Polar Plot and Nyquist Plot - Topic wise GATE previous questions on Control Systems (from 1987 onwards)

2003
1. 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

a) always stable
b) unstable with one closed loop right hand pole
c) unstable with two closed loop right hand poles
d) unstable with three closed loop right hand poles

Answer:A

Solution : https://www.youtube.com/watch?v=DuipmIw_dtI

2. The gain margin and the phase margin of a feedback system with G(s)H(s) = s/(s + 100)³ are
a) 0 dB, 0^o
b) ∞, ∞
c) ∞, 0^o
d) 88.5 dB, ∞

Answer:B

Solution : https://www.youtube.com/watch?v=n44i9T5koz4

2004
3. The gain margin for the system with open loop transfer function G(s)H(s) = 2(1 + s)/s², is
a) ∞
b) 0
c) 1
d) - ∞

Answer:B

Solution : https://www.youtube.com/watch?v=L2Y_rS_Zc9M

2005
4. Which one of the following polar diagrams corresponds to a lag network?

Answer:D

Solution : https://www.youtube.com/watch?v=essJrzYsfPg

5. 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

Answer:B

Solution : https://www.youtube.com/watch?v=1mBpd1vOX78

2006
6. The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through ( –1, j0) point on the GH – plane. The gain margin of the system in dB is equal to
a) infinite
b) greater than zero
c) less than zero
d) zero

Answer:D

Solution : https://www.youtube.com/watch?v=skWe48mXRqg

2009
Common Data Questions: (7 & 8)
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.

7. Which of the following statements is TRUE?
a) G(s) is an all pass filter
b) G(s) has a zero in the right half plane
c) G(s) is the impedance of a passive network
d) G(s) is marginally stable

Answer:B

Solution : https://www.youtube.com/watch?v=2t0EyW64kfI

8. The gain and phase margin of G(s) for closed loop stability are
a) 6 dB and 180^o
b) 3 dB and 180^o
c) 6 dB and 90^o
d) 3 dB and 90^o

Answer:C

Solution : https://www.youtube.com/watch?v=RlFKoEWXgw8

2011
9. for the transfer function G(jω) = 5 + jω, the corresponding Nyquist plot for positive frequency has the form

Answer:A

Solution : https://www.youtube.com/watch?v=F0oR9sCCy80

2014
10. Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which of the following conclusions is correct?

a) G(s) is an all pass filter
b) G(s) is a strictly proper transfer function
c) G(s) is a stable and minimum phase transfer function
d) The closed loop system is unstable for sufficiently large and positive k

Answer:D

Solution : https://www.youtube.com/watch?v=ujZuye5co_M

2015
11. The polar plot of the transfer function G(s) = 10(s+1)/(s+10) for 0 < ω < ∞ will be in the
a) first quadrant
b) second quadrant
c) third quadrant
d) fourth quadrant

Answer:A

Solution : https://www.youtube.com/watch?v=-2VWgQ6uM1I

Gain Margin and Phase Margin - Topic wise Questions in Control Systems (from 1987 onwards)

2003
1. The gain margin and the phase margin of a feedback system with G(s)H(s) = s/(s + 100)³ are
a) 0 dB, 0^o
b) ∞, ∞
c) ∞, 0^o
d) 88.5 dB, ∞

Answer:B

Solution : https://www.youtube.com/watch?v=n44i9T5koz4

2004
2. The gain margin for the system with open loop transfer function G(s)H(s) = 2(1 + s)/s², is
a) ∞
b) 0
c) 1
d) - ∞

Answer:B

Solution : https://www.youtube.com/watch?v=L2Y_rS_Zc9M

2005
Statement for Linked Answer Questions 3 & 4:
The open loop transfer function of a unity feedback is given by G(s) = 3e^–2s / [s(s + 2)].
3. The Gain and Phase cross over frequencies in rad/sec are, respectively
a) 0.932 and 1.26
b) 0.632 and 0.485
c) 0.485 and 0.632
d) 1.26 and 0.632

Answer:D

Solution : https://www.youtube.com/watch?v=eKZo_zPxjYI

4. based on the above results, the Gain and Phase Margins of the system will be
a) –7.09 dB and 87.5^o
b) 7.09 dB and 87.5^o
c) 7.09 dB and –87.5^o
d) –7.09 dB and –87.5^o

