Geodesic
Control of an Inverted Wheeled Pendulum
Russian journal of nonlinear dynamics, Tome 16 (2020) no. 3, pp. 421-436

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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. 
@article{ND_2020_16_3_a1,
     author = {O. M. Kiselev},
     title = {Control of an {Inverted} {Wheeled} {Pendulum}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {421--436},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2020_16_3_a1/}
}
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O. M. Kiselev. Control of an Inverted Wheeled Pendulum. Russian journal of nonlinear dynamics, Tome 16 (2020) no. 3, pp. 421-436. http://geodesic.mathdoc.fr/item/ND_2020_16_3_a1/