Hierarchical double integral sliding-mode control for second-order underactuated systems

This study presents a hierarchical double integral sliding-mode control (HDISMC) system for a class of second-order underactuated systems. First, the second order underactuated system is divided into two subsystems. Then, two levels double integral sliding surfaces are defined in HDISMC to drive the both subsystems toward the desired dynamics with an invariance property to uncertainties. In HDISMC, the control law is derived using Lyapunov theorem to guarantee the closed-loop stability. Moreover, the designed double integral sliding surface reinforces the control law with integral (I) control feature to eliminate the steady-state error more effectively. Finally, control simulation of an inverted pendulum cart system is given to illustrate the validities of the proposed control system using various operating conditions.