A Survey on High-Order Internal Model Based Iterative Learning Control

Abstract

Iterative learning control (ILC) has been developed for decades and is mainly used to solve the repetitive control tasks. However, in the actual operation of systems, there are many non-strictly repetitive or iteration-varying factors, such as the iteration-varying reference trajectory, non-repetitive system parameters, iteration-related initial states, iteration-dependent input and output disturbances, etc. In order to solve the non-strictly repetitive problems, the High-Order Internal Model (HOIM)-based ILC is proposed. HOIM can be formulated as a polynomial in the iteration domain, which is auto-regressive. HOIM-based ILC for nonlinear systems is more complex than HOIM-based ILC for linear systems, and when the system parameters change iteratively, the Lyapunov-based analysis method is used instead of traditional contraction mapping method. Not only can HOIM be integrated into the traditional ILC, it can be also combined with other control methods, such as adaptive control, terminal control, repetitive control and so on. In this paper, we review the advances in HOIM-based ILC, systematically sort out the development and main contents of HOIM, summarize its main applications and extensions, and finally put forward some further development directions. INDEX TERMS High-order internal model, iterative learning control, non-repetitiveness.

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

“…As a result, the ILC tracking error surfaces e (1) k (n 1 , n 2 ) at k � 3, 5, 7, 25, and e (2) k (n 1 , n 2 ) at k � 4, 6, 8, 24 are depicted in Figures 2 and 3, respectively. Also, Figure 4 presents the profiles of the ILC tracking error indexes MATE (1) k and MATE (2) k in iteration domain k by utilizing the ILC law (9). Obviously, it is observed from Figures 2-4 that the convergent effect of the ILC law (9) against the iterationinvariant boundary states is illustrated.…”

“…e repetitive index k implies that the ILC issue is investigated in the example. rough the discretization approximation on (60), system parameters and delay factors of 2-D LDFFM with input delay (37) are given as follows: (n (1) k and MATE (2) k with iteration number k by using the ILC law (9). Complexity 9…”

“…To the best of our knowledge, iterative learning control (ILC), as a data-driven and unsupervised control approach, does not require accurate knowledge of the controlled system, which makes ILC be widely prevalent in practical applications. A large number of 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). An optimal ILC algorithm was proposed in [16], such that the ILC tracking error converges to zero monotonically.…”

High-Order Internal Model Based Barrier Iterative Learning Control for Time-Iteration-Varying Parametric Uncertain Systems With Arbitrary Initial Errors

“…In recent years, the exploration on how to estimate and compensate for more general parametric uncertainties in ILC has never ceased. As a significant progress in this issue, Yin et al [19] proposed two adaptive ILC schemes for uncertain systems whose time-iteration-varying parameters are generated by high-order internal model (HOIM) [20], with zero initial error condition and alignment condition [21] considered, respectively. It should be noticed that resetting the controlled system to zero initial error at each iteration is an impossible job in real applications.…”

Adaptive iterative learning control for discrete‐time nonlinear systems with multiple iteration‐varying high‐order internal models

“…26 If the iteration-variation pattern is known, high-order internal model (HOIM) can be used to describe the iteration-varying pattern and was introduced into the iterative learning controller to completely eliminate the effect of non-repetitiveness. 22,28 The internal model principle was presented in Reference 29, providing a theoretical basis for a system to track reference signals perfectly without steady-state errors. A shift operator was introduced to describe the basic form of the HOIM.…”