Synchronization of pendulum like systems

Abstract

Synchronization is a phenomenon that is widely encountered in nature, life sciences and engineering. There exist various synchronization definitions in various research fields. The general definition for synchronization is the adjustment of rhythms of oscillating systems due to their weak interaction. Synchronization problem depends on the type of applications that require suitable properties and comparison functions. Different applications require different properties and comparison functions. Throughout our study, we choose the comparison function to be the difference of the states variables of the systems in hand. In this thesis, we will present types and methods of synchronization which has practical applications, i.e. mechanical systems. Then, we will investigate the passive controlled in-phase synchronization of spring-damper coupled single and double pendulum systems by using various stability analysis for both the system in hand and its appropriately defined error dynamics. We mostly achieved in-phase synchronization in these coupled pendulum systems with a few exceptions which are based on several conditions. Finally, we will explain the masterslave synchronization of two ball hoppers using two different gait controllers, namely, fully-actuated and under-actuated controllers. By using fully-actuated controller for the slave hopper, we achieved apex state synchronization and by using under-actuated controller for the slave hopper, we achieved apex position synchronization between these two hoppers in master slave configuration.