Abstract
A standard problem in hybrid control systems theory is to design discrete, or symbolic, feedback for a given continuous plant.When specifications are discrete, this problem can be solved by first approximating the continuous plant model by a (nondeterministic) automaton, and then synthesizing discrete (supervisory) control for the automaton. A necessary condition is that the approximation behaviour contains the behaviour of the underlying continuous plant model. Then, any controller forcing the approximation to obey the specifications will also force the continuous model to satisfy the specifications. We use a version of this approach which allows adjustment of approximation accuracy to address two simple process control problems: supervisory control of a three-tank laboratory experiment and safety enforcement for an evaporator. In both cases, the entire design process is carried through: we first determine a suitable abstraction, compute the minimally restrictive supervisor, and then present examples for closed loop trajectories.
Support from Deutsche Forschungsgemeinschaft under Grant Ra 516/3-1 and through “Sonderforschungsbereich” SFB 412 is gratefully acknowledged.
Research supported by the Information Technology Research Centre and Condata Technologies Ltd., both of Ontario, Canada.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. J. Antsaklis, J. A. Stiver, and M. Lemmon. Hybrid system modelling and autonomous control systems. In [6], pages 366–392.
P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, editors. Hybrid Systems Iv, Lecture Notes in Computer Science, Vol. 1273. Springer-Verlag, 1997.
B. A. Brandin and W. M. Wonham. Supervisory control of timed Discrete Event Systems. IEEE Trans. Automat. Contr., vol. 39, pp. 329–342, 1994.
J. C. Chou. Thermodynamic Properties of Aqueous Sodium Chloride Solutions from 32 to 350 F. Ph. D Thesis, Oklahoma State University, 1968.
K. Feldkamp Der Wärmeübergang beim Sieden von wässrigen Lösungen. Ph. D Thesis, Technische Universität Carolo-Wilhelmina, Braunschweig, 1969.
R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, editors, Hybrid Systems, Lecture Notes in Computer Science, Vol. 736. Springer-Verlag, 1993.
H.-M. Hanisch and S. Kowalewski. Diskontinuierlicher Misch-und Trennprozeß, Fallbeispiel für die Modellierung ereignisdiskreter Systeme und den systematischen Entwurf von Steuerungen. In: 3. Workshop GMA-Fachausschuß 1.8: Methoden der Steuerungstechnik. 1994.
T. Kailath, Linear Systems. Prentice-Hall, 1980.
J. Lunze. Qualitative modelling of linear dynamical systems with quantized state measurements. Automatica, 30:417–431, 1994.
I. N. Maksimova Determination of the Density of Aqueous Solutions. Russian Journal of Physical Chemistry, 39(3): 296–297, 1965.
J. Raisch. Nondeterministic automata as approximations for continuous systems-an approach with an adjustable degree of accuracy. Proc. 2nd MATHMOD (International Symposium on Mathematical Modelling), pp. 195–202. IMACS, Vienna. 1997.
J. Raisch and S. O’Young. A Totally Ordered Set of Discrete Abstractions for a given Hybrid or Continuous System. In [2], pp. 342–360.
J. Raisch and S. D. O’Young. Discrete approximation and supervisory control of continuous systems. Accepted for publication in IEEE Transactions on Automatic Control, Special Issue on Hybrid Systems.
J. Raisch. A Hierarchy of Discrete Abstractions for a given Hybrid Plant Model. Proc. ADPM’98 (Automatisation des Processus Mixtes: les Systèmes Dynamiques Hybrides), Reims, March 1998.
P. J. Ramadge and W. M. Wonham. Supervisory control of a class of discrete event systems. SIAM J. Control and Optimization, 25:206–230 1987.
P. J. Ramadge and W. M. Wonham. The control of discrete event systems. Proceedings of the IEEE, 77:81–98, 1989.
J. A. Stiver and P. Antsaklis. Modeling and analysis of hybrid control systems. In Proc. 31st IEEE Conference on Decision and Control, 1992.
Verein Deutscher Ingenieure (VDI)-Gesellschaft Verfahrenstechnik und Chemieingenieurswesen (GVC) (ed.) VDI-Wärmeatlas. VDI-Verlag, Frankfurt, 5.th edition, 1988.
J. C. Willems. Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control, 36:259–294, 1991.
I. D. Zaytsev and G. G. Aseyev Properties of Aqueous Solutions of Electrolytes. CRC Press, Boca Raton, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Raisch, J., Klein, E., Meder, C., Itigin, A., O’Young, S. (1999). Approximating Automata and Discrete Control for Continuous Systems — Two Examples from Process Control. In: Antsaklis, P., Lemmon, M., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems V. HS 1997. Lecture Notes in Computer Science, vol 1567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49163-5_16
Download citation
DOI: https://doi.org/10.1007/3-540-49163-5_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65643-2
Online ISBN: 978-3-540-49163-7
eBook Packages: Springer Book Archive