A model of maintaining balance by a person on the seesaw. Issue 4 (2016)

• Record Type: Journal Article
• Authors: Gugayev, K.V.; Kruchinin, P.A.; Formalskii, A.M.
• Is Part Of: Journal of applied mathematics and mechanics. Volume 80:Issue 4(2016)
• Page Start: 316
• Page End: 323
• Publication Date: 2016
• Subjects: Mechanics, Analytic -- Periodicals; Mechanics, Applied -- Periodicals; Applied mathematics -- Periodicals; Mécanique analytique -- Périodiques; Mécanique appliquée -- Périodiques; 531.01515
• DOI: 10.1016/j.jappmathmech.2016.09.006
• Languages: English
• ISSNs: 0021-8928

Abstract

Abstract: A very 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.