# DESIGN OF AN ITERATIVE LEARNING CONTROL FOR A SERVO SYTEM USING MULTI-DICTIONARY MATCHING PURSUIT

### Iuliana Rotariu, Erik Vullings

#### 2006

#### Abstract

Many motion systems repeatedly follow the same trajectory. However, in many cases, the motion system does not learn from tracking errors obtained in a previous cycle. Iterative Learning Control (ILC) resolves this issue by compensating for previous tracking errors, but it suffers from not being able to distinguish between tracking errors caused by machine dynamics versus errors caused by noise, and by trying to ’learn’ the noise, additional errors are introduced. In this paper we address this issue by using the servo error signal by identifying the time-varying nonlinear effects, which can be learned and therefore improve the position accuracy, versus the stochastic effects, which cannot be learned. The identification of these effects is performed by means of time-frequency analysis of the servo error and therefore our goal is to obtain a high-resolution time-frequency energy distribution of the analyzed signal. Here we compare the servo error energy distribution by three means: (1) Wigner distribution; (2) adaptive signal decomposition over one dictionary of modulated versions of wavelets (simple atomic dictionary); (3) and by means of combining several simple atomic dictionaries into a complex atomic dictionary. We show that the latter approach leads to the highest-resolution energy distribution and tracking performance.

#### References

- Buckheit, J., Chen, S., Donoho, D., Johnstone, I., and Scargle, J. (1995). Wavelab. In Tech. Rep., Stanford University.
- Cappellini, V. and Constantinides, A. (1984). Interference terms in the Wigner distribution. Digital Signal Proc.
- Casalino, G. and Bartolini, G. (1984). A learning procedure for the control of movements of robotic manipulators. In Proc. 4th IASTED Symp. Robotics Automation, pages 108-111.
- Chandroth, G. O. (1999). Diagnostic classifier ensembles: Enforcing diversity for reliability in the combination. In University of Sheffield, UK.
- Chang, C.-K., Longman, R. W., and Phan, M. Q. (1992). Techniques for improving transients in learning control systems. Adv. Astronautic. Sci, 76:20352052.
- Chen, Y. and Moore, K. (2001). Frequency domain adaptive learning feedforward control. In Proc. of the 2001 IEEE Int. Symp. Comp. Intell. Robotics and Automation, pages 396-401.
- Cohen, L. (1989). Time-frequency distributions - a review. Proc. IEEE, 77(7).
- Daubechies, I. (1991). Ten lectures on wavelets. Series in Applied mathematics, SIAM.
- Goh, C. J. (1994). A frequency domain analysis of learning control. J. Dynamic Syst., Measurement, Contr., 116:781-786.
- Mallat, S. and Zhang, Z. (1993). Matching pursuit with time-frequency dictionaries. IEEE Trans. on Signal Processing, 41(12):3397-3415.
- Margrave, G. F. (1998). Theory of nonstationary linear filtering in the fourier domain with applications to timevariant filtering. Geophysics, 63(1):244 - 259.
- Mecklenbräuker, W., Hlawatsch, F., and Janssen, A. (1997). The wigner distribution, theory and applications in signal processing. Elsevier.
- Moore, K. L. (1993). Iterative learning control for deterministic systems. Adv. in Ind. Control. SpringerVerlag.
- Norrlöf, M. (2002). Iteration varying filters in iterative learning control. In Proc. 4th Asian Control Conf., page 21242129.
- Rioul, O. and Vetterli, M. (1991). Wavelets and signal processing. IEEE Signal Processing Magazine, 8(4):14-38.
- Rotariu, I., Dijkstra, B., and Steinbuch, M. (2004). Comparison of standard and lifted ilc on a motion system. In 3rd IFAC Symp. Mechatronic Systems, Sydney, Australia, pages 211-6.
- Rotariu, I., Ellenbroek, R., and Steinbuch, M. (2003a). Time-frequency analysis of a motion system with learning control. In Proc. ACC Conf., pages 3650 - 3654. American Control Conf.
- Rotariu, I., Ellenbroek, R., and Steinbuch, M. (2006). Adaptive iterative learning control with application to a wafer stage. submitted to IEEE Transactions on Control Systems Technology.
- Rotariu, I., Ellenbroek, R., van Baars, G., and Steinbuch, M. (2003b). Scan-length independent iterative learning control applied to a wafer stage motion system. In Proc. ECC Conf.
- Struzik, Z. and Siebes, A. (1998). Wavelet transform in similarity paradigm i and ii. In Centrum voor Wiskunde en Informatica, Report,INS-R9802.
- Tang, X., Cai, L., and Huang, W. (2000). A learning controller for robot manipulators using fourier series. IEEE Trans. Robot. Automat., 16(1):3645.
- Tharayil, M. and Alleyne, A. (2004). Design and convergence of a time-varying iterative learning control law. In Proc. IMECE Int. Mech. Eng. Congr. and R&D Expo.
- Torresani, B. (1991). Wavelets associated with representations of the afine weyl-heisenberg group. J. Math Physics, 32(5):1273-9.
- Wirkander, S.-L. and Longman, R. (1999). Limit cycles for improved performance in self-tuning learning control. Adv. Astronautic. Sci., 102:763-781.
- Yen, G. and Lin, K. (2000). Wavelet packet feature extraction for vibration monitoring. IEEE Trans. Ind. Electronics, 47(3):650-67.
- Zhang, B., Wang, D., and Ye, Y. (2005). Wavelet transformbased frequency tuning ilc. IEEE Trans. Systems, Man & Cybernetics, Part B: Cybernetics, 35(1):107-114.
- Zheng, D. and Alleyne, A. (2001). Adaptive iterative learning control for systems with non-smooth nonlinearities. In Proc. ASME Conf., Pittsburgh, Pennsylvania. ASME Int. DETC.
- Zheng, D. and Alleyne, A. (2003). Stability of a novel iterative learning control scheme with adaptive filtering. In Proc. ACC Conf.

#### Paper Citation

#### in Harvard Style

Rotariu I. and Vullings E. (2006). **DESIGN OF AN ITERATIVE LEARNING CONTROL FOR A SERVO SYTEM USING MULTI-DICTIONARY MATCHING PURSUIT** . In *Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 978-972-8865-61-0, pages 24-31. DOI: 10.5220/0001206400240031

#### in Bibtex Style

@conference{icinco06,

author={Iuliana Rotariu and Erik Vullings},

title={DESIGN OF AN ITERATIVE LEARNING CONTROL FOR A SERVO SYTEM USING MULTI-DICTIONARY MATCHING PURSUIT},

booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2006},

pages={24-31},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001206400240031},

isbn={978-972-8865-61-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - DESIGN OF AN ITERATIVE LEARNING CONTROL FOR A SERVO SYTEM USING MULTI-DICTIONARY MATCHING PURSUIT

SN - 978-972-8865-61-0

AU - Rotariu I.

AU - Vullings E.

PY - 2006

SP - 24

EP - 31

DO - 10.5220/0001206400240031