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**Local bifurcation analysis in the Furuta pendulum via normal forms.**
*(English)*
Zbl 1090.70509

Summary: Inverted pendulums are very suitable to illustrate many ideas in automatic control of nonlinear systems. The rotational inverted pendulum is a novel design that has some interesting dynamics features that are not present in inverted pendulums with linear motion of the pivot. In this paper the dynamics of a rotational inverted pendulum has been studied applying well-known results of bifurcation theory. Two classes of local bifurcations are analyzed by means of the center manifold theorem and the normal form theory – first, a pitchfork bifurcation that appears for the open-loop controlled system; second, a Hopf bifurcation and its possible degeneracies, of the equilibrium point at the upright pendulum position, that is present in the controlled closed-loop system. Some numerical results are also presented in order to verify the validity of our analysis.

### MSC:

70K50 | Bifurcations and instability for nonlinear problems in mechanics |

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\textit{D. Pagano} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, No. 5, 981--995 (2000; Zbl 1090.70509)

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### References:

[1] | Äström K. J., Proc. 13th IFAC World Congress, San Francisco, USA pp 37– (1996) |

[2] | DOI: 10.1243/PIME_PROC_1992_206_043_02 |

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