GATE ECE

Frequency Response Analysis

Control Systems

(Past Years Questions)

Marks 1

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The number and direction of encirclements around the point −1 + j0 in the complex plane by the Nyquist plot of G(s) =$${...
GATE ECE 2016 Set 2
A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function
GATE ECE 2016 Set 1
The phase margin (in degrees) of the system G(s)=$${{10} \over {\left( {s + 10} \right)}}$$ is ___________.
GATE ECE 2015 Set 3
Consider the Bode plot shown in the figure. Assume that all the poles and zeroes are real-valued. The value of fH - fL ...
GATE ECE 2015 Set 3
The popular plot of the transfer function G(s)=$${{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}}$$ for $$0 ...
GATE ECE 2015 Set 1
In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-po...
GATE ECE 2014 Set 4
Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following con...
GATE ECE 2014 Set 1
The Bode plot of a transfer function G (s) is shown in the figure below. The gain (20 log $$\left| {G(s)} \right|$$ ...
GATE ECE 2013
A system with transfer function g(s) = $${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \rig...
GATE ECE 2012
For the transfer function G$$\left( {j\omega } \right) = 5 + j\omega ,$$ the corresponding Nyquist plot for positive f...
GATE ECE 2011
A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}},$$ has an output y(t)=$$\cos \left( {2t...
GATE ECE 2010
For the asymptotic Bode magnitude plot shown below, the system transfer function can be ...
GATE ECE 2010
If the closed-loop transfer function of a control system is given as T(s)=$${{s - 5} \over {(s + 2)(s + 3)}},$$ then it ...
GATE ECE 2007
In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be ...
GATE ECE 2006
The open-loop transfer function of a unity-gain feedback control system is given by $$G(s) = {K \over {(s + 1)(s + 2)}},...
GATE ECE 2006
Which one of the following polar diagrams corresponds to a lag network?
GATE ECE 2005
Figure shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a system. If G(s)H(s) has one right hand p...
GATE ECE 2003
The gain margin for the system with open-loop transfer function G(s)H(s)=$${{2(1 + s)} \over {{s^2}}}$$ is
GATE ECE 2003
The phase margin of a system with the open-loop transfer function G(s)H(s)=$${{(1 - s)} \over {(1 + s)(2 + s)}}$$ is?
GATE ECE 2002
The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure. if G(s...
GATE ECE 2001
The gain margin of a system having the loop transfer function G(s)H(s) =$${{\sqrt 2 } \over {s(s + 1)}}$$ is
GATE ECE 1999
The phase margin (in degrees) of a system having the loop transfer function is $$G(s)H(s) = {{2\sqrt 3 } \over {s(s + 1)...
GATE ECE 1999
In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over freque...
GATE ECE 1998
The Nyquist plot of a loop transfer function G$$(j\omega )$$ H$$(j\omega )$$, of a system encloses the (-1, j0) point. T...
GATE ECE 1998
Non - minimum phase transfer function is defined as the transfer function
GATE ECE 1995
The 3-dB bandwidth of a typical second- order system with the transfer function $${{C\left( s \right)} \over {R(s)}} = {...
GATE ECE 1994
The open loop frequency response of a system at two particular frequencies are given by: 1.2 $$\angle - 180^\circ $$ a...
GATE ECE 1994

