A model of maintaining balance by a person on the seesawстатья

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[1] Gugayev K. V., Kruchinin P. A., Formalskii A. M. A model of maintaining balance by a person on the seesaw // Journal of Applied Mathematics and Mechanics (English translation of Prikladnaya Matematika i Mekhanika). — 2016. — Vol. 80, no. 4. — P. 316–323. 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, whose axis is perpendicular to the pendulum. The support can oscillate by rolling on a horizontal surface, and the pendulum can oscillate in a plane that is perpendicular to the cylinder axis. 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 system in such a manner that the region of attraction of the linearized system would be the maximum possible. Several characteristic trajectories of the system for the control constructed are considered. [ DOI ]

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