Limit Cycle Behaviour of a Neural Controller with Delayed Bang-Bang Feedback

Authors: Travis Wiens, Greg Schoenau, Rich Burton

Abstract:

It is well known that a linear dynamic system including a delay will exhibit limit cycle oscillations when a bang-bang sensor is used in the feedback loop of a PID controller. A similar behaviour occurs when a delayed feedback signal is used to train a neural network. This paper develops a method of predicting this behaviour by linearizing the system, which can be shown to behave in a manner similar to an integral controller. Using this procedure, it is possible to predict the characteristics of the neural network driven limit cycle to varying degrees of accuracy, depending on the information known about the system. An application is also presented: the intelligent control of a spark ignition engine.

Keywords: Control and automation, artificial neural networks, limit cycle

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333875

References:

[1] T. Wiens, R. Burton, G. Schoenau, and M. Sulatisky, "Intelligent fuel air ratio control of gaseous fuel SI engines," Tech. Rep. MISC-0168, Saskatchewan Research Council, Saskatoon, 2006.
[2] J. Heywood, Internal Combustion Engine Fundamentals. New York: McGraw Hill, 1988.
[3] P. Werbos, "Backpropagation Through Time: What It Does and How to Do it," in Proceedings of the IEEE, vol. 78, pp. 1550-1560, 1990.
[4] D. Saad, ed., On-line Learning in Neural Networks. Cambridge: Cambridge University Press, 1998.
[5] T. Wiens, R. Burton, and G. Schoenau, "Algebraic inversion of an artifcial neural network classifer," in Proceedings of the European Symposium on Artificial Neural Networks, (Bruges), 2007.
[6] D. Zwillinger, CRC Standard Mathematical Tables and Formulae. Boca Raton: Chapman & Hall/CRC press, 2002.
[7] T. Wiens, R. Burton, G. Schoenau, M. Sulatisky, S. Hill, and B. Lung, "Preliminary experimental verification of an intelligent fuel air ratio controller," Tech. Rep. 2007-01-1339, Society of Automotive Engineers (SAE), 2007.