# Polar Nyquist and Bode Plot ยท Control Systems ยท GATE EE

Start Practice## Marks 1

GATE EE 2022

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, i...

GATE EE 2022

An LTI system is shown in the figure where $$G(s) = {{100} \over {{s^2} + 0.1s + 100}}$$. The steady state output of the system, to the input r(t), is...

GATE EE 2022

The open loop transfer function of a unity gain negative feedback system is given as
$$G(s) = {1 \over {s(s + 1)}}$$
The Nyquist contour in the s-plan...

GATE EE 2017 Set 1

The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$
Let the output of...

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 $${30^0}$$ is ____________. (...

GATE EE 2016 Set 1

The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady state $$y(t)$$ is $$Acos$$$$\...

GATE EE 2016 Set 1

The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}}}\,\,$$ in $$rad/s$$ is

GATE EE 2015 Set 2

Nyquist plots of two functions $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ are shown in figure.
Nyquist plot of the product of $${G_1}\...

GATE EE 2015 Set 1

A Bode magnitude plot for the transfer function $$๐บ(๐ )$$ of a plant is shown in the figure. Which one of the following transfer functions best descr...

GATE EE 2013

The Bode plot of a transfer function $$G(s)$$ is shown in the figure below.
The gain is $$\left( {20\log \left| {G\left( s \right)} \right|} \right...

GATE EE 2012

A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3...

GATE EE 2011

The frequency response of a linear system $$G\left( {j\omega } \right)$$ is provided in the tubular form below.
The gain margin and phase margin of t...

GATE EE 2011

An open loop system represented by the transfer function $$G\left( s \right) = {{\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 3} \...

GATE EE 2009

The polar plot of an open loop stable system is shown below. The closed loop systems is
...

GATE EE 2005

A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s ...

GATE EE 2005

The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( {s + 1} \right)} \over {{s^2}}}...

GATE EE 2004

The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1,j0)$$ in the $$G(s) H(s)$$ pla...

GATE EE 2001

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 one zero is shown in Fig. Its tr...

GATE EE 1996

The closed - loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}} = {1 \over {\left( {1 + s} \righ...

GATE EE 1992

A unity feedback system has the open loop transfer function $$G\left( s \right) = {1 \over {\left( {s - 1} \right)\left( {s + 2} \right)\left( {s + 3}...

GATE EE 1991

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.
...

## Marks 2

GATE EE 2016 Set 1

Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ is in $$rad/s$$)
Which one of the following transfer functions is best rep...

GATE EE 2016 Set 1

Loop transfer function of a feedback system is $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3} \right)}}.$$
Take the Nyquis...

GATE EE 2014 Set 3

The magnitude Bode plot of a network is shown in the figure
The maximum phase angle $${\phi _m}$$ and the corresponding gain $${G_m}$$ respectively ...

GATE EE 2014 Set 2

For the transfer function $$G\left( s \right) = {{5\left( {s + 4} \right)} \over {s\left( {s + 0.25} \right)\left( {{s^2} + 4s + 25} \right)}}.$$ The ...

GATE EE 2014 Set 1

The Bode magnitude plot of the transfer function $$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \right)} \over {s\left( {1 + {s \ov...

GATE EE 2010

The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plotted in the complex $$\,G\left( ...

GATE EE 2009

The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = \left( {{e^{ - 0.1s}}} \right)/s.$$
The gain margin of t...

GATE EE 2009

The asymptotic approximation of the log magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function i...

GATE EE 2008

The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure:
This transfer function has...

GATE EE 2007

If $$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$ and $$y = {\rm I}mG\left( {j\omega } \right)$$ then for $$\omega \to {0^ + },\,...

GATE EE 2006

The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {...

GATE EE 2006

Consider the following Nyquist plots of loop transfer functions over $$\omega = 0$$ to $$\omega = \infty .$$ Which of these plots represents a stabl...

GATE EE 2005

In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e^{ - 0.25s}}} \over s}$$ passe...

GATE EE 2005

If the compensated system shown in the figure has a phase margin of $${60^ \circ }$$ at the crossover frequency of $$1 rad/sec,$$ the value of the gai...

GATE EE 2004

The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s^2}}}.$$. The value of $$โaโ$$...

GATE EE 2004

In the system shown in figure, the input $$x(t)$$ $$=$$ $$sin$$ $$t.$$ In the steady-state, the response $$y(t)$$ will be
...

GATE EE 2003

The asymptotic Bode plot of the transfer function $${K \over {1 + {s \over a}}}$$. The error in phase angle and $$dB$$ gain at a frequency of $$\omega...

GATE EE 1999

The function corresponding to the Bode plot of Figure, is
...

GATE EE 1997

A unity feedback system with the open loop transfer function $$G\left( s \right) = {1 \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}$$ has gai...

GATE EE 1991

An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + ...

## Marks 5

GATE EE 2001

A unity feedback system has an open-loop transfer function of $$G\left( s \right) = {{10000} \over {s{{\left( {s + 10} \right)}^2}}}$$
(a) Determine t...

GATE EE 2000

Open-loop transfer function of a unity - feedback system is
$$$G\left( s \right) = {G_1}\left( s \right).{e^{ - s{\tau _D}}} = {{{e^{ - s{\tau _D}}}}...

GATE EE 1998

The asymptotic magnitude Body plot of a system is given in Figure. Find the transfer function of the system analytically. It is known that the system ...