A unity feedback control system is characterized by the open-loop transfer function \(G\left( s \right) = \frac{{10K\left( {s + 2} \right)}}{{{s^3} + 3{s^2} + 10}}\) The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below. If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right-half of the s-plane is

A unity feedback control system is characterized by the open-loop transfer function \(G\left( s \right) = \frac{{10K\left( {s + 2} \right)}}{{{s^3} + 3{s^2} + 10}}\) The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below. If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right-half of the s-plane is Correct Answer 2

Concept

From Nyquist criteria we have

N = P

Where,

N = Number of encirclements of point (-1, j0) by G(s) H(s) plot, the positive direction of encirclement being Anticlockwise.

P = Number of open loop poles in RHS of s-plane.

Z = Number of closed loop poles in RHS of s-plane

Calculations:

P = open loop RHS poles

C.E = s³ + 3s² + 0s +10

From RH Criteria

[ alt="12112" src="//storage.googleapis.com/tb-img/production/19/08/12112.PNG" style="width: 148px; height: 155px;">

Number of sign changes = P = 2

For 0 < K < 1

[ alt="1232" src="//storage.googleapis.com/tb-img/production/19/08/1232.PNG" style="width: 366px; height: 206px;">

N = 0

From Nyquist criteria

N = P – Z

= 2 – Z

Z = 2