Nonlinear related system of inverted pentulums control

In this paper we propose a linear and nonlinear mathematical model of linked inverse pendulums. We investigate dynamics of this mechanical system and determined the stability parameters. After that we presented results of experiments for various system configurations. In conclusion we constructed stability zones in the parameter space for linear and nonlinear systems. The system is controlled by feedback. The introduced nonlinear spring stiffness is part of the dynamic control. There are three stationary points in the phase space, however, only one of them has real coordinates. As a result of the study, it was shown that a complex unstable system consisting of oscillators with a nonlinear coupling can be described by a fairly simple system of equations, and its stabilization, under certain conditions, is possible with the help of a fairly simple control of the periodic feedback function.