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
DOI:10.20537/nd200302