A Lyapunov min̵max approach", IEEE Trans. Automat. Contr., vol. AC-24, pp. 437-449, 1979.
9.
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Berlin:Springer-Verlag, 1981.
10.
B. van Keulen, H\$_{infty}\$-Control for Distributed Parameter Systems: A State-Space Approach, MA, Boston:Birkhauser, 1993.
11.
A. A. Kirillov and A. D. Gvishiani, Theorems and Problems in Functional Analysis, New York:Springer-Verlag, 1982.
12.
M. A. Krasnoselskii, Integral Operators in Spaces of Summable Functions, Noordhoff:Leyden, 1976.
13.
S. G. Krein, Linear Differential Equations in Banach Space, RI, Providence:American Mathematical Society, 1971.
14.
Y. V. Orlov, "Application of Lyapunov method in distributed systems", Automation and Remote Contr., vol. 44, pp. 426-430, 1983.
15.
Y. V. Orlov, "Sliding mode̵Model reference adaptive control of distributed parameter systems", Proc. 32nd IEEE Conf. Decision and Control, pp. 2438-2445, 1993.
16.
Y. V. Orlov and V. I. Utkin, "Use of sliding modes in distributed system control problems", Automation and Remote Contr., vol. 43, pp. 1127-1135, 1982.
17.
Y. V. Orlov and V. I. Utkin, "Sliding mode control in infinite-dimensional systems", Automatica, vol. 23, pp. 753-757, 1987.
18.
V. I. Utkin, Sliding Modes in Control Optimization, Germany, Berlin:Springer-Verlag, 1992.
19.
V. I. Utkin and Y. V. Orlov, Theory of Sliding Mode Control in Infinite-Dimensional Systems, Russia, Moscow:Nauka, 1990.
20.
Deterministic Control of Uncertain Systems, U.K., London:Peter Peregrinus, 1990.
21.
T. Zolezzi, "Variable structure control of semilinear evolution equations" in Partial Differential Equations and The Calculus of Variations, MA, Boston:Birkhauser, vol. 2, pp. 997-1018, 1989.
