Stabilization of coupled inverted pendula: From discrete to continuous case

Abstract

This study is focused on the investigation of stabilization problem for the system of coupled inverted pendula. The corresponding algorithm of control is based on the feedback principles and demonstrates some features in the physical implementation of the stabilization process. In the discrete case, the wave-like motion appears and leads to an observable interference pattern. In the continuous case, the provided feedback algorithm allows to simulate the stabilization process for the initially unstable solid medium. In these case conditions, ensuring the stabilization process is presented in the form of corresponding physical restrictions on the wave motion. Also, within the small parameter method, we investigate the nonlinear oscillatory motion of the material (the solid medium is modeled by the proposed system with nonlinear coupling). Results of numerical simulation for the system under consideration are presented and discussed. Particularly, numerical results show that the nonlinear material exhibits greater stability than the linear one.