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“An Adaptive Controller Based upon Continuous Estimation of the Closed Loop Frequency Response”

Authors: Jens G. Balchen and Bernt Lie,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1987, Vol 8, No 4, pp. 223-240.

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Keywords: Adaptive control, frequency response, correlation methods, parameter estimation, process control

Abstract: An adaptive control algorithm based upon on-line estimation of the -180 degree shift frequency and the gain margin is investigated. The estimates are found by perturbing the system with a small signal and then correlating the system deviation with the excitation. As only two parameters are estimated, the algorithm is robust. Moreover, the estimator can be applied to non-minimum phase systems, including systems with a varying time-delay. The control algorithm can be of any form as long as there is a functional relationship between the estimated parameters and the control algorithm parameters. To avoid an excessive perturbation signal, the square of the amplitude of this signal is automatically adjusted to a certain ratio of the variance of the error signal. A mathematical analysis of convergence is presented and the theory is confirmed by experimental results.

PDF PDF (2066 Kb)        DOI: 10.4173/mic.1987.4.3



DOI forward links to this article:
  [1] Jens G. Balchen, Kåre Telnes and David Di Ruscio (1989), doi:10.4173/mic.1989.1.1
  [2] Pramod R. Raul and Prabhakar R. Pagilla (2014), doi:10.1016/j.isatra.2014.11.020
  [3] Niko Nevaranta, Stijn Derammelaere, Jukka Parkkinen, Bram Vervisch, Tuomo Lindh, Kurt Stockman, Markku Niemela, Olli Pyrhonen and Juha Pyrhonen (2016), doi:10.1109/TIE.2016.2574303
  [4] Niko Nevaranta, Stijn Derammelaere, Jukka Parkkinen, Bram Vervisch, Tuomo Lindh, Markku Niemelä and Olli Pyrhönen (2016), doi:10.4173/mic.2016.2.5
  [5] N. Nevaranta, M. Goubej, T. Lindh, M. Niemela and O. Pyrhonen (2016), doi:10.1109/EPE.2016.7695535


References:
[1] ÅSTRÖM, K.J., BORISSON, U., LJUNG, L., WITTENMARK, B. (1977). Theory and applications of self-tuning regulators, Automatica, 13, 457-476 doi:10.1016/0005-1098(77)90067-X
[2] FELDBAUM, A.A. (1960). Dual Control Theory I-II, Automation and Remote Control (Transl. from Russian), 21, 9 and 11 (Instrument Society of America).
[3] LJUNG, L. SÖDERSTRÖM, T. (1985). Theory and practice of recursive identification, 2nd ed..The MIT Press; Cambridge, Massachusetts.


BibTeX:
@article{MIC-1987-4-3,
  title={{An Adaptive Controller Based upon Continuous Estimation of the Closed Loop Frequency Response}},
  author={Balchen, Jens G. and Lie, Bernt},
  journal={Modeling, Identification and Control},
  volume={8},
  number={4},
  pages={223--240},
  year={1987},
  doi={10.4173/mic.1987.4.3},
  publisher={Norwegian Society of Automatic Control}
};

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