2D systems based robust iterative learning control using noncausal finite-time interval data

This paper uses a $2$D systems setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new $2$D systems based design algorithms enable the effective deployment of such information

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