Zeno behavior in electromechanical hybrid systems: From theory to experimental validation

Abstract

The goal of this paper is to assess the capacity of Zeno phenomena to correctly predict the behavior of real physical systems. We begin by considering electromechanical hybrid systems. Formal conditions are given on when systems of this form display Zeno behavior, in which case the hybrid model is completed to allow for solutions to be carried past the Zeno point. The end result is periods of unconstrained and constrained motion, with transitions to the constrained motion occurring at the Zeno point, i.e., a Zeno periodic orbit. We then consider a double pendulum with a mechanical stop controlled by a DC motor, use these formal methods to predict the existence of a Zeno periodic orbit in simulation, and verify through experimentation that Zeno behavior provides an accurate description of the behavior of the physical system.