A New Iterative Learning Control With Time Delays for LTI Systems in Frequency Domain

Abstract

In this paper, the problem of iterative learning control with time delay is studied for linear timeinvariant (LTI) systems in the frequency domain. In terms of the LTI systems, which are formulated as one type of open-loop stable and minimum-phase systems with relative degree equaling to one, three different learning control schemes are proposed, such that the convergence of the tracking error can be guaranteed. The first scheme using the D-type algorithm with prediction can achieve wide convergence range. The second scheme applies an algorithm named A-type, which decreases noise. The third scheme is an improvement of the second one, which is a new type (AP-type) combination of the A-type and P-type ones. Moreover, for the systems with open-loop instability, non-minimum phase, and relative degree non-one, the convergence of the tracking error can still be ensured. Finally, some simulation examples are given to show the effectiveness of the proposed three control algorithms. INDEX TERMS Iterative learning control, time delay, frequency domain, anticipatory learning control.

Frequency-Domain Based Iterative Learning Control for 2-D Discrete Systems

“…where b e1 ≥ 0 and b e2 ≥ 0 are unknown constants. Remark 2: Assumption 1 requires that all the zeros and poles of G p (z 1 , z 2 ) lie in the region |z 1 | < 1 and |z 2 | < 1, and can be widely found in [15], [23], and [24]. Additionally, Assumption 2, as a fundamental and reasonable assumption in robustness ILC analysis, shows the boundedness of boundary states, which is presented in [10].…”

“…For example, when ω h → ∞ and ω v → ∞, the inequality cos( ̸ G p (e jω h , e jω v )+ω h +ω v ) > 0 no longer holds. Hence, the frequency region ω h and ω v needs to be reduced into a learnable band [13] and [15]. Therefore, the learnable band is required to satisfy ω h ∈ ω min h , ω max h and ω v ∈ ω min v , ω max v .…”

“…Recently, frequency-domain based ILC achievements for 1-D systems have been extensively reported in [11], [12], [13], [14], and [15]. In [11], the convergence characteristics of the first-order and second-order PD-type ILC schemes for linear time-invariant systems in discrete spectrum is investigated.…”

“…In [13], frequency domain analysis and design of anticipatory-type ILC were addressed for SISO linear systems by providing an engineering design procedure and a guideline for self-tuning for anticipatory-type ILC. In [15], the ILC problem for linear time-invariant systems with input delay is investigated in the frequency domain and three different ILC schemes are proposed to guarantee the zero tracking error. To our knowledge, the frequency domain analysis method plays an important role in the application of ILC.…”

Time-varying pilot factor–iterative learning control algorithm with control parameter learning ability

“…Phase delay is a common phenomenon in control systems (Deng et al, 2019; Gu et al, 2019; Wang et al, 2019a), which means that the output signal of the system is always delayed compared with the input signal. This is the nature of the system itself, and some scholars have begun to study the system delay in iterative learning algorithms (Liang et al, 2018; Wang et al, 2019b). For example, if the phase delay of the system is j sampling times, that means the output signal bold-italicybold-italick(t+j) and control error bold-italicebold-italick(t+j) are influenced by the guidance signal bold-italicrbold-italick(t).…”