Brief Paper Stability analysis of learning feed-forward control q

AbstractInthispaper, alearningcontrolsystemisconsideredformotionsystemsthataresubjectto twotypesofdisturbances; reproducible disturbances, that re-occur each run in the same way, and random disturbances. In motion systems, a large part of the disturbancesappeartobereproducible.Inthecontrolsystemconsidered,thereproducibledisturbancesarecompensatedbyalearningcomponentconsisting of a B-spline neural network that is operated in feed-forward.The paper presents an analysis of stability properties of thecon"gurationincaseofalinearprocessandsecond-orderB-splines.TheoutcomesoftheanalysisarequantitativecriteriaforselectionofthewidthoftheB-splines,andofthelearningrate,forwhichthesystemisguaranteedtobestable.Thesecriteriafacilitatethedesignof a learning feed-forward controller. ( 2000 Elsevier Science Ltd. All rights reserved. Keywords: Learning feed-forward control; Adaptation; Neural networks; Iterative learning control; Stability analysis 1. IntroductionHigh-performancemotionsystemssuchas componentmounters require both accurate and robust control. Todesign a model-based controller that satis"es these re-quirements, an accurate model of the process is needed.However, due to factors like process uncertainties, pro-cessnon-linearitiesortime-varyingparameters,theiden-ti"cationandmodellingthat is needed might be di$cult,expensive and sometimes even impossible. To overcomethis, several learning control methods have been pro-posed(Ng,1997).Inlearningcontrol,thecontrollerisnotdesigned on the basis of a process model. The controlleris either trained on the basis of previously gathered dataor is trained during control.