H∞ Control of the Furuta Pendulum with Backlash and Analysis of the Effect of Bounded-Disturbance

Abstract

In this paper, we consider the $\mathcal{H}_{\infty}$ stabilization problem of the Furuta pendulum with backlash in the drive train and analyze the effect of fictitious bounded-disturbance approximately representing the nonlinearity. Based on the reachable set analysis of the disturbance with an $\mathcal{L}_{2}$ constraint, a subset of the reachable region with $\mathcal{L}_{\infty}$ constraint is computed. By estimating its volume in the state space, the performance against the backlash nonlinearity is evaluated. The behaviour of the closed-loop system is verified through numerical simulations of the time response.