GATE IN 2014 Question Paper (02-Feb-2014) (Shift 2)

The transfer function of a system is given by $G\left(s\right)=\frac{e^{-\frac{s}{500}}}{s+500}$

The input to the system is x(t) = sin 100 πt.

In a periodic steady-state, the output of the system is found to be y(t) = A sin (100 πt - ϕ). The phase angle (ϕ) in degrees is _______

In the microprocessor controlled measurement scheme shown in the figure, Rₓ is the unknown resistance to be measured, while R${}_{ref}$ and C${}_{ref}$ are known. C${}_{ref}$ is charged from voltage V${}_L$ to V${}_H$ (by a constant DC voltage source V${}_S$), once through R${}_{ref}$ in T${}_{ref}$ seconds and then discharged to V${}_L$ . It is again charged from voltage V${}_L$ to V${}_H$ through Rₓin Tₓ seconds.



If Tₓ = kT${}_{ref}$ then

Frequency of an analog periodic signal in the range of 5 kHz – 10 kHz is to be measured with a resolution of 100 Hz by measuring its period with a counter. Assuming negligible signal and transition delays the minimum clock frequency and minimum number of bits in the counter needed, respectively are:

The loop transfer function of a feedback control system is given by

$G\left(s\right)H\left(s\right)=\frac{1}{s\left(s+1\right)\left(9s+1\right)}$

Its phase crossover frequency (in rad/s), approximated to two decimal places is _______

Consider a transport lag process with a transfer function

𝐺${}_{\text{p}}$ (𝑠) = 𝑒${}^{-\text{s}}$.

The process is controlled by a purely integral controller with transfer function

$G_c(s)=\frac{K_i}{s}$

in a unity feedback configuration. The value of 𝐾${}_{\text{i}}$ for which the closed loop plant has a pole at 𝑠 = −1, is ___________.