The theory of the control of a monocycle

The forward motion of a monocycle is studied in terms of a mechanical model: a cylinder with an inverted pendulum attached to it by a hige. The rotation of the pendulum about the cylinder is implemented by an electric drive. The monocycle can be moved (rolled) over a surface with the help of the same drive. The control parameter is a voltage of bounded magnitude. A control law (with saturation), linear in the phase coordinates, is constructed, under which the pendulum is stabilized in the upper unstable equilibrium position, while the monocycle is maintained in position or moved. The domain of attraction of the desired steady state may be made the maximum possible (in the linear approximation). The domain of stability of the equilibrium state of the system is constructed in the plane of the following parameters: the total feedback gain and the delay. Delay appears in the control loop when there is an inductance in the rotor circuit of the motor.