Design of block backstepping based nonlinear state feedback controller for pendubot

Design of a novel block-backstepping based nonlinear stabilizing control law of a pendubot is presented in this paper. It is a 2-DOF underactuated with unactuated shape variable and second order nonholonomic constraint. At the onset of the design, state model of the pendubot has been transformed into the block-strict feedback form. Thereafter, a systematic approach has been utilized to devise a backstepping control law for the pendubot system, which eventually yields a control law that is more conducive to practical applications. Lyapunov stability criteria has been used to analyze the stability of the overall system. Furthermore, stability of the zero dynamics has also been investigated to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. Finally, performance of the proposed control law has been studied in simulation environment. Indeed, main novelty of the proposed approach lies in the fact that a systematic block backstepping control approach has been proposed to yield a solution for the control problem of pendubot.