# ROBUST ILC DESIGN USING MÖBIUS TRANSFORMATIONS

### C. T. Freeman, P. L. Lewin, E. Rogers

#### Abstract

In this paper a general ILC algorithm is examined and it is found that the filters involved can be selected to satisfy frequency-wise uncertainty limits on the plant model. The probability of the plant model being at a given point in the uncertainty space is specified, and the filters are then chosen to maximise the convergence rate that can be expected in practice. The magnitude of the change in input over successive trials and the residual error have also been incorporated into the cost function. Experimental results are presented using a non-minimum phase test facility to show the effectiveness of the design method.

#### References

- Bien, Z. and Xu, J. (1998). Iterative Learning Control, Analysis, Design, Integration and Applications. Kluwer Academic Publishers.
- Freeman, C. T., Lewin, P. L., and Rogers, E. (2005). Experimental evaluation of iterative control algorithms for non-minimum phase plants. International Journal of Control, 78(11):806-826.
- Jones, G. A. and Singerman, D. (2004). Complex Functions: An Algebraic and Geometric Viewpoint. Cambridge University Press.
- Longman, R. W. (2000). Iterative learning control and repetitive control for engineering practice. International Journal of Control, 73(10):930-954.
- Moore, K. L. (1993). Iterative Learning Control for Deterministic Systems. Springer-Verlag.
- Moore, K. L. (1998). Iterative learning control - an expository overview. Applied and Computational Controls, Signal Processing and Circuits, 1(1):151 - 214.
- Norrlöf, M. (2000). Comparative study on first and second order ilc- frequency domain analysis and experiments. In Proceedings of the 39th Conference on Decision and Control, pages 3415-3420.
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#### Paper Citation

#### in Harvard Style

T. Freeman C., L. Lewin P. and Rogers E. (2005). **ROBUST ILC DESIGN USING MÖBIUS TRANSFORMATIONS** . In *Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 972-8865-29-5, pages 141-146. DOI: 10.5220/0001172601410146

#### in Bibtex Style

@conference{icinco05,

author={C. T. Freeman and P. L. Lewin and E. Rogers},

title={ROBUST ILC DESIGN USING MÖBIUS TRANSFORMATIONS},

booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2005},

pages={141-146},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001172601410146},

isbn={972-8865-29-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - ROBUST ILC DESIGN USING MÖBIUS TRANSFORMATIONS

SN - 972-8865-29-5

AU - T. Freeman C.

AU - L. Lewin P.

AU - Rogers E.

PY - 2005

SP - 141

EP - 146

DO - 10.5220/0001172601410146