Global stabilization of inertia wheel systems with a novel sliding mode-based strategy

Inertia wheel pendulums are known as benchmark underactuated systems, which have attracted a lot of attention in recent years. However, the convergence time of existing control methods proposed for inertia wheel pendulums is usually very long. In view of this, we propose a novel sliding mode control strategy for inertia wheel systems in this paper, which can guarantee that the desired equilibrium point is quasi-exponentially stable even in the presence of persistent external disturbances. To be specific, we will first perform some model transformations about the system, by which the dynamic equations are separated into two parts, i.e., an unactuated quasi-linear part and an actuated nonlinear part. Based on the newly obtained model, an appropriate manifold is designed subsequently, and a sliding mode controller is constructed to keep the system state on the manifold. Furthermore, we demonstrate that the state variables will converge to their desired values quasi-exponentially fast as long as they are kept on the manifold. The performance of the closed-loop system is rigorously proved by Lyapunov techniques. Simulation tests are also carried out to validate the efficiency of the proposed controller.