GATE EE

Polar Nyquist and Bode Plot

Control Systems

(Past Years Questions)

Marks 1

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The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \ove...
GATE EE 2017 Set 1
Consider the unity feedback control system shown. The value of $$K$$ that results in a phase margin of the system to be ...
GATE EE 2017 Set 1
The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady...
GATE EE 2016 Set 1
The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}...
GATE EE 2016 Set 1
Nyquist plots of two functions $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ are shown in figure. Nyquist p...
GATE EE 2015 Set 2
A Bode magnitude plot for the transfer function $$𝐺(𝑠)$$ of a plant is shown in the figure. Which one of the following...
GATE EE 2015 Set 1
The Bode plot of a transfer function $$G(s)$$ is shown in the figure below. The gain is $$\left( {20\log \left| {G\le...
GATE EE 2013
A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left...
GATE EE 2012
The frequency response of a linear system $$G\left( {j\omega } \right)$$ is provided in the tubular form below. The ga...
GATE EE 2011
An open loop system represented by the transfer function $$G\left( s \right) = {{\left( {s - 1} \right)} \over {\left( {...
GATE EE 2011
The polar plot of an open loop stable system is shown below. The closed loop systems is ...
GATE EE 2009
A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\l...
GATE EE 2005
The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( {...
GATE EE 2005
The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1,...
GATE EE 2004
The polar plot of a type-$$1, 3$$-pole, open-loop system is shown in Fig. below. The closed loop system is ...
GATE EE 2001
The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and on...
GATE EE 2001
The closed - loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}} = ...
GATE EE 1996
A unity feedback system has the open loop transfer function $$G\left( s \right) = {1 \over {\left( {s - 1} \right)\left(...
GATE EE 1992
The system having the Bode magnitude plot shown in Fig. below has the transfer function ...
GATE EE 1991
Which of the following is the transfer function of a system having the Nyquist plot shown in Fig. below. ...
GATE EE 1991

Marks 2

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Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ is in $$rad/s$$) Which one of the following ...
GATE EE 2016 Set 1
Loop transfer function of a feedback system is $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3...
GATE EE 2016 Set 1
The magnitude Bode plot of a network is shown in the figure The maximum phase angle $${\phi _m}$$ and the correspondin...
GATE EE 2014 Set 3
For the transfer function $$G\left( s \right) = {{5\left( {s + 4} \right)} \over {s\left( {s + 0.25} \right)\left( {{s^2...
GATE EE 2014 Set 2
The Bode magnitude plot of the transfer function $$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \righ...
GATE EE 2014 Set 1
The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plott...
GATE EE 2010
The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = \left( {{e^{ - 0.1s}}} \rig...
GATE EE 2009
The asymptotic approximation of the log magnitude vs frequency plot of a system containing only real poles and zeros is ...
GATE EE 2009
The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure: This transfer function...
GATE EE 2008
If $$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$ and $$y = {\rm I}mG\left( {j\omega } \right)$$ the...
GATE EE 2007
The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 +...
GATE EE 2006
Consider the following Nyquist plots of loop transfer functions over $$\omega = 0$$ to $$\omega = \infty .$$ Which of ...
GATE EE 2006
In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e...
GATE EE 2005
If the compensated system shown in the figure has a phase margin of $${60^ \circ }$$ at the crossover frequency of $$1 r...
GATE EE 2005
In the system shown in figure, the input $$x(t)$$ $$=$$ $$sin$$ $$t.$$ In the steady-state, the response $$y(t)$$ will ...
GATE EE 2004
The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{...
GATE EE 2004
The asymptotic Bode plot of the transfer function $${K \over {1 + {s \over a}}}$$. The error in phase angle and $$dB$$ g...
GATE EE 2003
The function corresponding to the Bode plot of Figure, is ...
GATE EE 1999
A unity feedback system with the open loop transfer function $$G\left( s \right) = {1 \over {s\left( {s + 2} \right)\lef...
GATE EE 1997
An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {...
GATE EE 1991

Marks 5

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A unity feedback system has an open-loop transfer function of $$G\left( s \right) = {{10000} \over {s{{\left( {s + 10} \...
GATE EE 2001
Open-loop transfer function of a unity - feedback system is $$$G\left( s \right) = {G_1}\left( s \right).{e^{ - s{\tau ...
GATE EE 2000
The asymptotic magnitude Body plot of a system is given in Figure. Find the transfer function of the system analytically...
GATE EE 1998

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