Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-18T20:22:12.883Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of an adaptive third-order relay control system using non-linear switching surface theory

Published online by Cambridge University Press:  14 February 2012

A. S. I. Zinober
A. S. I. Zinober
Affiliation:
Department of Applied Mathematics and Computing Science, University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Synopsis

Using a non-linear transformation of the state space, the dynamic behaviour of an adaptive thirdorder relay system is analysed. The control strategy yields state paths close to the time-optimal trajectories.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 3 , 1977 , pp. 239 - 254
Copyright
Copyright © Royal Society of Edinburgh 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Zinober, A. S. I.. Adaptive relay control of second-order systems. Internal. J. Control 21 (1975), 81–98.CrossRefGoogle Scholar
2Flügge-Lotz, I. and Titus, H. A.. Optimum and quasi-optimum control of third-and fourth-order systems. Proc. Internat. Fed. Autom. Control Congress, Basel (1963), 363.Google Scholar
3Grensted, P. E. W.. and Fuller, A. T.. Minimization of integral-square-error for non-linear control systems of third and higher order. Internat. J. Control 2 (1965), 33–73.CrossRefGoogle Scholar
4Zinober, A. S. I.. and Fuller, A. T.. The sensitivity of nominally time-optimal control systems to parameter variation. Internat. J. Control 17 (1973), 673–703.Google Scholar
5Fuller, A. T.. Stability of relay control systems. Proc. Internat. Fed. Autom. Control Congress, Warsaw, 20 (1969), 32–42.Google Scholar
6Fuller, A. T.. Dimensional properties of optimal and sub-optimal nonlinear control systems. J. Franklin Inst, 289 (1970), 379–393.Google Scholar
7Flügge-Lotz, I.. Discontinuous automatic control (Princeton: University Press, 1953).Google Scholar
8André, J. and Seibert, P.. Über stückweise lineare Differentialgleichungen, dié bei Regelungsproblemen auftreten, I and II. Arch. Math. 7 (1956), 148–165.Google Scholar
9Weissenberger, S.. Stability-boundary approximation for relay-control systems with a steepest ascent construction of Lyapunov functions. J. Bas. Engrg 88 (1966), 419–428.Google Scholar
10Roberts, J. A.. Linear control of saturating control systems. Internal. J. Control 12 (1970), 239–255.CrossRefGoogle Scholar
11Fuller, A. T.. Sub-optimal nonlinear controllers for relay and saturating control systems. Internal.J. Control 13 (1971), 401–428.CrossRefGoogle Scholar
12Fuller, A. T.. Linear control of non-linear systems. Internat. J. Control 5 (1967), 197–243.CrossRefGoogle Scholar
13Zinober, A. S. I.. Relay control of plants subject to parameter uncertainty (Cambridge Univ.: Ph.D. Thesis, 1974).Google Scholar