Learning for Advanced Motion Control

Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the potential performance improvement of ILC prior to its actual implementation. Second, a frequency domain approach is presented, where fast learning is achieved through noncausal model inversion, and safe and robust learning is achieved by employing a contraction mapping theorem in conjunction with nonparametric frequency response functions. The approach is demonstrated on a desktop printer. Finally, a detailed analysis of industrial motion systems leads to several shortcomings that obstruct the widespread implementation of ILC algorithms. An overview of recently developed algorithms, including extensions using machine learning algorithms, is outlined that are aimed to facilitate broad industrial deployment.Comment: 8 pages, 15 figures, IEEE 16th International Workshop on Advanced Motion Control, 202

Optimal control of non-stationary differential linear repetitive processes

Differential repetitive processes are a distinct class of continuousdiscrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics

Modelling the influence of non-minimum phase zeros on gradient based linear iterative learning control

The subject of this paper is modeling of the influence of non-minimum phase plant dynamics on the performance possible from gradient based norm optimal iterative learning control algorithms. It is established that performance in the presence of right-half plane plant zeros typically has two phases. These consist of an initial fast monotonic reduction of the L2 error norm followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over finite trials is apparent convergence to a non-zero error. The source of this slow convergence is identified and a model of this behavior as a (set of) linear constraint(s) is developed. This is shown to provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm are obtained for single-input single-output systems with several right half plane zeroes using Lagrangian techniques and experimental results are given that confirm the practical validity of the analysis

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

Iterative Learning Control design for uncertain and time-windowed systems

Iterative Learning Control (ILC) is a control strategy capable of dramatically increasing the performance of systems that perform batch repetitive tasks. This performance improvement is achieved by iteratively updating the command signal, using measured error data from previous trials, i.e., by learning from past experience. This thesis deals with ILC for time-windowed and uncertain systems. With the term "time-windowed systems", we mean systems in which actuation and measurement time intervals differ. With "uncertain systems", we refer to systems whose behavior is represented by incomplete or inaccurate models. To study the ILC design issues for time-windowed systems, we consider the task of residual vibration suppression in point-to-point motion problems. In this application, time windows are used to modify the original system to comply with the task. With the properties of the time-windowed system resulting in nonconverging behavior of the original ILC controlled system, we introduce a novel ILC design framework in which convergence can be achieved. Additionally, this framework reveals new design freedom in ILC for point-to-point motion problems, which is unknown in "standard" ILC. Theoretical results concerning the problem formulation and control design for these systems are supported by experimental results on a SISO and MIMO flexible structure. The analysis and design results of ILC for time-windowed systems are subsequently extended to the whole class of linear systems whose input and output are filtered with basis functions (which include time windows). Analysis and design theory of ILC for this class of systems reveals how different ILC objectives can be reached by design of separate parts of the ILC controller. Our research on ILC for uncertain systems is divided into two parts. In the first part, we formulate an approach to analyze the robustness properties of existing ILC controllers, using well developed µ theory. To exemplify our findings, we analyze the robustness properties of linear quadratic (LQ) norm optimal ILC controllers. Moreover, we show that the approach is applicable to the class of linear trial invariant ILC controlled systems with basis functions. In the second part, we present a finite time interval robust ILC control strategy that is robust against model uncertainty as given by an additive uncertainty model. For that, we exploit H1 control theory, however, modified such that the controller is not restricted to be causal and operates on a finite time interval. Furthermore, we optimize the robust controller so as to optimize performance while remaining robustly monotonically convergent. By means of experiments on a SISO flexible system, we show that this control strategy can indeed outperform LQ norm optimal ILC and causal robust ILC control strategies