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Why do we need to know beforehand the number of open-loop unstable poles in order to tell stability from the Nyquist plot?
The Nyquist plot encirclements counts the difference in the number of zeros and the number of poles in the RHP of 1 + KDG. In order to know the number of zeros of this function (which are closed-loop poles and thus unstable poles of the closed loop), we must know the number of unstable open-loop poles for the plot.