Robust iterative learning control for distributed parameter systems with sensor/actuator networks based on high‐order internal model

Adaptive Iterative Learning Control of an Industrial Robot during Neuromuscular Training

In this paper, we present the design of a robust Iterative Learning Control (ILC) algorithm for a single flexible link in the presence of parametric uncertainty. The robust ILC design is formulated as a min-max problem with a quadratic performance index. An upper bound of the worst-case performance is employed in the min-max problem. Applying Lagrange duality to the min-max problem, we can reformulate the robust ILC design as a convex optimization over linear matrix inequalities (LMIs). An LMI algorithm for the robust ILC design is given. Finally, the simulation results for a single flexible link are presented to illustrate the effectiveness of the proposed robust ILC algorithm.

The work in this dissertation concerns the construction of a robust iterative learning control (ILC) algorithm for a class of systems characterized by measurement delays, parametric uncertainty, and linear parameter varying (LPV) dynamics. One example of such a system is the twin roll strip casting process, which provides a practical motivation for this research. I propose three ILC algorithms in this dissertation that advance the state of the art. The first algorithm compensates for measurement delays that are longer than a single iteration of a periodic process. I divide the delay into an iterative and residual component and show how each component effects the asymptotic stability properties of the ILC algorithm. The second algorithm is a coupled delay estimation and ILC algorithm that compensates for time-varying measurement delays. I use an adaptive delay estimation algorithm to force the delay estimate to converge to the true delay and provide stability conditions for the coupled delay estimation and ILC algorithm. The final algorithm is a norm optimal ILC algorithm that compensates for LPV dynamics as well as parametric uncertainty and time delay estimation error. I provide a tuning method for the cost function weight matrices based on a sufficient condition for robust convergence and an upper bound on the norm of the error signal. The functionality of all three algorithms is demonstrated through simulated case studies based on an identified system model of the the twin roll strip casting process. The simulation testing is also augmented with experimental testing of select algorithms through collaboration with an industrial sponsor.

Iterative learning control (ILC) is a high‐performance technique for repeated control tasks with design postulates on a fixed reference profile and identical initial conditions. However, the tracking performance is only critical at few points in point‐to‐point tasks, and their initial conditions are usually trial‐varying within a certain range in practice, which essentially degrades the performance of conventional ILC algorithms. Therefore, this study reformulates the ILC problem setup for point‐to‐point tasks and considers the effort of trial‐varying initial conditions in algorithm design. To reduce the tracking error, it proposes a worst‐case norm‐optimal problem and reformulates it into a convex optimisation problem using the Lagrange dual approach. In this sense, a robust ILC algorithm is derived based on iteratively solving this problem. The study also shows that the proposed robust ILC is equivalent to conventional norm‐optimal ILC with trial‐varying parameters. A numerical simulation case study is conducted to compare the performance of this algorithm with that of other control algorithms while performing a given point‐to‐point tracking task. The results reveal its efficiency for the specific task and robustness against trial‐varying initial conditions.

A Robust Iterative Learning Control with Neural Networks for Robot

In this work we focus on iterative learning control (ILC) for iteratively varying reference trajectories which are described by a high-order internal model. The high-order internal model (HOIM) is formulated as a polynomial between two consecutive iterations. The classical ILC with iteratively invariant reference trajectories, on the other hand, is a special case of HOIM where the polynomial renders to a unity coefficient, in other words, the 0th order internal model. By inserting the polynomial (HOIM) into the past control input of the ILC law, and designing appropriate learning control gains, the learning convergence in the iteration axis can be guaranteed for continuous-time linear time varying (LTV) systems. The initial condition, P-type and D-type ILC, and possible extension to nonlinear cases are also explored.

