GATE EE 2025 Question Paper (02-Feb-2025) (Shift-2)

An ideal low pass filter has frequency response given by
$H(j\omega )=\{\begin{array}{ll}1,& |\omega |\le 200\pi \\ 0,& \text{otherwise}\end{array}$
Let $h(t)$ be its time domain representation. Then $h(0)=$ ___________ (round off to the nearest integer)

Consider the state-space model
$\dot{x}(t)=Ax(t)+Bu(t)$
$y(t)=Cx(t)$
where $x(t)$, $r(t)$, $y(t)$ are the state, input and output, respectively. The matrices $A$, $B$, $C$ are given below
$A=\left[\begin{array}{cc}0& 1\\ -2& -3\end{array}\right]$, $B=\left[\begin{array}{c}0\\ 1\end{array}\right]$, $C=\left[\begin{array}{cc}1& 0\end{array}\right]$
The sum of the magnitudes of the poles is ___________ . (Round off to nearest integer)

Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be improved to 0.85 pf lag. The line current of the capacitor bank, in A, is ___________ . (Round off to one decimal places)

Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of 10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of 11,800 Rs./MWh is ___________ (round off to the nearest integer)

A controller $D(s)$ of the form $(1+K_{D}s)$ is to be designed for the plant $G(s)=\frac{1000\sqrt{2}}{s(s+10{)}^2}$ as shown in the figure. The value of $K_D$ that yields a phase margin of 45° at the gain cross-over frequency of 10 rad/sec is ___________ (round off to one decimal place).