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Dynamics of balance with act-and-wait control

University of British Columbia

In this thesis, we studied the act-and-wait control mechanism on the stabilization of the inverted pendulum in both piecewise constant feedback and continuously varying feedback models. We also extend the act-and-wait control mechanism with a more general model: the act-and-wait control with frequently varying feedback, which includes piecewise constant feedback and continuously varying feedback as two of its extreme cases. The frequently varying feedback model is valuable in approximating the continuously varying feedback system when the delay is large. The modeling error is discussed in the comparison of piecewise constant feedback and continuously varying feedback. The robustness of the three models are studied in the context of the parametric stability regions as well as for the interaction of delay and noise. We discovered that although act-and-wait control can stabilize the pendulum system even with large delay, the robustness is impaired by large delays. As a result, the piecewise constant feedback system is more sensitive to parametric noise than the frequently and continuously varying feedback models. The interplay of act-and-wait control and external noise leads the system to a periodically varying density for its state.

Text

2014-08-21

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50098

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/