GATE 2025 Electronics & Communication Q36

Question

Let $G(s) = \frac{1}{10s^2}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below.

Consider the following statements.

(i) There exists no controller of the form $M(s) = \frac{K_I}{s}$, where $K_I$ is a positive real number, such that the closed loop system is stable.

(ii) There exists at least one controller of the form $M(s) = K_P + sK_D$, where $K_P$ and $K_D$ are positive real numbers, such that the closed loop system is stable.

Which one of the following options is correct?

Accepted Answer

Both (i) and (ii) are TRUE

Answer

(i) is TRUE and (ii) is FALSE

Answer

(i) is FALSE and (ii) is TRUE

Answer

Both (i) and (ii) are FALSE