would like to use knots to get a formula for nyquist diagram however, no crossing, and have no experience in analysis of graph related to control, as i have no books mentioning this
and i observe phase diagram is like a distribution graph, is it useful to make a distribution to fit for it. if so, what is the usage of this distribution function for phase diagram?
expect an analysis of these graph and how to analysis these graph
right hand side is rlocus diagram, top left is bode, bottom is nyquist
What do you mean with "knot"?
The phase diagram does not look like a distribution plot in general. It just does in this particular case with a little imagination. So there is no use to make a distribution fit.
Further you might want to start of reading the wikipedia pages about bode plots, nyquist diagrams and rlocus plots. All these articles are pretty good. Further there is tons of material available online,
http://en.wikibooks.org/wiki/Control_Systems http://support.motioneng.com/utilities/bode/bode_16.html http://www.ece.utah.edu/~ee3110/bodeplot.pdf http://dora.eeap.cwru.edu/msb/246/bode.pdf http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/BookIndex.htm http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/Freq/Freq5.html http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/Freq/Nyquist2.html
If you really want a book most likely any book about control theory would suffice since, bode diagrams, nyquits plots and rlocus plots (I however rarely use the latter) are basics concepts of control theory and also many related fields.