Brief Stability analysis of learning feed-forward control

  • Authors:

  • Wubbe J. R. Velthuis;Theo J. A. De Vries;Pieter Schaak;Erik W. Gaal

  • Affiliations:

  • EL-RT, Drebbel Institute for Systems Engineering, University of Twente, P.O. Box 217, NL-7500 AE Enschede, The Netherlands;EL-RT, Drebbel Institute for Systems Engineering, University of Twente, P.O. Box 217, NL-7500 AE Enschede, The Netherlands;Dutch Aerospace Laboratory NLR, P.O. Box 90502, 1006 BM, Amsterdam, The Netherlands;Centre for Manufacturing Technology, Philips Electronics N.V., P.O. Box 218, 5600 MD, Eindhoven, The Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2000

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Abstract

In this paper, a learning control system is considered for motion systems that are subject to two types of disturbances; reproducible disturbances, that re-occur each run in the same way, and random disturbances. In motion systems, a large part of the disturbances appear to be reproducible. In the control system considered, the reproducible disturbances are compensated by a learning component consisting of a B-spline neural network that is operated in feed-forward. The paper presents an analysis of stability properties of the configuration in case of a linear process and second-order B-splines. The outcomes of the analysis are quantitative criteria for selection of the width of the B-splines, and of the learning rate, for which the system is guaranteed to be stable. These criteria facilitate the design of a learning feed-forward controller.