# GATE Questions & Answers of Transient and steady state analysis of LTI systems

## What is the Weightage of Transient and steady state analysis of LTI systems in GATE Exam?

Total 23 Questions have been asked from Transient and steady state analysis of LTI systems topic of Control Systems subject in previous GATE papers. Average marks 1.52.

In the circuit shown, the voltage VIN(t) is described by: ${\mathrm V}_\mathrm{IN}\left(t\right)=\left\{\begin{array}{lc}0,&\mathrm{for}\;\mathrm t<0\\15\;\mathrm{Volts},&\mathrm{for}\;\mathrm t\geq0\end{array}\right.$ where t is in second. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is_________.

The switch in the circuit, shown in the figure, was for a long time and is closed at t = 0.

The current i(t) (in ampere) at t = 0.5 seconds is________

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

The number and direction of encirclements around the point -1+0 in the complex plane by the Nyquist plot of $G\left(s\right)=\frac{1-s}{4+2s}$ is

In the feedback system shown below $G\left(S\right)=\frac{1}{\left(s+1\right)\left(s+2\right)\left(s+3\right)}$ .

The positive value of k for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is ________

The asymptotic Bode phase plot of $G\left(S\right)=\frac{k}{\left(s+0.1\right)\left(s+10\right)\left(s+{p}_{1}\right)}$ , with k and p1 both positive, is shown below.

The value of p1 is ________

In the circuit shown, the switch SW is thrown from position A to position B at time t= 0. The energy (in $\mathrm{μJ}$) taken from the 3 V source to charge the 0.1 $\mathrm{\mu }$F capacitor from 0 V to 3 V is

The polar plot of the transfer will be in the

In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of vc(t) (in Volts) at t = 1 sec is _____.

In the circuit shown, the initial voltages across the capacitors C1 and C2 are 1 V and 3 V, respectively. The switch is closed at time t =0. The total energy dissipated (in Joules) in the resistor R until steady state is reached, is _______.

The transfer function of a mass-spring damper system is given by

$G\left(s\right)=\frac{1}{M{s}^{2}+Bs+k}$

The frequency response data for the system are given in the following table.

 ω in rad/s |G(jω)| in dB arg (G(jω)) in deg 0.01 -18.5 -0.2 0.1 -18.5 -1.3 0.2 -18.4 -2.6 1 -16 -16.9 2 -11.4 -89.4 3 -21.5 -151 5 -32.8 -167 10 -45.3 -174.5

The unit step response of the system approaches a steady state value of____.

Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.

The value of fH – fL (in Hz) is ______.

The phase margin (in degrees) of the system $G\left(s\right)=\frac{10}{s\left(s+10\right)}$ is _____.

Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following conclusions is correct?

The phase margin in degrees of $G\left(s\right)=\frac{10}{\left(s+0.1\right)\left(s+1\right)\left(s+10\right)}$ calculated using the asymptotic Bode plot is ________.

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.

If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is_________.

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

For the transfer function $G\left(\mathrm{j\omega }\right)=5+\mathrm{j\omega },$ the corresponding Nyquist plot for positive frequency has the form

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the  stability of the closed loop system in the feedback configuration shown.

Which of the following statements is true?