Iterative Learning Control for varying tasks: Achieving optimality for rational basis functions

Iterative Learning Control (ILC) can achieve superior tracking performance for systems that perform repeating tasks. However, the performance of standard ILC deteriorates dramatically when the task is varied. In this paper ILC is extended with rational basis functions to obtain excellent extrapolation properties. A new approach for rational basis functions is proposed where the iterative solution algorithm is of the form used in instrumental variable system identification algorithms. The optimal solution is expressed in terms of learning filters similar as in standard ILC. The proposed approach is shown to be superior over existing approaches in terms of performance by a simulation example.

[1]  Tom Oomen,et al.  Rational Basis Functions in Iterative Learning Control—With Experimental Verification on a Motion System , 2015, IEEE Transactions on Control Systems Technology.

[2]  M Maarten Steinbuch,et al.  Using iterative learning control with basis functions to compensate medium deformation in a wide-format inkjet printer , 2014 .

[3]  M. Norrlof,et al.  Some aspects of an optimization approach to iterative learning control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  Krzysztof Galkowski,et al.  Control Systems Theory and Applications for Linear Repetitive Processes - Recent Progress and Open Research Questions , 2007 .

[5]  Jeroen van de Wijdeven,et al.  Using basis functions in iterative learning control: analysis and design theory , 2010, Int. J. Control.

[6]  Emre Kural,et al.  96 A Survey of Iterative Learning Control Al earning-based method for high-performance tracking control , 2006 .

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

[8]  A. H. Whitfield.  Asymptotic behaviour of transfer function synthesis methods , 1987 .

[9]  D. Bernstein.  Matrix Mathematics: Theory, Facts, and Formulas , 2009 .

[10]  MF Marcel Heertjes,et al.  Set-point variation in learning schemes with applications to wafer scanners , 2009 .

[11]  Heinz Unbehauen,et al.  Minmax and least squares multivariable transfer function curve fitting: error criteria, algorithms and comparisons , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[12]  P. Young,et al.  Optimal instrumental variable method for closed-loop identification , 2011 .

[13]  Minh Q. Phan,et al.  Learning control for trajectory tracking using basis functions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[14]  Xuemei Gao,et al.  An iterative learning control algorithm for portability between trajectories , 2014, 2014 American Control Conference.

[15]  Andrew G. Alleyne,et al.  Basis Task Approach to Iterative Learning Control With Applications to Micro-Robotic Deposition , 2011, IEEE Transactions on Control Systems Technology.

[16]  T. Hughes,et al.  Signals and systems , 2006, Genome Biology.

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

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

[19]  Maarten Steinbuch,et al.  Optimally conditioned instrumental variable approach for frequency-domain system identification , 2014, Autom..

[20]  Svante Gunnarsson,et al.  On the design of ILC algorithms using optimization , 2001, Autom..