Time-Varying Boundary Layer Based Iterative Learning Control for Nonlinearly Parametric Time-Delay Systems With Arbitrary Initial Errors and Iteration-Varying Reference Trajectories

Lingwei Wu,Qiuzhen Yan,Zhiming Lin,Xiangbin Liu,Youfang Yu

doi:10.1109/access.2021.3091527

Lingwei Wu, Qiuzhen Yan + Show 3 more

Open Access

https://doi.org/10.1109/access.2021.3091527

Copy DOI

Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Taizhou University, Beijing Jiaotong University

Abstract

In this paper, the tracking problem for a class of nonlinearly parametric time-delay systems with arbitrary initial state errors and iteration-varying reference trajectories is studied. An adaptive iterative learning control scheme is developed by using Lyapunov approach. A time-varying boundary layer is constructed for removing the zero initial error condition, which is necessary in normal iterative learning control algorithms. The time-varying nonlinearly parametric uncertainties and time-delay uncertainties are well compensated by using parameter separation technique, signal replacement mechanism and robust strategy. As the iteration number increases, the state tracking error asymptotically converges to a tunable residual set. In the end, a simulation example further verifies the theoretical results.

Highlights

Iterative learning control (ILC) is a well-known highprecision control strategy, which is usually used to deal with repeated tracking control or periodic disturbance rejection for nonlinear uncertain systems [1]- [4]
In general ILC algorithms, there exists a common assumption that the initial system error at each iterative cycle should be zero; Otherwise, a slight nonzero initial system error may result in divergence of tracking error, which is called initial position problem in ILC field
From what have been discussed above, it can be concluded that the issue on adaptive ILC scheme for timedelay parametric systems with arbitrary initial errors and iteration-varying reference trajectories is worthy to be further studied, which motivates the work of this paper

Summary

INTRODUCTION

Iterative learning control (ILC) is a well-known highprecision control strategy, which is usually used to deal with repeated tracking control or periodic disturbance rejection for nonlinear uncertain systems [1]- [4]. In [18], Wu et al developed a neural networkbased adaptive iterative learning control scheme to solve the trajectory tracking problem for rigid robot manipulators with arbitrary initial errors, where time-varying boundary layers are used to relax the zero initial error condition. From what have been discussed above, it can be concluded that the issue on adaptive ILC scheme for timedelay parametric systems with arbitrary initial errors and iteration-varying reference trajectories is worthy to be further studied, which motivates the work of this paper. We present a time-varying boundary layer based adaptive ILC scheme for a class of time-delay parametric systems with arbitrary initial errors and iteration-varying reference trajectories, which helps to widen the application scope of adaptive ILC in industrial processes. (3) A time-varying boundary layer is constructed to deal with the nonzero initial system error in adaptive ILC design for time-delay parametric systems with iteration-varying trajectories.

PROBLEM FORMULATION

ANALYSIS OF CONVERGENCE PROPERTY

Part 3: Convergence of closed-loop system

ILLUSTRATIVE EXAMPLE

CONCLUSION