A statistical analysis of certain iterative learning control algorithms

Iterative learning control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, first by a statistical analysis and then by simulation results and their application to a linear motor. New expressions for the expected value and variance of the controlled error are developed for each algorithm. The different algorithms are then tested in simulation and finally applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectra are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate.

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

[2]  Giovanni Ulivi,et al.  Disturbance rejection of iterative learning control applied to trajectory tracking for for a flexible manipulator , 1995 .

[3]  K. Moore.  Multi-loop control approach to designing iterative learning controllers , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[4]  Samer S. Saab.  Optimal selection of the forgetting matrix into an iterative learning control algorithm , 2005, IEEE Transactions on Automatic Control.

[5]  Svante Gunnarsson,et al.  On the disturbance properties of high order iterative learning control algorithms , 2006, Autom..

[6]  Svante Gunnarsson,et al.  Time and frequency domain convergence properties in iterative learning control , 2002 .

[7]  Samer S. Saab,et al.  A discrete-time stochastic learning control algorithm , 2001, IEEE Trans. Autom. Control..

[8]  Svante Gunnarsson,et al.  Disturbance aspects of iterative learning control , 2001 .

[9]  S. Saab.  Optimal Selection of the Forgetting Matrix into an Iterative Learning Control Algorithm , 2005 .

[10]  Mikael Norrlöf,et al.  An adaptive iterative learning control algorithm with experiments on an industrial robot , 2002, IEEE Trans. Robotics Autom..

[11]  K. M. Tao,et al.  Learning feedforward control , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  Kevin L. Moore,et al.  Iterative Learning Control: An Expository Overview , 1999 .

[13]  Suguru Arimoto.  Robustness of learning control for robot manipulators , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[14]  Jian-Xin Xu,et al.  Iterative Learning Control , 1998 .

[15]  R. Merry,et al.  The influence of disturbances in iterative learning control , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[16]  A.G. Alleyne,et al.  A survey of iterative learning control , 2006, IEEE Control Systems.

[17]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[18]  Zeungnam Bien,et al.  Iterative learning control: analysis, design, integration and applications , 1998 .

[19]  Mikael Norrlöf,et al.  DISTURBANCE REJECTION USING AN ILC ALGORITHM WITH ITERATION VARYING FILTERS , 2004 .

[20]  Fumio Miyazaki,et al.  Robust leaning control , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.