The complete Nyquist plot of the open-loop transfer function G(s) H(s) of a feedback control system is shown in the figure.

If G(s) H(s) has one zero in the right-half of the s-plane. the number of poles that the closed-loop system will have in the right-half of the s-plane is

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GATE EC 2021 Official Paper

Option 2 : 1

CT 1: Ratio and Proportion

2846

10 Questions
16 Marks
30 Mins

For the open-loop stability we have to find the encirclement about the origin:

N = P - Z

Where,

N = no. of encirclement about the origin in ACW direction, P = no. of RHP poles of GH, Z = no. of RHP zeros of GH

According to the problem,

N = -2, Z = 1

-2 = P - 1

P = -1

For the closed loop stability,

N = P - Z

Where,

N = no. of encirclement about the -1+j0 in ACW direction, P = no. of RHP poles of 1+GH, Z = no. of RHP zeros of 1+GH

We found, P = -1, N = 0 (according to the program), Z = ?

0 = -1 - Z

Z = -1