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- W2890615674 abstract "In this paper, bifurcation theory is used to classify dierent dynamical behaviors occurringin a mechanical system under bounded control actions. The example is a pendulumwith an inertia disc mounted in its free extreme. By design, the control action can only beintroduced by means of an external torque applied by a DC motor to the inertia disc. Imposinga bounded control action places an important obstacle to the design of a controllercapable to drive the pendulum from rest to the inverted position and to stabilize it there.The only way in which the pendulum can reach the inverted position is by oscillationsof increasing amplitudes. Due to the saturation of the control law the trivial equilibriumpoints -the rest and the inverted position- experiment a pitchfork bifurcation when onekey parameter is varied. Therefore, two additional equilibrium points associated to eachequilibrium of the non-forced system do appear. If another control parameter is varied,homoclinic and heteroclinic bifurcations, saddle-node bifurcations of periodic orbits, andHopf bifurcations of equilibria do appear. Some of these codimension one bifurcationsare organized in a codimension two Bogdanov-Takens bifurcation, when varying two parameterssimultaneously. The application of both numerical and analytical tools frombifurcation theory to understand and classify the dynamical behavior of the closed-loopsystem facilitates the control law design, as shown in the paper." @default.
- W2890615674 created "2018-09-27" @default.
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- W2890615674 date "2002-01-01" @default.
- W2890615674 modified "2023-09-26" @default.
- W2890615674 title "Bifurcation Theory In Mechanical Systems." @default.
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