Robust Iterative Learning Control for 2-D Singular Fornasini–Marchesini Systems with Iteration-Varying Boundary States

Deming Xu,Kai Wan,Heng Liu

doi:10.1155/2021/6686724

Abstract

This study first investigates robust iterative learning control (ILC) issue for a class of two-dimensional linear discrete singular Fornasini–Marchesini systems (2-D LDSFM) under iteration-varying boundary states. Initially, using the singular value decomposition theory, an equivalent dynamical decomposition form of 2-D LDSFM is derived. A simple P-type ILC law is proposed such that the ILC tracking error can be driven into a residual range, the bound of which is relevant to the bound parameters of boundary states. Specially, while the boundary states of 2-D LDSFM satisfy iteration-invariant boundary states, accurate tracking on 2-D desired surface trajectory can be accomplished by using 2-D linear inequality theory. In addition, extension to 2-D LDSFM without direct transmission from inputs to outputs is presented. A numerical example is used to illustrate the effectiveness and feasibility of the designed ILC law.

Highlights

Two-dimensional (2-D) singular dynamical systems derived from the discretization of spatiotemporal dynamical systems with singular matrices or singular distributed parameter systems have received much attention due to their extensive applications in physical phenomena and industrial processes, such as electrical circuits [1], nanoelectronics [2], transmission lines in signal propagation [3], and power systems [4]
In form-closure grasps, the immobilized manipulation of serial chains described by 2-D singular systems could be regarded as a repetitive control problem [8]
By using 2-D linear inequality theory, it can guarantee that the ultimate tracking error tends to a bounded range, the bound of which is relevant to the bound parameters of boundary states. e main contributions of this paper relative to the related works are summarized as follows: (1) In the existing iterative learning control (ILC) results for 2-D linear discrete systems [17,18,19,20,21,22,23,24], they are concerned on a nonsingular case

Summary

Introduction

Two-dimensional (2-D) singular dynamical systems derived from the discretization of spatiotemporal dynamical systems with singular matrices or singular distributed parameter systems have received much attention due to their extensive applications in physical phenomena and industrial processes, such as electrical circuits [1], nanoelectronics [2], transmission lines in signal propagation [3], and power systems [4]. In practical life and industry, there exist some 2-D singular dynamical systems, such as electrical circuits, transmission lines in signal propagation, and power systems, which are often required to execute some specific tracking control tasks repetitively. Based on these practical applications, it is essential to exploit ILC techniques for 2-D singular dynamical systems. E main aim of this paper is to investigate the robustness and convergence property of P-type ILC law for two classes of two-dimensional linear discrete singular Fornasini–Marchesini systems (2-D LDSFM) under iteration-varying boundary states.

Problem Description

Extension to 2-D LDSFM with D 0

Illustrative Examples

Conclusions