# Time Response Analysis · Control Systems · GATE ECE

Start Practice## Marks 1

GATE ECE 2022

Two linear time-invariant systems with transfer functions
$${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = {{10} \over {{s^2} + s\sqrt {10...

GATE ECE 2022

The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r...

GATE ECE 2017 Set 1

The open loop transfer function $$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\mathrm p\left(\mathrm s\;+\;2\ri...

GATE ECE 2016 Set 2

The response of the system
$$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$
to the unit step input u(t) is y(t).
The v...

GATE ECE 2016 Set 3

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as $$G\left(s\right)\;=\;\frac2{s\left(s\;+\;...

GATE ECE 2015 Set 2

A unity negative feedback system has an open–loop transfer function $$G\left(s\right)=\frac K{s\left(s+1\right)}$$.The
gain K for the system to have a...

GATE ECE 2014 Set 4

For the second order closed-loop system shown in the figure, the natural frequency (in rad/s)
is
...

GATE ECE 2014 Set 3

The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer
fu...

GATE ECE 2014 Set 2

The natural frequency of an undamped second-order system is 40 rad/s. If the system is
damped with a damping ratio 0.3, the damped natural frequency i...

GATE ECE 2011

The differential equation
$$$100\frac{\mathrm d^2\mathrm y}{\mathrm{dt}^2}-20\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm y=\mathrm x\left(\mathrm t\right)...

GATE ECE 2008

Step responses of a set of three second-order underdamped systems all have the
same percentage overshoot. Which of the following diagrams represents t...

GATE ECE 2007

If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final value is:

GATE ECE 2002

Consider a system with the transfer function
$$$G\left(s\right)=\frac{s+6}{Ks^2+s+6}$$$
Its damping ratio
will be 0.5 when the value of K is

GATE ECE 2001

If the characteristic equation of a closed-loop system is s2 + 2s + 2 =0, then the
system is

GATE ECE 1999

For a second-order system with the closed-loop transfer function
$$$T\left(s\right)=\frac9{s^2+4s+9}$$$ the settling time for 2% band in seconds is

GATE ECE 1998

Consider a unity feedback control system with open-loop transfer function
$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)}$$ .
The steady state er...

GATE ECE 1998

If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\left(t\right),\;\left\{where\;F\l...

GATE ECE 1998

Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+...

GATE ECE 1995

For a second order system, damping ratio $$\left(\xi\right)$$ , is 0 < $$\xi$$ < 1 ,then the roots of the characteristic polynomial are

GATE ECE 1995

The final value theorem is used to find the

GATE ECE 1995

If $$L\left(f\left(t\right)\right)=\frac{2\left(s+1\right)}{s^2+2s+5}$$ then f(0+) and f($$\infty$$) are given by
[Note: 'L' stands for 'Laplace Trans...

GATE ECE 1995

The step error coefficient of a system G(s)=$$\frac1{\left(s+6\right)\left(s+1\right)}$$ with unity feedback is

GATE ECE 1994

The poles of a continuous time oscillator are ___________.

## Marks 2

GATE ECE 2016 Set 2

In the feedback system shown below
$$$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$
The step response of the closed-loop system should have minimum settl...

GATE ECE 2016 Set 1

The open-loop transfer function of a unity-feedback control system is
$$$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$
For the peak overshoot of the close...

GATE ECE 2015 Set 2

The output of a standard second–order system for a unit step input is given as $$$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}\cos\left(\sqrt3t\;-\;\frac{\m...

GATE ECE 2015 Set 1

The damping ratio of a series RLC circuit can be expressed as

GATE ECE 2014 Set 3

The steady state error of the system shown in the figure for a unit step input is _______.
...

GATE ECE 2014 Set 1

For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of the step
response is required t...

GATE ECE 2013

The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, when
connected in fee...

GATE ECE 2009

The unit step response of an under-damped second order system has steady state value of -2.
Which one of the following transfer function has these pro...

GATE ECE 2008

A linear, time-invariant, causal continuous time system has a rational transfer
function with simple poles at s=-2 and s=-4, and one simple zero at s=...

GATE ECE 2008

Group I lists a set of four transfer functions. Group II gives a list of possible step
responses y(t). Match the step responses with the corresponding...

GATE ECE 2007

The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$ .The step response of the s...

GATE ECE 2007

The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order
approximation of T (s) using d...

GATE ECE 2006

The unit impulse response of a system is:
$$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$
For this system, the steady-state value of the output for unit st...

GATE ECE 2006

The unit-step response of a system starting from rest is given by
$$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm ...

GATE ECE 2005

A ramp input applied to an unity feedback system results in 5% steady state
error. The type number and zero frequency gain of the system are respectiv...

GATE ECE 2005

In the derivation of expression for peak percent overshoot,$$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\times100\%$$$ .Which one of the ...

GATE ECE 2004

A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$
is excited with 10u(t).
The time at which the output reaches 99% ...

GATE ECE 2004

A system described by the following differential equation
$$$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$$ is initially at rest. For input x(...

GATE ECE 2003

A second-order system has the transfer function $$\frac{C\left(s\right)}{R\left(s\right)}=\frac4{s^2+4s+4}$$. With r(t) as the unit-step function, the...

GATE ECE 2002

The transfer function of a system is $$G\left(s\right)\;=\;\frac{100}{\left(s\;+\;1\right)\left(s\;+\;100\right)}$$.For a unit step input
to the syste...

GATE ECE 1999

If the closed-loop transfer function T(s) of a unity negative feedback system is
given by $$$T\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1s^{n-1}+.....+...

GATE ECE 1998

The unit impulse response of a linear time invariant system is the unit step
function u(t). For t>0, the response of the system ot an excitation e-...

GATE ECE 1994

The response of an LCR circuit to a step input is
(a) Over damped
(b) Critically damped
(c) Oscillatory
If the transfer function has
(1) poles on the...

GATE ECE 1994

Match the following with List-1 with List-2
List-1
(a) Very low response at very high frequencies.
(b) Overshoot
(c) Synchro-control transformer outp...

GATE ECE 1991

A unity feedback control system has the open loop transfer function
$$G\left(s\right)\;=\;\frac{4\left(1\;+\;2s\right)}{s^2\left(s\;+\;2\right)}$$ .I...

GATE ECE 1991

A second order system has a transfer function given by $$\mathrm G\left(\mathrm s\right)\;=\;\frac{25}{\mathrm s^2\;+\;8\mathrm s\;+\;25}$$ .If the sy...

GATE ECE 1990

The steady state error of a stable 'type 0' unity feedback system for a unit step function is

GATE ECE 1988

A critically damped, continuous-time, second order system, when sampled, will have ( in Z domain)

## Marks 5

GATE ECE 2000

The block diagram of a feedback system is shown in Figure.
(a) Find the closed loop transfer function.
(b) Find the minimum value of G for which the...

GATE ECE 1997

Following fig. shows the block diagram representation of control system. The system in
block A has an impulse response
h(t ) = e−t u(t ).
The system i...

## Marks 8

GATE ECE 2000

For the linear, time-invariant system whose block diagram is shown in Fig.
with input x(t) and output y(t),
(a) Find the transfer function.
(b) For ...

GATE ECE 1992

Block diagram model of a position control system is shown in figure.
(a) In absence of derivative feedback (Kt=0) , determine damping ratio of the
sy...

## Marks 10

GATE ECE 1998

Consider the system shown in Fig. Determine the value of 'a' such that the
damping ratio is 0.5. Also obtain the values of the rise time 'tr' and ma...