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    Control of an Inverted Wheeled Pendulum on a Soft Surface

    Received 16 December 2019; accepted 19 May 2020

    2020, Vol. 16, no. 3, pp.  421-436

    Author(s): Kiselev O. M.

    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
    Citation: Kiselev O. M., Control of an Inverted Wheeled Pendulum on a Soft Surface, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 3, pp.  421-436

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