Abstract
In this chapter the mathematical tools from bifurcation theory are used within the framework of feedback control systems. The first part deals with a simple example where the amplitude of limit cycles and the appearance of period-doubling bifurcations are controlled using a method derived from the frequency domain approach. In the second part, bifurcation theory is used to analyze the dynamical behavior of an inverted pendulum with saturated control. The main objective is to find appropriate values of the controller parameters to achieve the stabilization of the pendulum at the inverted position and, at the same time, to obtain the largest basin of attraction.
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Alonso, D.M., Berns, D.W., Paolini, E.E., Moiola, J.L. Bifurcation Control in Feedback Systems. In: Chen, G., Hill, D.J., Yu, X. (eds) Bifurcation Control. Lecture Notes in Control and Information Science, vol 293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44925-6_10
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DOI: https://doi.org/10.1007/978-3-540-44925-6_10
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40341-8
Online ISBN: 978-3-540-44925-6
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