Inverted pendulum stabilization via a Pyragas-type controller: revisiting the triple zero singularity

Abstract : The use of Pyragas-Type controller proved interest in the stabilization of unstable periodic orbits. The stabilization problem of a balancing inverted pendulum on an horizontally moving cart by the use of such a controller is considered. The main objective of the paper is to propose delayed control law containing only proportional gains able to stabilize the inverted pendulum by avoiding the existence of a triple zero eigenvalue at the origin. We analyze the center dynamics described by a three dimensional system of ordinary differential equations (ODEs) with a codimension-three triple zero bifurcation. Furthermore, the stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium is also proposed. This analysis is done in order to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01062776
Contributor : Irinel-Constantin Morarescu <>
Submitted on : Wednesday, September 10, 2014 - 3:12:55 PM
Last modification on : Tuesday, June 4, 2019 - 11:08:06 AM

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  • HAL Id : hal-01062776, version 1

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Islam Boussaada, Irinel-Constantin Morarescu, Silviu-Iulian Niculescu. Inverted pendulum stabilization via a Pyragas-type controller: revisiting the triple zero singularity. 19th IFAC World Congress on International Federation of Automatic Control (IFAC 2014), Aug 2014, Cape Town, South Africa. ⟨hal-01062776⟩

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