The paper discusses the relatively new approach of relay autotuning and shows how a sound understanding of the approach requires knowledge of two approaches introduced early in the search for methods to study nonlinear control systems. The two approaches - the describing function method and procedures for evaluating limit cycles exactly in relay systems - are first reviewed. After a short section on techniques for choosing parameters of fixed controllers it is shown how relay autotuning can be used for PID controllers based on either plant critical point information or the estimation of a plant model. Finally some examples are given which illustrate the controller design techniques presented.
Åström, K. J.1970: Introduction to Stochastic Control Theory. New York: Academic Press.
2.
Åström, K. J. and Hägglund, T.1984: Auto-Åstromatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica20, 645-651.
3.
Atherton, D. P.1975: Nonlinear control engineering - describing function analysis and design. New York: Van Nostrand Reinhold Co.
4.
Atherton, D. P.1982: Oscillations in relay systems. Transactions of the Institute of Measurement and Control3, 171-184.
5.
Atherton, D. P. 1997: Improving the accuracy of autotuning parameter estimates. Proceedings, IEEE International Conference on Control Applications, Hartford, USA, 51-56.
6.
Atherton, D. P.1999: PID controller tuning. Computing and Control Engineering Journal, April, 175-179.
7.
Atherton, D. P. and Boz, A. F. 1997: Autotuning of phase lead controllers. 4th IFAC Workshop on Algorithms and Architectures for Real-Time Control (AARTC ’97), Vilamoura, Portugal, 111-116.
8.
Atherton, D. P., Benouarets, M. and Nanka-Bruce, O. 1993: Design of nonlinear PID controllers for nonlinear plants. Proceedings, IFAC World Congress ’93, Volume 3, Sydney, Australia, 355-358.
9.
Boz, A. F. and Atherton, D. P. 1998: Using standard forms for controller design. Proceedings, UKAAC International Conference on Control 1998 (Control ’98), University of Wales, Swansea, 1066-1071.
10.
Chung, J. K.-C. and Atherton, D. P.1966: The determination of periodic modes in relay systems using the state space approach. International Journal of Control4, 105-126.
11.
Graham, D. and Lathrop, R. C.1953: The synthesis of optimum response: criteria and standard forms II. Transactions of the AIEE72, 273-288.
12.
Hamel, B. 1949: Contribution á l’etude mathématique des systémes de réglage par tout-ou-rien. CEMV, Service Technique Aeronautique, Volume 17.
13.
Johansson, K.H. 1997: Relay feedback systems and multivariable control. PhD Thesis, Lund Institute of Technology, Sweden.
14.
Kaya, I. and Atherton, D. P. 1998. An improved mathe parameter estimation method using limit cycle data. Proceedings, UKACC International Conference on Control 1998 (Control ’98), University of Wales, Swansea, 682-687.
15.
Majhi, S. 1999: Relay feedback process identification and controller design. DPhil Thesis, University of Sussex.
16.
Majhi, S. and Atherton, D. P. 1998: Stability of limit cycles in relay control systems. Proceedings of the 4th IFAC Nonlinear Control Systems Design Symposium NOLCOS ’98, University of Twente, Enschede, The Netherlands, 89-94.
17.
Majhi, S. and Atherton, D. P.1999: Autotuning and controller design for proceses with small time delays. IEE Proceedings, Control Theory and Applications146, 415-425.
18.
Tsypkin, Y. Z.1984: Relay control systems. Cambridge, MA: Cambridge University Press.
19.
Yu, Cheng-Ching1999: Autotuning of PID controllers. London: Springer-Verlag.
20.
Zhuang, M. and Atherton, D. P.1993: Automatic tuning of optimum PID controllers. IEEE Proceedings, Control Theory and Applications140, 216-224.
21.
Ziegler, J. G. and Nichols, N. B.1942: Optimum settings for automatic controllers. Transactions of the ASME64, 759-768.
