Composite energy function‐based iterative learning control for systems with nonparametric uncertainties

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.

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.

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

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.

This paper aims at providing a practical iterative learning control (ILC) scheme for a wide class of heat transfer systems in the sense that it avoids high‐gain learning of ILC, thus a potential non‐monotonic convergence issue, and the risk of violating the hardware limitation of input profile in implementation. Meanwhile, the ILC scheme guarantees the identical initial condition of heat process. As a result, the output tracking precision may be improved while not reducing the anticipatory step size as in . All the benefits of the proposed ILC scheme are achieved by applying a heuristic selection algorithm for the anticipatory step size and rectifying the output reference simultaneously.

It is eminent that iterative learning control algorithm is of high significance due to its speciality of tracking control for systems developed from real‐world phenomena that occurs repeatedly. Singular systems are well‐known for their applications in network analysis, biological systems, economic systems, social systems, engineering systems, time‐series analysis, and many other areas of science and technology. In this article, we investigate and analyze the convergence characteristic of PD‐type iterative learning control (ILC) scheme for linear discrete‐time singular system. We reformulate the discrete‐time singular system as a kind of algebraic input‐output transmission based on the lifted vector technique. The monotonic convergence has been deduced in the sense of 2‐norm for the first‐order as well as second‐order PD‐type ILC scheme. It is shown that the second‐order PD‐type ILC algorithm has good tracking performance than the first‐order on the whole time interval. Finally, we perform comparative analysis to validate the results numerically.

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.

We propose a simple recursive iterative learning control (ILC) scheme for a class of uncertain time-varying nonlinear systems. The proposed constructive backstepping-like procedure provides, in a systematic way, a control Lyapunov-like function leading to a simple recursive ILC scheme guaranteeing the existence of a finite time-interval on which a perfect tracking can be achieved when the number of iteration goes to infinity. Simulation results are also provided to show the effectiveness of the proposed ILC scheme.

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 Y-shaped microfluidic chip, the laminar flow refers to a phenomenon that two fluids introduced from two inlets flow side by side without turbulence and form two stable streams in outlet with a common interface. The interface position of laminar flow has significant influence in some experiment analysis of life science, such as molecule diffusion and solvent extraction, where there are still a series of problems associated with the manipulation of interface position. In this brief, an iterative learning control (ILC) scheme is proposed for precise control of the laminar flow position. ILC can improve the current input signal iteratively based on the experimental results achieved in the previous trials and eventually produce the desired interface position in output channel. To verify the effectiveness of the proposed ILC scheme, we design and fabricate the Y-shaped microfluidic chips. Furthermore, two different scenarios are considered, where the results show that an appropriate input signal achieving the desired output can be promptly obtained via ILC. The three main advantages of the proposed control scheme lie in: 1) the simple structure and the feedforward characteristic of the control scheme make it implementable in an easy way; 2) it is a partially model-free method, and hence, no accurate model of laminar flow is required and system uncertainties can be dealt with rigorously when designing the controller; and 3) compared with the well-adopted traversal methods in life science research, the idea of ILC reduces the number of experimental trials remarkably.

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

This paper presents a model-free iterative learning control (ILC) scheme for multi-objective temperature control in Selective Laser Melting (SLM). The goal is to ensure that while temperature distribution in the selected region is sufficient to cause melting and fusion, the meltpool is not overheated. We first formulate this goal as an optimization problem with the power profile as the decision variable and the cost function to be minimized being the sum of two unidirectional error terms (for upper and lower temperature bounds, respectively). Given the difficulty in analytically modeling the temperature-laser power relationship in SLM for gradient computations as in standard ILC, we solve the minimization problem using a model-free ILC scheme. In this scheme, the control input that minimizes the cost function is learned through a data-driven gradient descent update that uses the process itself to compute the gradient direction. The gradient descent algorithm proposed here accounts for the time-varying behavior of the SLM thermal dynamics because of the scan path. This is accomplished by feeding the temperature output error, reversed in time, through the process itself with a reversed scan path direction. For validation, this multi-objective gradient-based ILC algorithm is implemented on a three-phase high-fidelity simulation of the SLM process. The results demonstrate the algorithm’s ability to drive the temperature distribution to within a prescribed range in scenarios where standard (single-objective constant gain) ILC fails.

This work focuses on the model-free iterative learning control (ILC) design with good transient performance and fast convergence rate that is employed for precision control of a wafter stage. First, the experimental setup, the mathematical model, and the desired reference are introduced. Notice that the desired reference and its internal model (IM) are known in advance. Then, based on the internal model principle (IMP), a new ILC scheme, named as 1M-based ILC, is proposed by incorporating the 1M of the reference. The proposed 1M-based ILC is model-free, that is, independent on the system model of the controlled plant. The 1M -based ILC is carefully constructed to track the reference along the time axis while tracking/rejecting repetitive variations along the iteration axis. Precisely because of the tracking capability along the time axis in every iteration, the 1M-based ILC can achieve satisfactory performance even in the 0th iteration and improve the transient performance and the convergence speed. In addition, the 2-D $H_{\infty}$ theory is used to establish the design criterion for the 1M-based ILC. Finally, in the experiments, the efficiency of the 1M-based ILC is illustrated by comparing with a P-type ILC and a model-based one.

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.

Two-dimensional delay compensation based iterative learning control scheme for batch processes with both input and state delays