List of top Control Systems Questions asked in GATE Electrical Engineering

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time constant (in seconds) of the system is:

\[ \begin{array}{|c|c|} \hline \textbf{Time (sec)} & \textbf{Output} \\ \hline 0.6 & 0.78 \\ 1.6 & 2.8 \\ 2.6 & 2.98 \\ 10 & 3 \\ \infty & 3 \\ \hline \end{array} \]

Assuming ideal op-amps, the circuit represents:
 

Which of the following statements is true about the small signal voltage gain of MOSFET-based single-stage amplifiers?
The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system \( S \). The output is observed to be the continuous-time unit step signal \( u(t) \). Which one of the following statements is true?
Consider a continuous-time signal \[ x(t) = -t^2 \left[ u(t+4) - u(t-4) \right] \] where \( u(t) \) is the continuous-time unit step function. Let \( \delta(t) \) be the continuous-time unit impulse function. The value of \[ \int_{-\infty}^{\infty} x(t) \delta(t+3) \, dt \text{ is:} \]
A 3-phase, 400 V, 4 pole, 50 Hz star-connected induction motor has the following parameters referred to stator: \[ R'_1 = 1 \, \text{ohm}, \, X_s = X'_1 = 2 \, \text{ohm} \] Stator resistance, magnetizing reactance, and core loss of the motor are neglected. The motor is run with constant \( v/f \) control. The output frequency from the drive is closest to:
The open-loop system is stable. The Nyquist plot encircles \( (-1, 0) \) once in the anti-clockwise direction. Find the closed-loop system stability.