Frequency Response Analysis · Control Systems · GATE ECE
Marks 1
1
The Nyquist plot of a system is given in the figure below. Let $\omega_{\mathrm{P}}, \omega_Q, \omega_R$, and $\omega_{\mathrm{S}}$ be the positive frequencies at the points $P, Q, R$, and $S$, respectively. Which one of the following statements is TRUE?
GATE ECE 2025
2
In the context of Bode magnitude plots, 40 dB/decade is the same as ______.
GATE ECE 2024
3
The open loop transfer function of a unity negative feedback system is $$G(s) = {k \over {s(1 + s{T_1})(1 + s{T_2})}}$$, where $$k,T_1$$ and $$T_2$$ are positive constants. The phase cross-over frequency, in rad/s, is
GATE ECE 2023
4
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 the transfer function G(s) is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ___________.
GATE ECE 2022
5
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 2
6
A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer
function
GATE ECE 2016 Set 1
7
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 3
8
The phase margin (in degrees) of the system
G(s)=$${{10} \over {\left( {s + 10} \right)}}$$ is ___________.
GATE ECE 2015 Set 3
9
The popular plot of the transfer function
G(s)=$${{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}}$$ for $$0 \le \omega < \infty $$ will be in the
GATE ECE 2015 Set 1
10
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 2014 Set 1
11
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 4
12
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 and 10rad/s respectively. The phase is negative for all $$\omega .$$ Then G(s) is
The gain (20 log $$\left| {G(s)} \right|$$ ) is 32 dB and -8dB at 1rad/s and 10rad/s respectively. The phase is negative for all $$\omega .$$ Then G(s) is
GATE ECE 2013
13
A system with transfer function
g(s) = $${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}},$$ is excited by $$\sin \left( {\omega t} \right).$$ The steady-state output of the system is zero at
GATE ECE 2012
14
For the transfer function G$$\left( {j\omega } \right) = 5 + j\omega ,$$ the corresponding Nyquist plot for
positive frequency has the form
GATE ECE 2011
15
A system with the transfer function
$${{Y(s)} \over {X(s)}} = {s \over {s + p}},$$ has an output
y(t)=$$\cos \left( {2t - {\pi \over 3}} \right),$$ for input signal
x(t)=$$p\cos \left( {2t - {\pi \over 2}} \right).$$ Then the system parameter 'p' is
GATE ECE 2010
16
For the asymptotic Bode magnitude plot shown below, the system transfer function
can be
GATE ECE 2010
17
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 2007
18
In the system shown below, x(t)=(sin t). In steady-state, the response y(t) will be
GATE ECE 2006
19
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 system in dB is given by
GATE ECE 2006
20
Which one of the following polar diagrams corresponds to a lag network?
GATE ECE 2005
21
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
22
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
23
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
24
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 half of s-plane,
the number of roots of the system characteristic equation in the right half
of s-plane is
GATE ECE 2001
25
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
26
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
27
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 phase margin of the system is
GATE ECE 1998
28
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 is
GATE ECE 1998
29
Non - minimum phase transfer function is defined as the transfer function
GATE ECE 1995
30
The open loop frequency response of a system at two particular frequencies are given by: 1.2 $$\angle - 180^\circ $$ and 1.0 $$\angle - 190^\circ $$. The closed loop unity feedback control system is then
GATE ECE 1994
31
The 3-dB bandwidth of a typical second- order system with the transfer function
$${{C\left( s \right)} \over {R(s)}} = {{\omega _n^2} \over {{s^2} + 2\xi {\omega _n}s + \omega _n^2}}$$, is given by
GATE ECE 1994
Marks 2
1
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $$(s) = {{k{{(s + z)}^a}} \over {{s^b}{{(s + p)}^c}}}$$, where $$k,z,p,z,b$$ and $$c$$ are positive constants. The value of $$(a + b + c)$$ is ___________ (rounded off to the nearest integer)
GATE ECE 2023
2
A system with transfer function $G(s)=\frac{1}{(s+1)(s+a)}, a>0$ is subjected to input $5 \cos 3 t$. The steady state output of the system is $\frac{1}{\sqrt{10}} \cos (3 t-1.892)$. The value of $a$ is
GATE ECE 2020
3
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 Mr of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.
$$G(s) = {K \over {s\left( {s + 2} \right)}}$$
The peak resonant magnitude Mr of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.
GATE ECE 2018
4
The figure below shows the Bode magnitude and phase plots of a stable transfer function
$$G(s) = {{{n_0}} \over {{s^3} + {d_2}{s^2} + {d_1}s + {d_0}}}$$.
