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.

本文解决了离散时间设置中全驱动机械系统控制中输入扰动的衰减问题。首先，针对 n 自由度 (DOF) 完全驱动的机械系统，提出了一种具有浸没和不变性 (I&I) 方法的离散时间干扰估计器设计。然后，建立了一个离散时间组合的反馈线性化和反步控制，该控制器使用估计的扰动信息。利用 Lyapunov 稳定性理论，在任意大的紧集中显示了估计器的全局渐近稳定性和整个闭环系统的局部渐近稳定性。为了展示所提出的基于复合观测器的离散时间控制方法的有效性，将其应用于三自由度机器人机械手。通过仿真，将建议的具有离散时间 I&I 观测器的直接离散时间组合反馈线性化和反步控制器的性能与具有另一个离散时间非线性扰动观测器的直接离散时间常规二阶滑模控制器的性能进行了比较。仿真结果证明了所提方法的优越性能。