Discrete-Time Backstepping Control for Underactuated Mechanical System with a Novel Coordinate Transformation

Abstract

In this study, a discrete-time backstepping control is proposed for n-dof nonlinear mechanical systems via discrete-time partial feedback linearization and a novel discrete-time coordinate transformation. Firstly, the discrete-time model of the considered class of system is obtained using Forward Euler approximation. Then, a partial feedback controller is established in the discrete-time setting. Afterwards, a novel coordinate transformation that enables the discrete-time backstepping controller construction is proposed for the considered partially linearized systems. After applying the coordinate transformation, the discrete-time backstepping controller design is performed. The Lyapunov stability of the closed-loop system is shown. The proposed method is tested on the cart-pendulum system by simulations.