# Frequency Response Analysis · Control Systems · GATE ECE

Start Practice## Marks 1

GATE ECE 2022

Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2. The complete Nyquist plot of t...

GATE ECE 2016 Set 2

The number and direction of encirclements around the point −1 + j0 in the complex plane by the
Nyquist plot of G(s) =$${{1 - s} \over {4 + 2s}}$$ is

GATE ECE 2016 Set 1

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

GATE ECE 2015 Set 3

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 (in Hz) is ______.
...

GATE ECE 2015 Set 1

The popular plot of the transfer function
G(s)=$${{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}}$$ for $$0 \le \omega < \infty $$ wil...

GATE ECE 2014 Set 4

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

GATE ECE 2014 Set 1

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?
...

GATE ECE 2013

The Bode plot of a transfer function G (s) is shown in the figure below.
The gain (20 log $$\left| {G(s)} \right|$$ ) is 32 dB and -8dB at 1rad/s ...

GATE ECE 2012

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

GATE ECE 2011

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

GATE ECE 2010

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

GATE ECE 2010

A system with the transfer function
$${{Y(s)} \over {X(s)}} = {s \over {s + p}},$$ has an output
y(t)=$$\cos \left( {2t - {\pi \over 3}} \right),$$ ...

GATE ECE 2007

If the closed-loop transfer function of a control system is given as
T(s)=$${{s - 5} \over {(s + 2)(s + 3)}},$$ then it is

GATE ECE 2006

The open-loop transfer function of a unity-gain feedback control system is given
by
$$G(s) = {K \over {(s + 1)(s + 2)}},$$ the gain margin of the syst...

GATE ECE 2006

In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be
...

GATE ECE 2005

Which one of the following polar diagrams corresponds to a lag network?

GATE ECE 2003

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 pole, the closed loop system is
...

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 2002

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 2001

The Nyquist plot for the open-loop transfer function G(s) of a unity negative
feedback system is shown in figure. if G(s) has no pole in the right hal...

GATE ECE 1999

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 1998

In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over frequency is $$ - 125^\circ $$. The ...

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. The gain margin of the system i...

GATE ECE 1995

Non - minimum phase transfer function is defined as the transfer function

GATE ECE 1994

The 3-dB bandwidth of a typical second- order system with the transfer function
$${{C\left( s \right)} \over {R(s)}} = {{\omega _n^2} \over {{s^2} + 2...

GATE ECE 1994

The open loop frequency response of a system at two particular frequencies are given by: 1.2 $$\angle - 180^\circ $$ and 1.0 $$\angle - 190^\circ $...

## Marks 2

GATE ECE 2018

The figure below shows the Bode magnitude and phase plots of a stable transfer function
$$G(s) = {{{n_0}} \over {{s^3} + {d_2}{s^2} + {d_1}s + {d_0}}}...

GATE ECE 2018

For a unity feedback control system with the forward path transfer function
$$G(s) = {K \over {s\left( {s + 2} \right)}}$$
The peak resonant magnitude...

GATE ECE 2017 Set 1

The Nyquist plot of the transfer function
$$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$
does not encircle the point (-...

GATE ECE 2017 Set 2

A unity feedback control system is characterized by the open loop transfer function
$$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^...

GATE ECE 2016 Set 2

The asymptotic Bode phase plot of
$${\rm{G(s) = }}{k \over {\left( {s + 0.1} \right)\left( {s + 10} \right)\left( {s + {p_1}} \right)}},$$
with k an...

GATE ECE 2016 Set 2

In the feedback system shown below
$${\rm{G(s) = }}{1 \over {\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}$$
The positive ...

GATE ECE 2015 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 frequency response data for the sy...

GATE ECE 2014 Set 2

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 config...

GATE ECE 2014 Set 1

The phase margin in degrees of G(s)=$${{10} \over {\left( {s + 0.1} \right)\left( {s + 1} \right)\left( {s + 10} \right)}},$$
using the asymptotic Bo...

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 placed in a unity negative feed...

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 placed in a unity negative feed...

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 closed loop system in the feedba...

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 closed loop system in the feedba...

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 the unit step function.
The fre...

GATE ECE 2008

The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {\sqrt 3 }}$$ at 5 $$\sqrt 2 $$...

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 the unit step function.
The ou...

GATE ECE 2007

The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this bode plot is
...

GATE ECE 2006

Consider two transfer functions
$${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$
Th...

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 margin of the system in dB is ...

GATE ECE 2006

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$
The value of 'a', so that the s...

GATE ECE 2006

Consider a unity-gain feedback control system whose open-loop transfer function is
G(s)=$${{as + 1} \over {{s^2}}}$$.
With the value of "a" set for p...

GATE ECE 2005

The open loop transfer function of a unity feedback system is given by
G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$
The gain and phase...

GATE ECE 2005

The polar diagram of a conditionally stable system for open loop gain K=1 is
shown in figure. The open loop transfer function of the system is known t...

GATE ECE 2005

The open loop transfer function of a unity feedback system is given by
g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$
Based on the above ...

GATE ECE 2004

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 response at 20 Hz is

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 gain margin and the phase margin of a feedback system with
G(s)H(s)=$${s \over {{{\left( {s + 100} \right)}^3}}}$$ are

GATE ECE 2002

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

GATE ECE 2001

The open-loop DC gain of a unity negative feedback system with closed-loop
transfer function $${{s + 4} \over {{s^2} + 7s + 13}}$$ is

GATE ECE 1992

Bode plot of a stable system is shown in fig. The transfer function of the system is
...

GATE ECE 1991

The open-loop transfer function of a feedback control system is
G(s)=$${1 \over {{{\left( {s + 1} \right)}^3}}}$$The gain margin of the system is

GATE ECE 1989

From the Nicholas chart, one can determine the following quantities pertaining to a closed loop system:

GATE ECE 1987

The popular plot of G(s)=$${{10} \over {s{{\left( {s + 1} \right)}^2}}},$$ intercepts real axix at $$\omega = {\omega _0}$$ Then, the real part and $...

GATE ECE 1987

A system has fourteen poles and two zeroes. Its high frequency asymptote, in its magnitude plot, has having a slope of

## Marks 5

GATE ECE 2002

The Nyquist plot of an all-pole second order open-loop system is shown in Figure.
Obtain the transfer function of the system.
...

GATE ECE 1999

The asymptotic bode plot of the minimum phase open-loop transfer function G(s)H(s) is as shown in the figure. Obtain the transfer function G(s)H(s)
...

GATE ECE 1999

Consider a feedback system with the open loop transfer function given by
$$G(s)H(s) = {K \over {s\left( {2s + 1} \right)}}.$$
Examine the stability of...

GATE ECE 1998

The loop transfer function of a single loop control system is given by
$$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$
Using Ny...

## Marks 8

GATE ECE 1992

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

GATE ECE 1987

The magnitude plot of the open loop transfer function G(s), of a certain system is given in fig,
(a) Determine G(s), if it is known that the system i...

## Marks 10

GATE ECE 1989

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