Consider the negative unity feedback configuration with gain k in the feedforward path. The closed loop is stable for k < k0. The maximum value of k0 is ______.
$$G(s) = {{{n_0}} \over {{s^3} + {d_2}{s^2} + {d_1}s + {d_0}}}$$.
Consider the negative unity feedback configuration with gain k in the feedforward path. The closed loop is stable for k < k0. The maximum value of k0 is ______.
GATE ECE 2018
5
A unity feedback control system is characterized by the open loop transfer function
$$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^2} + 10} \right)}}$$
The Nyquist path and the corresponding Nyquist plot of g(s) are shown in the figures below.
If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is
If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is
GATE ECE 2017 Set 2
6
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 (-1+j0) for K = 10 but does encircle the point (-1+j0) for K = 100. Then the closed loop system (having unity gain feedback) is
GATE ECE 2017 Set 1
7
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 and p1 both positive, is shown below.
The value of p1 is ________
The value of p1 is ________GATE ECE 2016 Set 2
8
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 value of 𝑘 for which the gain margin of the loop is exactly 0 dB and the phase margin
of the loop is exactly zero degree is ____
The positive value of 𝑘 for which the gain margin of the loop is exactly 0 dB and the phase margin
of the loop is exactly zero degree is ____GATE ECE 2016 Set 2
9
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 system are given in the following table.
The unit step response of the system approaches a steady state value of ______.
The unit step response of the system approaches a steady state value of ______.
GATE ECE 2015 Set 2
10
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 Bode plot is ______
GATE ECE 2014 Set 1
11
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 configuration, the steady state error of the closed loop system, to a unit ramp input, is
GATE ECE 2014 Set 2
12
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 feedback configuration as shown in the figure below.
The signal flow graph that DOES NOT model the plant transfer function H(s) is
The signal flow graph that DOES NOT model the plant transfer function H(s) is
GATE ECE 2011
13
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 feedback configuration as shown in the figure below.
The gain margin of the system under closed loop unity negative feedback is
The gain margin of the system under closed loop unity negative feedback isGATE ECE 2011
14
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 feedback configuration shown.
Which of the foloowing statements is true?
Which of the foloowing statements is true?
GATE ECE 2009
15
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 feedback configuration shown.
The gain and phase margins of G(s) for closed loop stability are
The gain and phase margins of G(s) for closed loop stability are GATE ECE 2009
16
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 output of this system to the sinusoidal input x(t) = 2cos(t) for all time 't' is
GATE ECE 2008
17
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 frequency response H(ω) of the system in terms of angular frequency 'ω' is given by h( ω)
GATE ECE 2008
18
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 $$\sqrt 2 $$ rad/sec. The transfer function of the system is
GATE ECE 2008
19
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 2007
20
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 phase-margin of $$\pi $$/4, the value of unit-impulse response of the open-loop system at t = 1 second is equal to
GATE ECE 2006
21
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 equal to
GATE ECE 2006
22
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 system has a phase-margin equal to $$\pi $$/4 is approximately equal to
GATE ECE 2006
23
Consider two transfer functions
$${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$
The 3-dB bandwidths of their frequency responses are, respectively
GATE ECE 2006
24
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 crossover frequencies in rad/sec are, respectively
GATE ECE 2005
25
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 to be
stable. The closed loop system is stable for
GATE ECE 2005
26
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 results, the gain and phase margins of the system will be
GATE ECE 2005
27
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 2004
28
Consider the Bode magnitude plot shown in figure. The transfer function H(s) is
GATE ECE 2004
29
The approximate Bode magnitude plot of a minimum-phase system is shown in
figure. The transfer function of the system is
GATE ECE 2003
30
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 2003
31
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 2002
32
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 2001
33
Bode plot of a stable system is shown in fig. The transfer function of the system is
GATE ECE 1992
34
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
The gain margin of the system is
GATE ECE 1991
35
From the Nicholas chart, one can determine the following quantities pertaining to a closed loop system:
GATE ECE 1989
36
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 $${\omega _0}$$ are respectively given by
GATE ECE 1987
37
A system has fourteen poles and two zeroes. Its high frequency asymptote, in its magnitude plot, has having a slope of
GATE ECE 1987
Marks 5
1
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 2002
2
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
3
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 the closed-loop system using Nyquist stability.
GATE ECE 1999
4
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 Nyquist criterion, find the condition for the closed loop system to be stable.
GATE ECE 1998
Marks 8
1
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 the system and there from obtain the gain margin and the phase margin.
GATE ECE 1992
2
The magnitude plot of the open loop transfer function G(s), of a certain system is given in fig,
(b) Estimate the phase at each of the corner frequencies.
(a) Determine G(s), if it is known that the system is of minimum phase type.
(b) Estimate the phase at each of the corner frequencies.
GATE ECE 1987