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Here is what I understood so far:

Nyquist criterion is based on the Cauchy's Principle of Argument. It says that after a contour has been transformed to a new plane, it encircles the origin of that plane N times, where N is (no. of zeroes - no. of poles) of the transforming function. The direction of encirclement matters, and opposite direction indicate a negative encirclement. So for a control system, where the gain is G(s) and feedback element is H(s) we plot the poles of the open loop transfer function G(s)H(s), since the poles of this function is same as the poles of the characteristic equation of the closed loop transfer function.

That is all I got so far. Most pages talk about the encirclement of the point -1+j0, and say that the no. of encirclements of this point is the no. of poles on the RHP (or something like that.) Some books plot the open loop function, while others plot the characteristic equation. I am really confused as to why the point (-1,0) matters, and what actually is the Nyquist criterion, and how does it help us in forming a Nyquist plot.

If possible please explain with a simple example ( 1/(s+1), or something of that sort). Help is appreciated.

Thanks in advance.