Swing-Up and Stabilization Control of Inverted-Pendulum Systems via Coupled Sliding-Mode Control Method

This paper presents a coupled sliding-mode control (SMC) of inverted-pendulum systems. An SMC law is designed to force a coupled sliding surface (which consists of sliding surfaces of both actuated and unactuated subsystems) to be reached in finite time, such that zero dynamics are generated in the form of a second-order damped and forced nonlinear differential equation. The stability analysis is provided to show that the resulting zero dynamics is guaranteed to be semiglobally asymptotically stable over the upper half-plane as well as over the whole plane except the horizon. This property is maintained even in the presence of the matched disturbance by virtue of the sliding-mode approach. Using the semiglobal nature of the stability of the zero dynamics, the aggressive swing-up (in one time, without swinging motion) and stabilization control can be achieved by a single coupled SMC law, without involving the switching (or hybrid) scheme in the previous works. The performance of the proposed method is demonstrated in both numerical simulations and experiments for the swing-up and stabilization control of inverted-pendulum systems such as cart-pendulum and Furuta-pendulum.