Polar Nyquist and Bode Plot · Control Systems · GATE EE

Marks 1

In the Nyquist plot of the open-loop transfer function

$$G(s)H(s) = {{3s + 5} \over {s - 1}}$$

corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

GATE EE 2023

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, is $$-$$180$$^\circ$$. This system has

GATE EE 2022

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 the system be $${v_0}\left( t \right) = {v_m}\sin \left( {\omega t + \phi } \right)$$ for the input $${v_i}\left( t \right) = {v_m}\sin \left( {\omega t} \right).$$ Then the minimum and maximum values of ϕ (in radians) are respectively

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 ____________. (Give the answer up to two decimal places).

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 state $$y(t)$$ is $$Acos$$$$\left( {2t + \phi } \right)$$ for the input $$\cos \left( {2t} \right).$$ The values of $$A$$ and $$\phi ,$$ respectively are

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 2016 Set 1

A Bode magnitude plot for the transfer function $$𝐺(𝑠)$$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

GATE EE 2015 Set 1

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 $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ is

GATE EE 2015 Set 2

The Bode plot of a transfer function $$G(s)$$ is shown in the figure below.

The gain is $$\left( {20\log \left| {G\left( s \right)} \right|} \right)$$ is $$32$$ $$dB$$ and $$–8$$ $$dB$$ at $$1$$ $$rad/s$$ and $$10$$ $$rad/s$$ respectively. The phase is negative for all $$\omega .$$ Then $$G(s)$$ is

GATE EE 2013

A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}}$$ is excited by $$\sin \left( {\omega t} \right).$$ The steady-state output of the system is zero at

GATE EE 2012

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

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 the system are

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 $$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s + 4} \right)}}.$$ The system output is zero at the frequency

GATE EE 2005

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

GATE EE 2005

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

GATE EE 2004

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 transfer functions is

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 closed - loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}} = {1 \over {\left( {1 + s} \right)}}$$
For the input $$\,r\left( t \right)\,\, = \,\,\sin \,t,$$ the steady state value of $$c(t)$$ is equal to

GATE EE 1996

A unity feedback system has the open loop transfer function $$G\left( s \right) = {1 \over {\left( {s - 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}$$
The Nyquist plot of $$G$$ encircle the origin

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

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20$ dB/decade at least till $100$ rad/sec with the gain crossover frequency being $10$ rad/sec. The asymptotic Bode phase plot remains constant at $-90^{o}$ at least till $\omega = 10$ rad/sec. The steady-state error of the closed-loop system for a unit ramp input is ________________ (rounded off to 2 decimal places).

GATE EE 2024

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $G(s)$ are given in the table. The value of the gain $K_I$ ($>0$) for a $50^\circ$ phase margin is _____ (rounded off to 2 decimal places).

$\omega$ in rad/sec	Magnitude in dB	Phase in degrees
0.5	−7	−40
1.0	−10	−80
2.0	−18	−130
10.0	−40	−200

GATE EE 2024

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

GATE EE 2023

Consider a lead compensator of the form

$$K(s) = {{1 + {s \over a}} \over {1 + {s \over {\beta a}}}},\beta > 1,a > 0$$

The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of $$K(s)$$, is 6 dB. The values of $$a,\beta$$, respectively, are

GATE EE 2023

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 given as y(t) = a + b sin(10t + $$\theta$$). The values of a and b will be

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-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point ($$-$$1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

GATE EE 2022

Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ is in $$rad/s$$)

Which one of the following transfer functions is best represented by the above Bode magnitude plot?

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 Nyquist contour in the clockwise direction. Then, the Nyquist plot of $$G(s)$$ $$H(s)$$ encircles $$-1+j0$$

GATE EE 2016 Set 1

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 values of the constant gain term and the highest corner frequency of the Bode plot respectively are

GATE EE 2014 Set 2

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 are

GATE EE 2014 Set 3

The Bode magnitude plot of the transfer function $$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \right)} \over {s\left( {1 + {s \over 8}} \right)\left( {1 + bs} \right)\left( {1 + {s \over {36}}} \right)}}$$ is shown below: Note that $$-6$$ $$dB/octave=-20$$ $$dB/decade.$$ The value of $${a \over {bK}}$$ is _______.

GATE EE 2014 Set 1

The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plotted in the complex $$\,G\left( {j\omega } \right)$$ plane $$\left( {for\,\,0 < \omega < \infty } \right)$$ is

GATE EE 2010

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

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 this system is

GATE EE 2009

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

This transfer function has

GATE EE 2008

If $$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$ and $$y = {\rm I}mG\left( {j\omega } \right)$$ then for $$\omega \to {0^ + },\,\,$$ the Nyquist plot for $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$

GATE EE 2007

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

GATE EE 2006 Control Systems - Polar Nyquist and Bode Plot Question 11 English 1

GATE EE 2006 Control Systems - Polar Nyquist and Bode Plot Question 11 English 2

GATE EE 2006

The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {100 + j\omega } \right)}^2}}}$$ is

GATE EE 2006

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 gain $$K$$ is

GATE EE 2005

In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e^{ - 0.25s}}} \over s}$$ passes through the negative real axis at the point

GATE EE 2005

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

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 $$‘a’$$ to give a phase margin of $${45^0}$$ is equal to

GATE EE 2004

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 $$\omega = 0.5a$$ are respectively

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 $$G\left( s \right) = {1 \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}$$ has gain margin of ... $$dB.$$

GATE EE 1997

An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\,\,$$ has frequency response plot shown in Fig. below, then the system gain $$K$$ is __________ and the damping factor is approximately _______

GATE EE 1991

Marks 5

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 the magnitude of $$G\left( {j\omega } \right)$$ in dB at an angular frequency of $$\omega = 20rad/\sec .$$
(b) Determine the phase margin in degrees.
(c) Determine the gain margin in $$dB.$$
(d) Is the system stable or unstable?

GATE EE 2001

Open-loop transfer function of a unity - feedback system is $$$G\left( s \right) = {G_1}\left( s \right).{e^{ - s{\tau _D}}} = {{{e^{ - s{\tau _D}}}} \over {s\left( {s + 1} \right)\left( {s + 2} \right)}}$$$
Given : $$\,\left| {{G_1}\left( {j\omega } \right)} \right| \approx 1$$ when $$\omega = 0.446$$

(a) Determine the phase margin when $${\tau _D} = 0$$
(b) Comment in one sentence on the effect of dead time on the stability of the system.
(c) Determine the maximum value of dead time $${\tau _D}$$ for the closed-loop system to be stable.

GATE EE 2000

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 is minimal phase system.

GATE EE 1998