I have been looking at a lot of documents and tutorials and all of them seem to explain things after certain steps only. But I am struggling first with : How to draw the closed contour from the transfer function? I seem to find no resources to draw this. Then I can move on with translation of this to contour map.
Could anyone explain ideas involved first in drawing the closed contour Or a PDF or video reference please?

One may be stupid question. Is it even possible to draw nyquist diagram by hand in relatively short time?

Thanks in advance.

 

Yes it is possible, and you can do it in two different ways.

1. In Cartesian coordinates, with frequency as a parameter, plot the real part of the transfer function G(s) on the X-axis and plot the Imaginary part of the transfer function on the imaginary axis. For any given frequency there will be a unique point on the Nyquist locus.
2. In polar coordinates, with frequency as a parameter, plot the magnitude as the radial component and plote the phase as the angular component.

Just remember the ladies in "Hidden Figures" that did this kind of stuff by hand, day in and day out, and I'm sure you will be inspired.
You can mechanize the computations and the plotting with a LibreOffice spreadsheet. Easy Peazy