Talk:Describing function
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More details
editI can add some more details but only with german references. Can this be accepted?--hfst~~ —Preceding unsigned comment added by Hfst (talk • contribs) 21:53, 16 February 2009 (UTC)
- I don't think that would be a problem. If you think you can improve/expand the article, then please feel free to do so. -Roger (talk) 02:46, 17 February 2009 (UTC)
- Moreover, these pages get translated into localized versions of Wikipedia, and so references that require a little extra legwork to be useful in English may be immediately useful in some of the localized versions. Regardless, plenty of academic papers (and encyclopedia articles) reference sources in other languages. Sometimes it's not possible to do otherwise. —TedPavlic (talk/contrib/@) 15:57, 15 June 2011 (UTC)
Justification of DFM
editI think it would be correct to add something about justifications and limitation of application of DFM:
The describing function method (DFM, which is also known as harmonic balance method), is a widely used approximate method (that is, not rigorously mathematically substantiated) of searching for oscillations which are close to the harmonic periodic oscillations of non-linear dynamical systems. But it is well known that DFM can lead to incorrect results. Such examples for the first time have been presented by Tzypkin in a bang-bane systems (Tsypkin Ya.Z., Relay Control Systems. Cambridge: Univ Press; 1984).
Also, in the case when conditions of Aizerman's or Kalman conjectures are fulfilled, there is no periodic solutions by DFM, but counterexamples with periodic solutions are well known (Bragin V.O., Vagaitsev V.I., Kuznetsov N.V., Leonov G.A., Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits, Journal of Computer and Systems Sciences International, 2011, Vol. 50, No. 4, pp. 511-543; Aizerman's and Kalman's conjectures and DFM).
- I think (IMO) the article does an OK job explaining that the DFM is an approximate method. However, certainly comments on its limitations could be added. There are only a few hints in the current text that the DFM may not be appropriate in all cases. So I think you should be WP:BOLD and add some text similar to what you mention above. —TedPavlic (talk/contrib/@) 21:27, 24 September 2011 (UTC)