GATE 2024 Control Systems Foundation Quiz 71

The characteristic equation of a feedback control system is given by  Where k>0.

Nyquist plot of two functions G₁(s) and G₂(s) are shown below

Nyquist plot for product of G₁(s) and G₂(s) is

Consider the following statements regarding the unity negative feedback system and its Nyquist plot as shown below:

Select the correct statement(s) given below:
S₁: For k = 1, the closed-loop system will be stable when and only when the open-loop system is stable.

S₂: For k = 100, the closed-loop system will be stable when and only when the open-loop system is stable.

The open loop of a unity feedback control system G(s) is unstable and has three poles on the right-hand side of the s-plane. However, the close loop system is stable. The number of encirclements mode by Nyquist plot of the (– 1, 0) point in the G(s) plane is

The pole-zero map and the Nyquist plot of the open-loop transfer function G(s) H(s) of a feedback system are shown below. For this