Abstract
Analysis of linear systems with relay feedback is a classical field. The early work on relay feedback was motivated by using relays as amplifiers. These applications became less interesting, because the development of electronic technology made relay amplifiers obsolete. A discussion of relay feedback is found in the classical book [12]. Analysis of systems with relay feedback were given by [27],[10],[11],[22],[23],[24],[25],[7],[16],[18],[19]. Much of the analysis of relay feedback has been done using the describing function, see [5] and [8]. An interesting discussion of the validity of the describing function approximation is found in 20. Exact conditions for limit cycle oscillations under relay feedback were developed in the papers by Hamel and Tsypkin. Tsypkin’s work is particularly interesting because of its close relation with the approximate methods. An extensive treatment is found in [26], which is an English translation of a book that was first published in Russian in 1974.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Årzén, K. E., Realization of Expert System Based Feedback Control, PhD thesis TFRT-1029, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden (1987).
Åström, K.J. AND T. Hägglund, “Automatic tuning of simple regulators with specifications on phase and amplitude margins,” Automatica, 20 (1984), pp. 645–651.
Åström, K.J. AND T. Hägglund, Automatic Tuning of PID Controllers, Instrument Society of America, Research Triangle Park, North Carolina (1988).
Åström, K.J. AND B. Wittenmark, Computer Controlled Systems-Theory and Design, Prentice-Hall, Englewood Cliffs, New Jersey, second edition (1990).
Atherton, D.P., Nonlinear Control Engineering-Describing Function Analysis and Design, Van Nostrand Reinhold Co., London, UK (1975).
Cook, P.A., “Simple feedback systems with chaotic behaviour,” Systems and Control Letters, 6 (1985), pp. 223–227.
Eckman, D.P., “Phase-plane analysis. A general method of solution for two-position process control,” Trans. ASME, 76 (1954), pp. 109–116.
Gelb, A. AND W.E.V. Velde, Multiple-Input Describing Functions and Nonlinear System Design, McGraw-Hill, New York (1968).
Hägglund, T. AND K.J. Åström, “Industrial adaptive controllers based on frequency response techniques,” Automatica, 27 (1991), pp. 599–609.
Hamel, B., “Étude mathématique des systèmes à plusieurs degres de liberte décrits par des équations linéaires avec un terme de commande discontinu,” in Proceedings of the Journées d’Ètudes des Vibrations A.E.R.A., Paris, France (1950).
Hamel, B., “A mathematical study of on-off controlled higher order systems,” in Proceedings of the Symposium on Nonlinear Circuit Analysis, Polytechnic Institute of Brooklyn, New York, volume 6 (1956), pp. 225–232.
Hazen, H.L., “Theory of servomechanisms,” J. Franklin Institute, 218 (1934), pp. 279–330.
Holmberg, U., Relay Feedback of Simple Systems, PhD thesis TFRT-1034, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden (1991).
Horowitz, I.M., “Comparison of linear feedback systems with self-oscillating adaptive systems,” IEEE Transactiosn on Automatic Control, AC-9 (1964),pp. 386–392.
Horowitz, I.M., J.W. Smay, AND A. Shapiro, “A synthesis theory for self-oscillating adaptive systems (soas),” Automatica, 10 (1974), pp. 381–392.
Lozier, J.C., “Carrier-controlled relay servos,” Elec. Eng., 69 (1950), pp. 1052–1056.
Lundh, M. AND K.J. Åström, “Automatic initialization of robust adaptive controllers,” in Preprints 4th IFAC Symposium on Adaptive Systems in Control and Signal Processing, Grenoble (1992), pp. 439–444.
Maeda, H. AND S. Kodama, “Stability of a relay servosystem,” IEEE Transactions on Automatic Control, 14 (1969), pp. 555–558.
Maeda, H. AND S. Kodama, “A new stability criterion of a relay servosystem,” IEEE Transactions on Automatic Control, 15 (1970), pp. 275–276.
Mees, A.I., Dynamics of Feedback Systems, John Wiley & Sons, New York (1981).
Schuck, O.H., “Honeywell’s history and philosophy in the adaptive control field,” in Proc. Self Adaptive Flight Control Symposium, Wright Patterson AFB, Ohio. Wright Air Development Center, P.C. Gregory, ed. (1959).
Tsypkin, Ya.Z., “Theory of intermittent control,” Avtomatika i Telemekhanika, Vol. 10 (1949) Part I, pp. 189–224; Part II, pp. 342–361; Vol. 11 (1950) Part III, pp. 300–331.
Tsypkin, Ya.Z., “Stability and self-oscillations in relay systems of automatic control,” Trudy LKVVIA, No. 32 (1950), pp. 38–66.
Tsypkin, Ya.Z., “On the stability of periodic modes in relay systems of automatic control,” Avtomatika i Telemekhanika, 14:5 (1953), pp. 638–646.
Tsypkin, Ya.Z., “On the determination of steady-state oscillations of on-off feedback systems,” Trans. IRE Circuit Theory, CT-9 (1962), p. 279.
Tsypkin, Ya.Z., Relay Control Systems, Cambridge University Press, Cambridge, UK (1984).
Weiss, H.K., “Analysis of relay servomechanisms,” J. Aeronautical Sciences, 13 (1946), pp. 364–376.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this paper
Cite this paper
ÅStröM, K.J. (1995). Oscillations in Systems with Relay Feedback. In: Åström, K.J., Goodwin, G.C., Kumar, P.R. (eds) Adaptive Control, Filtering, and Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8568-2_1
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8568-2_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6439-2
Online ISBN: 978-1-4419-8568-2
eBook Packages: Springer Book Archive