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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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Bibliographic databases:

MSC: 37N35, 70E60, 70Q05
Received: 16.12.2019
Accepted:19.05.2020
Language:

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}


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