a State Nyquist stability criterion and explain how it follo

(a) State Nyquist stability criterion and explain how it follows from the theorem that a clockwise tracing of a closed contour in S-plane maps onto a closed contour in the plane of complex function F(s) that encircles the origin a number of times equal to (Z-P) where Z and P are number of zeros and poles, respectively, with multiplicities taken into account (No proof required). (b) How the criterion is modified when there are some open loop poles on the imaginary axis? (c) With the help of Nyquist plot, show that a closed loop system with an unstable open loop transfer function G(s)H(s) = K_1(1 + K_2s)/s(s - 1) is stable for K_1K_2 > 1

Solution

Solution :-

Option C is not correct.

From Bernoulli\'s equation

A₁V₁ = A₂V₂ ........ (1)

Since the pipe has constant diameter. Therefore A₁ = A₂

Therefore from the above equation V₁ = V₂

ie the velocity doesn\'t vary along the length of the pipe.