A COMPUTER ORIENTED ALGORITHM FOR ANALYZING LIMIT CYCLES IN DISCRETE CONTROL SYSTEMS

M. Utrilla-Manso, R. Jiménez-Martínez, R. Mallol-Poyato, J. Sánchez-Golmayo, F. López-Ferreras

2005

Abstract

In this paper a new and fast algorithm for characterizing the behaviour of zero-input limit cycles that can appear in digital control systems when finite precision computer is used. This proposed algorithm suggests a practical approach to determine the impact of these parasitic oscillations against difficult theoretical solutions limited to simple systems and very conservatives in some cases. This algorithm is applicable to any kind of discrete system described by its difference equations and quantized by any quantization scheme and supply practical results in considerable less time that other exhaustive formulations. Some tables show the feasibility of the algorithm compared with exhaustive searches and theoretical calculations to characterize the limit cycles and its applicability for any kind of discrete system as different digital filters and digital control systems where different controllers are applied.

References

  1. Bauer, P.H.; Leclerc, L.-J., Nov. 1991. A Computer-Aided test for the Absence of Limit Cycles in Fixed-Point Digital Filters. In ICEIS'99, IEEE Trans. Sig. Proc., vol. 39, no. 11, pp. 2400-2409.
  2. Premaratne, K.; Kulasekere, E.C.; Bauer, P.H.; Leclerc, L.-J., 1995. An Exhaustive Search Algorithm for Checking Limit Cycle Behavior of Digital Filters. Proc. IEEE ISCAS, Seattle, pp. 2035-2038.
  3. B.D. Green, L.E. Turner., 1988. New Limit Cycle Bounds for Digital Filters. In IEEE Trans. Circuits and System, vol. 35 ,no.4,
  4. S. Yakowitz, S.R. Parker., 1973. Computation of bounds for digital quantization errors In In IEEE Trans. Circuit Theory CT.-20 (July 1973) pp. 391-396, pp. 391-396
  5. M. Utrilla Manso, F. López Ferreras; D. Osés-del Campo, R. Jiménez-Martínez., 2000. A DSP-Oriented Fast Algorithm to Detect and Characterize Limit Cycles in Digital Filters. In Problems in Modern Applied Mathematics ISBN 960-8052-15-7, pp.198-203, Ed. World Scientific and Engineering Society Press
  6. D. Osés-Del Campo; F.López-Ferreras; M. UtrillaManso;F.Cruz-Roldán., 2000. Fast Algorithms for the Analysis and Characterisation of Limit Cycles in Fixed-Point Digital Filters. In Problems in Modern Applied Mathematics ISBN 960-8052-15-7, pp.187- 191, Ed. World Scientific and Engineering Society Press.
  7. A. Djebbari, M.F. Belbachir, J.M. Rouvaen., 1998. A fast exhaustive search algorithm for checking limit cycles in fixed-point digital filters. In Signal Processing 69, Elsevier Science pp. 199-205
  8. Franklin, G. F. y Powell J.D., Nov. 1997.. Digital control of dinamics systems. Addison Wesley
  9. Kat. Ogata., Nov. 1996. Sistemas de Control en Tiempo Discreto. Pearson Education 2nd Ed.
  10. John B. Slaughter, 1963. Quantization Errors in Digital Control System In IEEE Transactions on Automatic Control. pp: 69-74..
  11. P.Diniz, E Silva and S. Netto., 2002. Digital Signal Processing: system and analysis, Cambridge University Press.
  12. C.L. Phillips, H.T. Nagle, 1990, Digital Control System Analysis and Design, 2nd Ed, Prentice Hall.
  13. A. V. Oppenheim, R. W. Schafer, 1999, Discrete-Time Signal Processing, 2nd Ed, Prentice Hall.
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Paper Citation


in Harvard Style

Utrilla-Manso M., Jiménez-Martínez R., Mallol-Poyato R., Sánchez-Golmayo J. and López-Ferreras F. (2005). A COMPUTER ORIENTED ALGORITHM FOR ANALYZING LIMIT CYCLES IN DISCRETE CONTROL SYSTEMS . In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 972-8865-31-7, pages 155-160. DOI: 10.5220/0001182401550160


in Bibtex Style

@conference{icinco05,
author={M. Utrilla-Manso and R. Jiménez-Martínez and R. Mallol-Poyato and J. Sánchez-Golmayo and F. López-Ferreras},
title={A COMPUTER ORIENTED ALGORITHM FOR ANALYZING LIMIT CYCLES IN DISCRETE CONTROL SYSTEMS},
booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2005},
pages={155-160},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001182401550160},
isbn={972-8865-31-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - A COMPUTER ORIENTED ALGORITHM FOR ANALYZING LIMIT CYCLES IN DISCRETE CONTROL SYSTEMS
SN - 972-8865-31-7
AU - Utrilla-Manso M.
AU - Jiménez-Martínez R.
AU - Mallol-Poyato R.
AU - Sánchez-Golmayo J.
AU - López-Ferreras F.
PY - 2005
SP - 155
EP - 160
DO - 10.5220/0001182401550160