Answer:D

Solution : https://www.youtube.com/watch?v=aHVPuRMM0q8

2006
5. The open loop transfer function of a unity gain feedback control system is given by G(s) = K/[(s + 1)(s + 2)]. The gain margin of the system in dB is given by
a) 0
b) 1
c) 20
d) ∞

Answer:D

Solution : https://www.youtube.com/watch?v=_GEVQWlLBOs

Statement for Linked Answer questions: (6 and 7)
Consider a unity gain feedback control system whose open loop transfer function is G(s) = (as + 1)/s².
6. The value of "a" so that the system has a phase margin equal to π/4 is approximately equal to
a) 2.40
b) 1.40
c) 0.84
d) 0.74

Answer:C

7. With the value of "a" set for phase margin of π/4, the value of unit impulse response of the open loop system at t = 1 second is equal to
a) 3.40
b) 2.40
c) 1.84
d) 1.74

Answer:C

Solution (10 & 11) : https://www.youtube.com/watch?v=DlzZDVlirog

2011
Common Data Questions 8 & 9:
The input – output transfer function of a plant H(s) = 100/s(s+10)². The plant is placed in a unity negative feedback configuration as shown in figure below.

8. The signal flow graph that DOES NOT model the plant transfer function H(s) is

Answer:D

Solution : https://www.youtube.com/watch?v=gSg5jPv06fQ

9. The gain margin of the system under closed loop unity negative feedback is
a) 0 dB
b) 20 dB
c) 26 dB
d) 46 dB

Answer:C

Solution : https://www.youtube.com/watch?v=HreyReFPqag

2012
10. A system with transfer function is excited by sin(ωt).

The steady state output of the system is zero at
a) ω = 1 rad/sec
b) ω = 2 rad/sec
c) ω = 3 rad/sec
d) ω = 4 rad/sec

Answer:C

Solution : https://www.youtube.com/watch?v=UYEEuh71lxc

2014
11. The phase margin in degrees of

calculated using the asymptotic Bode plot is ____________

Answer:45

Solution : https://www.youtube.com/watch?v=ZwdvClI0_mU

2015
12. The phase margin (in degrees ) of the system G(s) = 10 /s(s+10) is _____________

Answer:83

Solution : https://www.youtube.com/watch?v=WXHKVhdLeOc

P, PD and PID controllers & Lead and Lag Compensators - Topic wise Questions in Control Systems ( from 1987)

2003
1. A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has
a) a higher type number
b) reduced damping
c) higher noise amplification
d) larger transient overshoot

Answer:C

Solution : https://www.youtube.com/watch?v=flVQh4IItX4

2005
2. Which one of the following polar diagrams corresponds to a lag network?

Answer:D

Solution : https://www.youtube.com/watch?v=essJrzYsfPg

2006
3. The transfer function of a phase lead compensator is given by G_c(s) = (1 + 3Ts)/(1 + Ts) where T ≥ 0. The maximum phase shift provided by such a compensator is
a) π/2
b) π/3
c) π/4
d) π/6

Answer:D

Solution : https://www.youtube.com/watch?v=B6_LDoAZ3-I

2007
4. A control system with a PD controller is shown in the figure.

If the velocity error constant K_v = 1000 and the damping ratio ξ = 0.5, then the values of K_p and K_D are
a) K_p = 100, K_D = 0.09
b) K_p = 100, K_D = 0.9
c) K_p = 10, K_D = 0.09
d) K_p = 10, K_D = 0.9

Answer:B

Solution : https://www.youtube.com/watch?v=vxHx4zTs5vg

5. The open loop transfer function of a plant is given as G(s) = 1/(s² – 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

Answer:A

Solution : https://www.youtube.com/watch?v=HJ09FtxcO-I

2008
6. Group – I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition R₂C₂>R₁C₁. The transfer function V_o/V₁ represents a kind of controller. Match the impedance's in Group – I with the types of controllers in Group – II.

a) Q – 1, R – 2
b) Q – 1, R – 3
c) Q – 2, R – 3
d) Q – 3, R – 2

Answer:B

Solution : https://www.youtube.com/watch?v=Q3O1G2CU5Xw

2009
7. The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensator has such a magnitude plot?

a) Lead compensator
b) Lag compensator
c) PID compensator
d) Lead – Lag compensator

