Stabilization of Furuta Pendulum: A backstepping based hierarchical sliding Mode approach with disturbance estimation

An adaptive backstepping sliding mode controller, which combines both the merits of adaptive backstepping control and sliding mode control, is proposed to address the control problem of the Furuta Pendulum in the presence of external disturbances. At first, the underactuated state model of the Furuta Pendulum has been divided into two separate subsystems. Then a pair of first layer sliding surfaces is defined for each second-order subsystem. Two separate adaptive backstepping based control law is designed for each of the subsystem to ensure the states of each subsystem approach to their own sliding mode surface. Based on this two first layer sliding surfaces, a second layer sliding surface is defined correspondingly, through which a total control law is derivedto make sure that all states can converge to their desired value via Lyapunov stability theorem. The asymptotic stability of all the sliding surfaces has proven theoretically, and simulation results show the controller´s validity and its adaptive abilities for all kinds of extraneous disturbances.