Immersion and invariance disturbance observer-based nonlinear discrete-time control for fully actuated mechanical systems

This paper addresses the attenuation problem of input disturbances in the control of fully actuated mechanical systems in the discrete-time setting. Firstly, a discrete-time disturbance estimator design with immersion and invariance (I&I) approach is presented for the n-degrees of freedom (DOF) fully actuated mechanical systems. Then, a discrete-time combined feedback linearising and backstepping control is established that this controller uses the estimated disturbance information. Global asymptotic stability of the estimator and local asymptotic stability of the entire closed-loop system in an arbitrarily large compact set are shown utilising the Lyapunov stability theory. In order to show the effectiveness of the proposed composite observer-based discrete-time control method, it is applied to the 3-DOF robotic manipulator. Performance of proposed direct discrete-time combined feedback linearising and backstepping controller with discrete-time I&I observer is compared with a direct discrete-time conventional second-order sliding mode controller with another discrete-time nonlinear disturbance observer via simulations. The superior performance of the proposed method is demonstrated with simulation results.