Limit Cycle Behaviour of a Neural Controller with Delayed Bang-Bang Feedback
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56557", author = "Travis Wiens and Greg Schoenau and Rich Burton", title = "Limit Cycle Behaviour of a Neural Controller with Delayed Bang-Bang Feedback", 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", volume = "1", number = "12", pages = "717-6", }