Analysis of Transient Growth in Iterative Learning Control Using Pseudospectra

In this paper we examine the problem of transient growth in Iterative Learning Co ntrol (ILC). Transient growth is generally avoided in design by using robust monotonic convergence (RMC) criteria. However, RMC leads to fundamental performance limitations. We consider the possibility of allowing safe transient growth in ILC algorithms as a means to circumvent these limitations. Here the pseudospectra is used for the first time to study transient growth in ILC. Basic properties of the pseudospectra that are relevant to the ILC problem are presented. Two ILC design problems are considered and examined using pseduospectra. The pseudospectra provides new results for these problems and illuminates the oft-misunderstood problem of transient growth

Multi-Objective Iterative Learning Control: An Advanced ILC Approach for Application Diversity.

While ILC has been applied to repetitive applications in manufacturing, chemical processing, and robotics, several key assumptions limit the extension of ILC to various applications. Conventional ILC focuses on improving the performance of a single metric, such as tracking performance through iterative updates of the time domain control input. The application range is limited to systems that satisfy the assumption of iteration invariance of the plant, reference signal, initial conditions, and disturbances. We aim to relax this assumption to gain significant advantages. More specifically we focus on relaxing the strict reference tracking requirement to address multiple performance metrics and define the stability bounds across temporal and spatial domains. The aim of this research is expanding the application space of ILC towards non-traditional applications. Chapter III presents an initial framework to provide the foundation for the multi-objective ILC. This framework is validated by simulation and experimental tests with a wheeled mobile robot. Chapter IV extends the initial framework from the temporal domain to the spatial domain. The initial framework is generalized to address four classifications of performance objectives. Stability and performance analysis for each classification is provided. Simulation results on a high-resolution additive manufacturing system validate the extended framework. For the generalized framework, we present a distributed approach in which additional objectives are considered separately. Chapter V evaluates the difference between this distributed approach, and a centralized approach in which the objectives are combined into a single matrix depending on the classification. Chapter VI extends the multi-objective ILC to incorporate a region-based tracking problem in which reference uncertainty is addressed through the development of a bounded region. A multi-objective region-to-region ILC is developed and validated by a simulation of a surveillance problem with an UAV and multiple unattended ground sensors. Comparisons with point-to-point ILC, region-to-region ILC, and multi-objective region-based ILC demonstrate the performance flexibility that can be achieved when leveraging the regions. This dissertation provides new approaches for relaxing the classical assumption of iteration invariant reference tracking. New stability and convergence analysis is provided, resulting in a design methodology for multi-objective ILC. These approaches are validated by simulation and experimental results.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120875/1/ingyulim_1.pd

Frequency Domain Based Analysis and Design of Norm-Optimal Iterative Learning Control

In this thesis, novel frequency domain based analysis and design methods on Norm-Optimal Iterative Learning Control (NO-ILC) are developed for Single-Input-Single-Output (SISO) Linear Time Invariant (LTI) systems. Modeling errors in general degrade the convergence performance of NO-ILC and hence ensuring Robust Monotonic Convergence (RMC) against model uncertainties is important. Although the robustness of NO-ILC has been studied in the literature, determining the allowable range of modeling errors for a given NO-ILC design is still an open research question. To fill this gap, a frequency domain analysis with a multiplicity formulation of model uncertainty is developed in this work to quantify and visualize the allowable modeling errors. Compared with the traditional formulation, the proposed new uncertainty formulation provides a less conservative representation of the allowable model uncertainty range by taking additional phase information into account and thus allows for a more complete evaluation of the robustness of NO-ILC. The analysis also clarifies how the RMC region changes as a function of NO-ILC weighting terms and therefore leads to several frequency domain design tools to achieve RMC for given model uncertainties. Along with this frequency domain analysis, rather than some qualitative understanding in the literature, an equation quantitatively characterizing the fundamental trade-off of NO-ILC with respect to robustness, convergence speed and steady state error at each frequency is presented, which motivates the proposed loop-shaping like design methods for NO-ILC to achieve different performance requirements at various frequencies. The proposed analysis also demonstrates that NO-ILC is the optimal solution for general LTI ILC updating laws in the scope of balancing the trade-off between robustness, convergence speed and steady state error.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137007/1/gexinyi_1.pd