Stability analysis of learning feed-forward control

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.

[1]  Theodorus J.A. de Vries,et al.  Linear motor motion control using a learning feedworward controller , 1997 .

[2]  M. Kawato,et al.  Hierarchical neural network model for voluntary movement with application to robotics , 1988, IEEE Control Systems Magazine.

[3]  Erik Gadt.  Experimental verification of the stability analysis of Learning Feed-Forward Control , 1998 .

[4]  S. Hara,et al.  Repetitive control system: a new type servo system for periodic exogenous signals , 1988 .

[5]  J. van Amerongen,et al.  Learning feedforward controller for a mobile robot vehicle , 1996 .

[6]  J. van Amerongen,et al.  Learning feed forward controller for a mobile robot , 1995 .

[7]  Kevin L. Moore,et al.  Iterative learning control: A survey and new results , 1992, J. Field Robotics.

[8]  Michael J. Grimble,et al.  Iterative Learning Control for Deterministic Systems , 1992 .

[9]  Roberto Horowitz,et al.  A new adaptive learning rule , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[10]  J. van Amerongen.  Learning feed forward control of a flexible beam , 1996 .

[11]  Martin Brown,et al.  Neurofuzzy adaptive modelling and control , 1994 .

[12]  Chuen-Chien Lee.  FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[13]  Ming-Shong Lan,et al.  Application Of Neural Networks To Adaptive Control , 1988, Twenty-Second Asilomar Conference on Signals, Systems and Computers.

[14]  Tom Kavli.  Frequency domain synthesis of trajectory learning controllers for robot manipulators , 1992, J. Field Robotics.

[15]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. I , 1990, IEEE Trans. Syst. Man Cybern..

[16]  W.J.R. Velthuis,et al.  Experimental verification of the stability analysis of learning feed-forward control , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[17]  G. W. Ng.  application of Neural Networks to Adaptive Control of Nonlinear Systems , 1997 .