Iterative Learning Control for Linear Differential Systems With Additional Performance Requirements

Lei Wang,Huizhong Yang,Wojciech Paszke,Hongfeng Tao

doi:10.1109/access.2020.3000252

Abstract

This paper develops the systematic procedure for designing of iterative learning control (ILC) algorithms through the differential repetitive process setting. This means that the proposed approach can be directly applied to plants with differential dynamics and allows to satisfy the additional requirements on the resulting dynamics. In particular, the proposed design procedure enforces a required frequency attenuation over a finite frequency range and includes regional pole constraints. Additionally, an important result extension to the plants with relative degree greater than unity is presented. The sufficient conditions for the existence of the controllers are derived in terms of linear matrix inequalities, which are immediately extended to deal with time varying uncertainties. Finally, the simulations for a typical actuator of tracking servo system prove that the design is effective and brings some advantages when compared to the existing alternatives.

Highlights

Iterative learning control (ILC) is a popular control scheme applicable to the systems that perform a given task iteratively [1], [2]
The developed results allows a designer to specify and/or maximize, frequency ranges where the error convergence condition has to be satisfied. This allows design procedures over convex sets and they are amenable to effective algorithmic solution in terms of linear matrix inequalities (LMIs) [13]
An ILC scheme described as a repetitive process of the form (6) has the stability along the trial property over the finite frequency ranges defined in Table 1 and all eigenvalues of A are located in the circle of radius r with center at (−c, 0)

Summary

INTRODUCTION

Iterative learning control (ILC) is a popular control scheme applicable to the systems that perform a given task iteratively [1], [2]. When designing ILC schemes it is preferred to impose specific performance requirements (for both transient and convergence) Often these requirements are defined over the complete frequency spectrum. The generalized version of Kalman-Yakubovich-Popov (KYP) lemma [12] is extensively used to permit control law design over selected frequency ranges These controller design procedures can include multiple design specifications (e.g. reject disturbances at specific frequencies), whereas the vast majority of currently known designs cannot impose many relevant additional performance specifications. The developed results allows a designer to specify and/or maximize, frequency ranges where the error convergence condition has to be satisfied This allows design procedures over convex sets and they are amenable to effective algorithmic solution in terms of linear matrix inequalities (LMIs) [13].

BACKGROUND

DESIGN OF MONOTONICALLY CONVERGENT ILC SCHEMES FOR AN UNCERTAIN PLANT MODEL

SIMULATION BASED CASE STUDY

Findings

CONCLUSIONS