Convergence Analysis of Iterative Learning Control for Two Classes of 2-D Linear Discrete Fornasini–Marchesini Model

Kai Wan

doi:10.1155/2020/6843730

Abstract

This paper first investigates convergent property of two iterative learning control (ILC) laws for two kinds of two-dimensional linear discrete systems described by the first Fornasini–Marchesini model (2-D LDFFM with a direct transmission from inputs to outputs and 2-D LDFFM with input delay). Different from existing ILC results for 2-D LDFFM, this paper provides convergence analysis in a three-dimensional (3-D) framework. By using row scanning approach (RSA) or column scanning approach (CSA), it is theoretically proved no matter which method is adopted, perfect tracking on the desired reference surface is accomplished. In addition, linear matrix inequality (LMI) technique is utilized to computer the learning gain of the ILC controller. The effectiveness and feasibility of the designed ILC law are illustrated through numerical simulation on a practical thermal process.

Highlights

In practical industrial applications for two-dimensional (2-D) dynamical systems, for example, in form-closure grasps, the immobilized manipulation of 2-D serial chains could be regarded as a repetitive control problem [1]
A large number of iterative learning control (ILC) research results reported in the past few decades have fundamentally designed for one-dimensional (1-D) dynamical systems [6,7,8,9,10,11,12,13,14], only very few results involved in 2-D dynamical systems [15,16,17,18,19,20,21,22], which concentrate on mainly 2-D linear discrete first Fornasini–Marchesini model (2-D LDFFM)
Using the column scanning approach (CSA) as [18], to track a class of nonrepetitive reference surface described by a high-order internal model operator (HOIM), two HOIM-based ILC laws were, respectively, investigated in [23] for 2-D LDFFM by using 2-D HOIM-based linear inequality theory, but the ultimate ILC tracking error can only converge to a bounded range

Summary

Introduction

In practical industrial applications for two-dimensional (2-D) dynamical systems, for example, in form-closure grasps, the immobilized manipulation of 2-D serial chains could be regarded as a repetitive control problem [1]. Using the CSA as [18], to track a class of nonrepetitive reference surface described by a high-order internal model operator (HOIM), two HOIM-based ILC laws were, respectively, investigated in [23] for 2-D LDFFM by using 2-D HOIM-based linear inequality theory, but the ultimate ILC tracking error can only converge to a bounded range. To this end, adaptive ILC approach was proposed in [21, 22] to identify all unknown system parameters of 2-D. Im denotes identity matrix with dimension m × m. ρ(·) represents spectral radius of matrix

Problem Formulation and Some Preliminaries

Extension to 2-D LDFFM with Input Delay

Illustrative Examples

Conclusions