ИСТИНА

Relatively simple model of the process of maintaining balance by a person standing on a seesaw is considered. The model consists of a planar single-link inverted pendulum, which is connected by means of a cylindrical hinge, i.e., an “ankle joint”, to a support in the form of a segment of cylinder (seesaw), whose axis is perpendicular to the pendulum. The support can oscillate by rolling on a horizontal surface, and the pendulum can oscillate in the same plane as seesaw. The studied system has unstable equilibrium with vertical inverted pendulum and horizontal upper surface of the seesaw. The control is a torque applied on the axis of the hinge. This torque is assumed to have a restricted absolute value. A control law is constructed in the form of feedback along a single “unstable” coordinate of the open loop system in such a manner that the region of attraction of the unstable equilibrium would be the maximum possible. Several characteristic trajectories of the nonlinear system for the control constructed are considered.