This paper is concerned with iterative learning control (ILC) algorithms for two-dimensional (2-D) linear discrete systems described by the first Fornasini–Marchesini model (FMMI) with iteration-varying reference trajectories/profiles. The variation of reference trajectories in iteration domain is represented by a high-order internal model (HOIM) formula. Robustness and convergence of two types of HOIM-based ILC laws with different boundary conditions are investigated, respectively. A strategy employed in this paper is to reconstruct the HOIM-based ILC process of the 2-D linear FMMI system into a set of 2-D linear inequalities or a 2-D linear Roesser model such that sufficient robustness/convergence conditions of the HOIM-based ILC laws are obtained. Under random boundary conditions, the designed ILC law (9) is capable to drive the ILC tracking error into a bounded range. Moreover, under the HOIM-based boundary conditions, a perfect tracking to the iteration-varying reference trajectories can be achieved by utilizing the proposed ILC law (32). Two simulation examples are given to validate the effectiveness of the two proposed ILC algorithms.

In this paper, an iterative learning control algorithm was proposed for improving the permanent magnet linear motor (PMLM) velocity tracking performance under iteration-varying desired trajectories. A high-order internal model (HOIM) was utilized to describe the variation of desired trajectories in the iteration domain. By incorporating the HOIM into P-type ILC, the convergence of tracking error can be guaranteed. The rigorous proof was presented to show that the system error converge well. The simulation results indicate that the proposed high-order internal models based approach yields a good performance and achieves perfect tracking.Keywordsiterative learning algorithmhigh-order internal modelsdiscretetime plantpermanent magnet linear motors

The traditional iterative learning control (ILC) algorithm improves the control performance by updating the control input to implicitly compensate the periodic uncertainties. In order to enhance the convergence rate of ILC, a new concept, iterative extended state observer (IESO), is presented which can estimate explicitly the periodic uncertainties during the process of iterations and be used to update the control input directly. The explicit estimation of the uncertainty by the linear IESO in the iteration domain is used to construct a new ILC algorithm based on active disturbance rejection (ADR). The ADR-based ILC algorithm and its corresponding theorem are given in detail and proven by using Lyapunov-like approach. Simulation results verify the effectiveness of the proposed ILC algorithm, and the iterative learning efficiency is improved greatly by using ADR-based ILC algorithm.

In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iteration-varying desired trajectories. A high-order internal model (HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors (PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.

Typically, iterative learning control (ILC) is applied based on a core hypothesis that the strict repetitiveness of control environment, task, and model should be satisfied by the controlled system. The problem of interest in this paper is: whether and how can ILC robustly work for controlled systems subject to iteration-dependent environments, tasks and models? To successfully solve this problem, an ILC algorithm using a high-order internal model (HOIM) is proposed and convergence conditions are developed. It is shown that HOIM-based ILC both possesses robustness against iteration-dependent uncertainties from initial states, disturbances, and plant models and tracks iteration-dependent references. Also, simulation tests validate the effectiveness of HOIM-based ILC.

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.

In this paper a new robust steepest-descent algorithm for discrete-time iterative learning control is introduced for plant models with multiplicative uncertainty. A theoretical analysis of the algorithm shows that if a tuning parameter in the algorithm is selected to be sufficiently large, the algorithm will result in monotonic convergence if the plant uncertainty satisfies a positivity condition. This is a major improvement when compared to the standard steepest-descent algorithm, which lacks a mechanism for finding a balance between convergence speed and robustness. Experimental work on a gantry robot is performed to demonstrate that the algorithm results in near perfect tracking in the limit.

In this paper, iterative learning control (ILC) design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models (HOIM). An HOIM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOIM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOIM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.

The purpose of this work is to improve the tracking performance of the iterative learning control (ILC) by designing a new learning law that has the ability to update the input along both the time and iterative axes. First, the reference is generated by a high-order internal model (HOIM) along the iterative axis and can be approximated by an HOIM along the time axis. Then, the HOIM-based repetitive control (RC) and ILC design methods are introduced, which can update the input along the time and iterative axes, respectively. Inspired by the design methods of the HOIM-based RC and ILC, a new ILC scheme, named as repetitive iterative learning control (RILC), is constructed by incorporating both the HOIMs of the reference along the time and iterative axes. Due to the additional use of the time-varying information of the reference, it is verified that the RILC is superior to the ILC. Finally, a microscale robotic deposition system is given to illustrate the advantage of the proposed RILC scheme.