A Novel Predefined Time PD-Type ILC Paradigm for Nonlinear Systems

Abstract

Intelligent robotics has drawn a great deal of attention due to its high precision, stability, and reliability, which are the basic key factors for industrial automation. This paper proposes an iterative learning control (ILC) technique with predefined-time convergence as a solution to an applied engineering problem, namely, that local time cannot be preset when a second-order nonlinear system undertakes control of the accurate tracking of local time under any initial iterative value. A time-varying sliding surface with an initial value of zero was designed, and it was theoretically proven that the trajectory tracking error in the sliding surface could converge to zero within a predefined time. The iterative control problem of trajectory tracking was thus changed to an iterative control problem of time-varying sliding-mode surface tracing with a starting value of zero. A PD-type closed-loop ILC with a time-varying sliding mode surface was designed such that the trajectory tracking error converged and stabilized on the sliding mode surface after a finite number of learning iterations. The control goal for the system’s output was the ability to track the desired trajectory accurately within a predefined time interval, and it was achieved by combining this with the predefined time convergence characteristics of the time-varying sliding mode surface. Numerical simulation of trajectory tracking control of a repetitive motion manipulator was used to verify the effectiveness of the proposed controller and its robustness in the face of external disturbances.

Iterative Learning Control for High Relative Degree Discrete-Time Systems with Random Initial Shifts

“…For nonlinear systems with varying initial iteration errors and tracking trajectories, the study in [28] proposed two adaptive ILC laws to achieve a complete reference trajectory tracking. The study in [29] presented a ILC method with a time-varying sliding mode, which enables random initial state errors to converge to zero beyond a initial time interval. This strategy achieves complete tracking for second-order nonlinear systems.…”