Reverse Time Filtering Based ILC

  • Danwei WangEmail author
  • Yongqiang Ye
  • Bin Zhang
Part of the Advances in Industrial Control book series (AIC)


The best phase lead is the one that can exactly compensate the phase lag of a system. A zero phase learning control using reversed time input runs is proposed, utilizing a simple phase lead generation method. The plant itself or a nominal model is used to obtain the desired phase lead. Then the results for SISO ILC system are extended to MIMO ILC system in two different ways, leading to two parallel MIMO learning control laws. These two MIMO schemes need no high order derivatives of error signals and no numerical differentiation, and thus generate little noise.


Phase lead Reverse time Clean system inversion System Hermitian 


  1. 1.
    Ye Y, Wang D (2003) Better robot tracking accuracy with phase lead compensated ILC. In: Proceedings of the 2003 IEEE international conference on robotics and automation, Taipei, Taiwan, pp 4380–4485, September 2003Google Scholar
  2. 2.
    Chien C-J (1996) A discrete iterative learning control of nonlinear time-varying systems. In: Proceedings of the 35th IEEE conference on decision and control, Kobe, Japan, pp 3056–3061, December 1996Google Scholar
  3. 3.
    Driessen BJ, Sadegh N (2002) Convergence theory for multiple-input discrete-time iterative learning control with Coulomb frictions, continuous outputs and input bounds. In: Proceedings of the 2002 IEEE southeast conference, Columbia, SC, USA, pp 287–293, April 2002Google Scholar
  4. 4.
    Elci H, Longman RW, Phan MQ, Juang J-N, Ugoletti R (1994) Automated learning control through model updating for precision motion control. In: Garcia E, Cudney H, Dasgupta A (eds) Adaptive structures and composite materials: analysis and application: presented at the 1994 International Mechanical Engineering Congress and Exposition, vol AD-Vol 45/MD-Vol 54. American Society of Mechanical Engineers, Chicago, IL, USA, pp 299–314Google Scholar
  5. 5.
    Hideg LM (1994) Stability of linear time varying multiple input multiple output continuous time learning control systems: a sufficient condition. In: Proceedings of the 1994 IEEE international symposium on intelligent control, Columbus, OH, USA, pp 285–290, September 1994Google Scholar
  6. 6.
    Lee-Glauser GJ, Juang J-N, Longman RW (1996) Comparison and combination of learning controllers: computational enhancement and experiments. AIAA J Guidance Control Dyn 19:1116–1123CrossRefzbMATHGoogle Scholar
  7. 7.
    Moore KL, Bahl V (2000) Iterative learning control for multivariable systems with an application to mobile robot path tracking. In: Proceedings of the 6th international conference on control, automation, robotics and vision, Singapore, December 2000Google Scholar
  8. 8.
    Saab SS (1995) A discrete-time learning control algorithm for a class of linear time-invariant systems. IEEE Trans Autom Control 40:1138–1142CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Phan MQ, Longman RW (1988) A mathematical theory of learning control for linear discrete multivariable systems. In: Proceedings of the 1988 AIAA/AAS astrodynamics specialist conference, Minneapolis, MN, USA, pp 740–746, August 1988Google Scholar
  10. 10.
    Jang HS, Longman RW (1994) A new learning control law with monotonic decay of the tracking error norm. In: Proceedings of the 32nd Allerton conference on communication, control, and computing, University of Illinois, Urbana, USA, pp 314–323, September 1994Google Scholar
  11. 11.
    Jang HS, Longman RW (1996) An update on a monotonic learning control law and some fuzzy logic learning gain adjustment techniques. Adv Astronaut Sci 90:301–318Google Scholar
  12. 12.
    Longman RW, Songchon T (1999) Trade-offs in designing learning/repetitive controller using zero-phase filter for long term stabilization. Adv Astronaut Sci 102:673–692Google Scholar
  13. 13.
    Elci H, Longman RW, Phan MQ, Juang J-N, Ugoletti R (1994) Discrete frequency based learning control for precision motion control. In: Proceedings of the 1994 IEEE international conference on systems, man, and cybernetics, San Antonio, TX, USA, pp 2767–2773, October 1994Google Scholar
  14. 14.
    Elci H, Longman RW, Phan MQ, Juang J-N, Ugoletti R (2002) Simple learning control made practical by zero-phase filtering: application to robotics. IEEE Trans Circuits Syst -1: Fundam Theory Appl 49:753–767CrossRefGoogle Scholar
  15. 15.
    Longman RW (2000) Iterative learning control and repetitive control for engineering practice. Int J Control 73:930–954CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    The MathWorks Inc (1997) Signal processing toolbox - user’s guide, Version 5, Natick, MAGoogle Scholar
  17. 17.
    Ambardar A (1995) Analog and digital signal processing. PWS Publishing Company, BostonGoogle Scholar
  18. 18.
    Yamakita M, Furuta K (1991) Iterative generation of virtual reference for a manipulator. Robotica 9:71–80CrossRefGoogle Scholar
  19. 19.
    Kinoshita K, Sogo T, Adachi N (2002) Iterative learning control using adjoint systems and stable inversion. Asian J Control 4:60–67CrossRefGoogle Scholar
  20. 20.
    Ghosh J, Paden B (1999) Iterative learning control for nonlinear nonminimum phase plants with input disturbance. In: Proceedings of the 1999 American control conference, San Diego, CA, USA, pp 2584–2589, June 1999Google Scholar
  21. 21.
    Le Page WR (1980) Complex variables and the Laplace transform for engineers. Dover Publications, New YorkGoogle Scholar
  22. 22.
    Longman RW, Wirkander S-L (1998) Automated tuning concepts for iterative learning and repetitive control laws. In: Proceedings of the 37th IEEE conference on decision and control, Tampa, FL, USA, pp 192–198, December 1998Google Scholar
  23. 23.
    Wirkander S-L, Longman RW (1999) Limit cycles for improved performance in self-tuning learning control. Adv Astronaut Sci 102:763–781Google Scholar
  24. 24.
    Longman RW, Wang Y (1996) Phase cancellation learning control using FFT weighted frequency response identification. Adv Astronaut Sci 93:85–101Google Scholar
  25. 25.
    Longman RW (1998) Designing iterative learning control and repetitive controllers. In: Bien Z, Xu J-X (eds) Iterative learning control: analysis, design, integration and applications. Kluwer, Boston, pp 107–146CrossRefGoogle Scholar
  26. 26.
    Moon J-H, Doh T-Y, Chung MJ (1997) An iterative learning control scheme for manipulators. In: Proceedings of the 1997 international conference on intelligent robots and systems, Grenoble, France, pp 759–765, September 1997Google Scholar

Copyright information

© Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  3. 3.Department of Electrical EngineeringUniversity of South CarolinaColumbiaUSA

Personalised recommendations