An Internal Model Based Iterative Learning Control for Wafer Scanner Systems

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

A pseudo-downsampled iterative learning control (ILC) scheme with a time shift along iteration axis is proposed. In this scheme, there are two sampling rates: a system with a fast sampling rate and an ILC scheme with a downsampled slow sampling rate. After one cycle, the input update points of ILC are shifted one sampling period w.r.t. fast system sampling rate. That is, there is always a time shift for ILC input updates points along iteration axis for two successive cycles. This process is repeated so that the input on every point w.r.t. fast system sampling rate can be updated once every several cycles. Theoretical basis and the design of the proposed ILC are given. The advantages include that it can guarantee the good learning transient; it can track high frequency trajectory; it needs not a filter design; and it can deal with initial position offset. Experimental results are presented to verify the proposed scheme

This paper presents a model-free adaptive iterative learning control (ILC) scheme called a proportional-type ILC scheme for non-linear systems. The obvious characteristic of the proposed ILC scheme is that we can easily finish the ILC task just utilising the Lipschitz constant of the system. In the proposed ILC scheme, the time-vary learning gain can be produced merely by input and output (I/O) measurements. Moreover, the convergence conclusion can be expressed by the ranges of the pseudo-partial derivative and the learning gain. In actual operation, a reasonable and useful convergence condition by a constant is also provided for selection. At last, the effectiveness of the proposed ILC scheme is shown by simulations.

In this work, two practical iterative learning control (ILC) schemes are analyzed and compared in frequency domain. Both ILC schemes consist of a feedback and a learning based feedforward compensation. Through analysis, we show that the difference in the learning updating mechanisms, in the sequel, exploit the circumstances where one ILC scheme can outperform the other. Based on the system Bode plots, we can easily check the learning convergence condition, the complementary property of feedback and feedforward compensation, and which ILC scheme can perform better. For the purpose of comparison and verification, both ILC schemes are applied to a real-time ball-and-beam system.

In this technical note, we propose a new iterative learning control (ILC) scheme for nonlinear systems with parametric uncertainties that are temporally and iteratively varying. The time-varying characteristics of the parameters are described by a set of unknown basis functions that can be any continuous functions. The iteratively varying characteristics of the parameters are described by a high-order internal model (HOIM) that is essentially an auto-regression model in the iteration domain. The new parametric learning law with HOIM is designed to effectively handle the unknown basis functions. The method of composite energy function is used to derive convergence properties of the HOIM-based ILC, namely the pointwise convergence along the time axis and asymptotic convergence along the iteration axis. Comparing with existing ILC schemes, the HOIM-based ILC can deal with nonlinear systems with more generic parametric uncertainties that may not be repeatable along the iteration axis. The validity of the HOIM-based ILC under identical initialization condition (i.i.c.) and the alignment condition is also explored.

This paper presents a P-type iterative learning control (ILC) scheme for a class of fractional order distributed parameter switched systems. First, by analyzing of the control and learning processes, a discrete system for P-type ILC is established and the ILC design problem is then converted to a stabilization problem for such a discrete system. Next, a sufficient condition for the convergence of the tracking errors is obtained, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

This paper aims at iterative learning control (ILC) design and analysis for a class of linear distributed parameter systems (DPSs) that may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the linear characteristic of systems, the system equations are first cast into a matrix form in the Laplace transform domain. Then, through determination of a fundamental matrix, the system transfer function is precisely evaluated in a closed form. The derived transfer function clearly demonstrates the input-output relationship of system, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and makes full use of the process repetition, while avoids any simplification or discretization for the 3D dynamics of distributed parameter systems in the time, space, and iteration domains. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

Iterative learning control (ILC) is one of the most popular tracking control methods for systems that repeatedly execute the same task. A system model is usually used in the analysis and design of ILC. Model‐based ILC results in general in fast convergence and good performance. However, the model uncertainties and nonrepetitive disturbances hamper its practical applications. One of the commonly used solutions is the introduction of a low‐pass filter, namely, the Q‐filter. However, it is indicated in this paper that the existing Q‐filter configurations compromise the servo performance, although improving the robustness. Motivated by the combination of performance and robustness, a novel Q‐filter configuration in ILC is presented in this paper. Some practical considerations, such as the configuration of ILC in a feedback control system, the time delay compensation, and the learning coefficient, are provided in the implementation of the proposed ILC algorithm. The effectiveness and superiority of the proposed ILC versus existing Q‐filter ILC are demonstrated by both theoretical analysis and experimental verification on a wafer stage.

The problem of iterative learning control is considered for linear discrete-time systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of P-type discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

Since they were first introduced by Arimoto, iterative learning control (ILC) methods have received lots of attention because of their effectiveness and briefness. In this paper, an open-closed-loop PID-type ILC scheme with bounded learning matrixes for the control of nonlinear time-varying systems are studied. Under a few reasonable restrictions that are very common, as in other ILC research papers on the convergence problem, sufficient conditions for guaranteeing the convergence of ILC systems are given and then proved with linear operator theory. Both the system and the ILC scheme described have very general forms. It is shown that the convergence condition is weaker than some known results for a similar ILC scheme.

In this paper we present a mathematical formulation of the problem of robust iterative learning control (ILC) design when the system is subject to data dropout. It is assumed that an ILC scheme is implemented via a networked control system (NCS) and that during the data transfer from the remote plant to the ILC controller data dropout occurs, resulting in what we call intermittent measurement. Using the Kalman filtering approach, we show that it is possible to design a learning gain such that the system eventually converges to a desired trajectory as long as there is not complete data dropout.

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

In this paper, we present an iterative learning control (ILC) framework for tracking problems with predefined data points that are desired points at certain time instants. To design ILC systems for such problems, a new ILC scheme is proposed to produce output curves that pass close to the desired points. Unlike traditional ILC approaches, an algorithm will be developed in which the control signals are generated by solving an optimal ILC problem with respect to the desired sampling points. In another word, it is a direct approach for the multiple points tracking ILC control problem where we do not need to divide the tracking problem into two steps separately as trajectory planning and ILC controller. The strength of the proposed formulation is the methodology to obtain a control signal through learning law only considering the given data points and dynamic system, instead of following the direction of tracking a prior identified trajectory. The key advantage of the proposed approach is to significantly reduce the computational cost. Finally, simulation results will be introduced to confirm the effectiveness of proposed scheme.

SUMMARYIn this work, we propose new iterative learning control (ILC) schemes that deal with nonlinear multi‐input multi‐output systems under alignment condition with nonparametric uncertainties. A major contribution of this work is to remove the classical resetting condition. Another major contribution of this work is to deal with norm‐bounded nonlinear uncertainties that satisfy local Lipschitz condition, in particular to deal with nonlinear uncertain state‐dependent input gain matrix that could be non‐square left invertible and local Lipschitzian. Two types of composite energy function are proposed to facilitate the ILC design and property analysis. Through rigorous analysis, we show that the new ILC schemes proposed warrant the asymptotical tracking convergence of system states. In the end, an illustrative example is provided to demonstrate the efficacy of the proposed ILC scheme. Copyright © 2013 John Wiley & Sons, Ltd.