GATE IN 2017 Question Paper (12-Feb-2017) (Shift 2)

The block diagram of a closed-loop control system is shown in the figure. The values of k and kₚ are such that the system has a damping ratio of 0.8 and an undamped natural frequency ωₙ of 4 rad/s respectively. The value of kₚ will be __________ .

The loop transfer function of a closed-loop system is given by $G\left(s\right)H\left(s\right)=\frac{K\left(s+6\right)}{s\left(s+2\right)}$. The breakaway point of the root-loci will be ______.

A closed-loop system is shown in the figure. The system parameter α is not known. The condition for asymptotic stability of the closed loop system is

The overall closed loop transfer function $\frac{C\left(s\right)}{R\left(s\right)},$ represented in the figure, will be

Assuming the Op-Amp shown in the figure to be ideal, the frequency at which the magnitude of Vₒ will be 95% of the magnitude of Vᵢₙ is ________ kHz. (Take C = 10 nC)