Power-continuous synchronisation of oscillators: A novel, energy-free way to synchronise dynamical systems

Abstract

Synchronisation is an essential part of many controlled dynamical systems, in particular in the limb motion of legged robots. In this paper we introduce a novel control strategy that allows synchronisation of two oscillators without using any external power, but by modulating the power flow between the two oscillators. We then derive a separate energy-level controller that regulates the oscillation amplitude, again without changing the system's total energy. Finally, we show that the strategy works on a realistic mechanical system, by synchronising the phase difference and apex height of two bouncing masses.