The number of direction of encirclements around the point -1 + j0 in the complex plane by the Nyquist plot of  is:

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  1. zero
  2. three, anticlockwise
  3. two, anticlockwise
  4. two, clockwise

Answer (Detailed Solution Below)

Option 1 : zero
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Detailed Solution

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Concept:

The Nyquist plot is used to assess the stability of a closed-loop control system using the open-loop transfer function .

Given transfer function:

Poles of G(s): and ⇒ Both in Left Half Plane (LHP), so open-loop system is stable.

According to the Nyquist criterion:

, where:

  • N = number of encirclements of point (clockwise = negative, anticlockwise = positive)
  • Z = number of right-half plane poles of closed-loop transfer function
  • P = number of right-half plane poles of open-loop transfer function (here, P = 0)

Since the open-loop poles are in LHP, the Nyquist plot of does not encircle .

Hence, the number of encirclements is: zero

Final Answer:  zero

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