<h2>AAS 95-376</h2><h2>The Use of the Euler Operator in Learning and Repetitive Control</h2><h4>P. Oh, R. W. Longman and  L. Yao, Columbia University, New York, NY</h4><h2> Abstract </h2>The simplest form of repetitive control makes use of the concept of integration in the repetition domain to eliminate tracking errors in a repetitive control process.  The implementation of such control laws is necessarily in discrete time.  The process of discretizing a continuous system having a pole excess of two or more generically introduces additional zeros that are not images of continuous time zero.  And these new zeros are often nonminimum phase.  By viewing the behavior of repetitive control in terms of root locus plots, one can see the effect of these zeros on the stability of the learning process.  In other contexts the Euler operator was introduced to eliminate some of the bad effects of such zeros in digital control.  This paper studies the usefulness of the Euler operator in eliminating convergence problems in repetitive control.<br><br>