Marks 2

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The figure below shows the Bode magnitude and phase plots of a stable transfer function $$G(s) = {{{n_0}} \over {{s^3} +...
GATE ECE 2018
For a unity feedback control system with the forward path transfer function $$G(s) = {K \over {s\left( {s + 2} \right)}}...
GATE ECE 2018
A unity feedback control system is characterized by the open loop transfer function $$G(s) = {{10k\left( {s + 2} \right...
GATE ECE 2017 Set 2
The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ ...
GATE ECE 2017 Set 1
In the feedback system shown below $${\rm{G(s) = }}{1 \over {\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3...
GATE ECE 2016 Set 2
The asymptotic Bode phase plot of $${\rm{G(s) = }}{k \over {\left( {s + 0.1} \right)\left( {s + 10} \right)\left( {s +...
GATE ECE 2016 Set 2
The transfer function of a mass-spring damper system is given by $${\rm{G(s) = }}{1 \over {M{s^2} + Bs + K}}$$ The freq...
GATE ECE 2015 Set 2
The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. If the system is connected in a ...
GATE ECE 2014 Set 2
The phase margin in degrees of G(s)=$${{10} \over {\left( {s + 0.1} \right)\left( {s + 1} \right)\left( {s + 10} \right)...
GATE ECE 2014 Set 1
The input-output transfer function of a plant is h(s)=$${{100} \over {s{{\left( {s + 10} \right)}^2}}}$$. The plant is p...
GATE ECE 2011
The input-output transfer function of a plant is h(s)=$${{100} \over {s{{\left( {s + 10} \right)}^2}}}$$. The plant is p...
GATE ECE 2011
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the cl...
GATE ECE 2009
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the cl...
GATE ECE 2009
The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {...
GATE ECE 2008
The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes ...
GATE ECE 2008
The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes ...
GATE ECE 2008
The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this...
GATE ECE 2007
Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s ...
GATE ECE 2006
The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain ...
GATE ECE 2006
Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ T...
GATE ECE 2006
Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$. W...
GATE ECE 2006
The polar diagram of a conditionally stable system for open loop gain K=1 is shown in figure. The open loop transfer fu...
GATE ECE 2005
The open loop transfer function of a unity feedback system is given by G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \r...
GATE ECE 2005
The open loop transfer function of a unity feedback system is given by g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \ri...
GATE ECE 2005
Consider the Bode magnitude plot shown in figure. The transfer function H(s) is ...
GATE ECE 2004
A system has poles at 0.01 Hz, 1Hz and 80 Hz; zeroes at 5hz, 100 Hz and 200 Hz. The approximate phase of the system resp...
GATE ECE 2004
The gain margin and the phase margin of a feedback system with G(s)H(s)=$${s \over {{{\left( {s + 100} \right)}^3}}}$$ ...
GATE ECE 2003
The approximate Bode magnitude plot of a minimum-phase system is shown in figure. The transfer function of the system is...
GATE ECE 2003
The system with the open loop transfer function G(s)H(s)=$${1 \over {s\left( {{s^2} + s + 1} \right)}},$$ has a gain ma...
GATE ECE 2002
The open-loop DC gain of a unity negative feedback system with closed-loop transfer function $${{s + 4} \over {{s^2} + 7...
GATE ECE 2001
Bode plot of a stable system is shown in fig. The transfer function of the system is ...
GATE ECE 1992
The open-loop transfer function of a feedback control system is G(s)=$${1 \over {{{\left( {s + 1} \right)}^3}}}$$The g...
GATE ECE 1991
From the Nicholas chart, one can determine the following quantities pertaining to a closed loop system:
GATE ECE 1989
A system has fourteen poles and two zeroes. Its high frequency asymptote, in its magnitude plot, has having a slope of
GATE ECE 1987
The popular plot of G(s)=$${{10} \over {s{{\left( {s + 1} \right)}^2}}},$$ intercepts real axix at $$\omega = {\omega _...
GATE ECE 1987

Marks 5

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The Nyquist plot of an all-pole second order open-loop system is shown in Figure. Obtain the transfer function of the ...
GATE ECE 2002
The asymptotic bode plot of the minimum phase open-loop transfer function G(s)H(s) is as shown in the figure. Obtain the...
GATE ECE 1999
Consider a feedback system with the open loop transfer function given by $$G(s)H(s) = {K \over {s\left( {2s + 1} \right)...
GATE ECE 1999
The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \r...
GATE ECE 1998

Marks 8

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A unity feedback system has open-loop transfer function $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right...
GATE ECE 1992
The magnitude plot of the open loop transfer function G(s), of a certain system is given in fig, (a) Determine G(s), if...
GATE ECE 1987

Marks 10

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Nyquist plot consider a feed back system where the OLTF is: $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \r...
GATE ECE 1989

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