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 Rus. J. Nonlin. Dyn., 2020, Volume 16, Number 3, Pages 421–436 (Mi nd719)

Nonlinear physics and mechanics

Control of an Inverted Wheeled Pendulum on a Soft Surface

O. M. Kiselev

Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Science, ul. Chernyshevskogo 112, Ufa, 450008 Russia

Abstract: The dynamics of an inverted wheeled pendulum controlled by a proportional plus integral plus derivative action controller in various cases is investigated. The properties of trajectories are studied for a pendulum stabilized on a horizontal line, an inclined straight line and on a soft horizontal line. Oscillation regions on phase portraits of dynamical systems are shown. In particular, an analysis is made of the stabilization of the pendulum on a soft surface, modeled by a differential inclusion. It is shown that there exist trajectories tending to a semistable equilibrium position in the adopted mathematical model. However, in numerical simulations, as well as in the case of real robotic devices, such trajectories turn into a limit cycle due to round-off errors and perturbations not taken into account in the model.

Keywords: pendulum, control, stability, differential inclusion

DOI: https://doi.org/10.20537/nd200302

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MSC: 37N35, 70E60, 70Q05
Accepted:19.05.2020
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Citation: O. M. Kiselev, “Control of an Inverted Wheeled Pendulum on a Soft Surface”, Rus. J. Nonlin. Dyn., 16:3 (2020), 421–436

Citation in format AMSBIB
\Bibitem{Kis20} \by O. M. Kiselev \paper Control of an Inverted Wheeled Pendulum on a Soft Surface \jour Rus. J. Nonlin. Dyn. \yr 2020 \vol 16 \issue 3 \pages 421--436 \mathnet{http://mi.mathnet.ru/nd719} \crossref{https://doi.org/10.20537/nd200302} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4159465} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85095437338}