Abstract
The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis in a suitable frequency band. Moreover, due to the existing connection between limit cycle bifurcations and routes to chaos, the obtained predictions can also give a rough indication of possible regions of chaotic dynamics. Based on these analysis results, an approach to limit cycle bifurcation control is then proposed. The control design is based on a frequency interpretation of the bifurcation conditions obtained via harmonic balance approach. Examples of the control technique for a number of important bifurcations are reported.
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Basso, M., Genesio, R. Analysis and Control of Limit Cycle Bifurcations. 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_7
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DOI: https://doi.org/10.1007/978-3-540-44925-6_7
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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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