Answer:C

Solution : https://www.youtube.com/watch?v=JVBUSrYEb7Q

8. If the transfer function of the following circuit is V_o(s)/V_i(s) = 1/(2+sCR), then the value of the load resistor R_L is

a) R/4
b) R/2
c) R
d) 2R

Answer:C

Solution : https://www.youtube.com/watch?v=0bJX_BCy6bc

2010
9. A unity negative feedback closed loop system has a plant with the transfer function G(s) = 1/(s² + 2s + 2) and a controller G_c(s) in the feed forward path. For a unit step input, the tranfer function of the controller that gives minimum steady state error is

Answer:D

Solution : https://www.youtube.com/watch?v=zdwjtNkiBxg

2012
Statement for Linked Answer Questions : 10 and 11
The transfer function of a compensator is given as G_c(s)= (s+a)/(s+b).
10. G_c(s) is a lead compensator if
a) a = 1, b =2
b) a = 3, b =2
c) a = –3, b = –1
d) a = 3, b =1

Answer:A

11. The phase of the above lead compensator is maximum at
a) √2 rad/sec
b) √3 rad/sec
c) √6 rad/sec
d) 1/√3 rad/sec

Answer:A

Solution (6 & 7) : https://www.youtube.com/watch?v=CSWEFDPoSsA

2015
12. A lead compensator network includes a parallel combination fo R and C in the feed-forward path. If the transfer function of the compensator is GC(s) = (s+2)/(s+4) , the value of RC is ___________

Answer:0.5

Solution : https://www.youtube.com/watch?v=DeKH-DPUdMo

13. The transfer function of a first order controller is given as Gc(s) = K(s+a) / (s+b), where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is
a) a < b
b) a > b
c) K < ab
d) K > ab

Answer:A

Solution : https://www.youtube.com/watch?v=uKr3VkkMkow

Bode Plots (Bode Magnitude and Phase Plots) - Topic wise Questions in Control Systems ( from 1987)

2003
1. The approximate Bode magnitude plot of a minimum phase system is shown in figure. The transfer function of the system is

Answer:A

Solution : https://www.youtube.com/watch?v=BXoIP2em_cc


2004


2. Consider the Bode magnitude plot shown in figure. The transfer function H(s) is

Answer:C

Solution : https://www.youtube.com/watch?v=0K0Ls-_nRDQ


3. A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is
a) - 90^o
b) 0^o
c) 90^o
d) - 180^o

Answer:A

Solution : https://www.youtube.com/watch?v=8SWwr0wlV0E

2006


4. Consider two transfer functions G₁(s) = 1 / (s² + as + b) and G₂(s) = s / (s² + as + b). The 3 dB bandwidths of their frequency responses are, respectively

Answer:C

Solution :


2007


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

Answer:D

Solution : https://www.youtube.com/watch?v=fpM5ezwr90c

2008


6. The magnitude of frequency response of an under damped second order system is 5 at 0 rad/sec and peaks to 10/√3 at 5√2 rad/sec. The transfer function of the system is

Answer:A

Solution : https://www.youtube.com/watch?v=3a4n-8XUFCg

2010


7. A system with transfer function Y(s)/X(s) = s/(s + p) has an output y(t) = cos(2t – π/3) for the input signal x(t) = p cos(2t – π/2). Then, the system parameter 'p' is
a) √3
b) 2/√3
c) 1
d) √3/2

Answer:B

Solution : https://www.youtube.com/watch?v=3WAIkGRRes4


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

Answer:A

Solution : https://www.youtube.com/watch?v=Tt58Wfn-dsQ

2013


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

The gain (20log|G(s)|) is 32 dB and – 8 dB at 1 rad/sec and 10 rad/sec respectively. The phase is negative for all ω. Then G(s) is
a) 39.8/s
b) 39.8/s²
c) 32/s
d) 32/s²

Answer:B

Solution : https://www.youtube.com/watch?v=YkPfY-Gufmg

2014


10. 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 _____________

Answer:0.5

Solution : https://www.youtube.com/watch?v=fBTMa-Ql07A

11. In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4^th order all pole system?
a) – 80 dB/decade
b) – 40 dB/decade
c) + 40 dB/decade
d) + 80 dB/decade

Answer:A

Solution : https://www.youtube.com/watch?v=bTwOnjuzVX8

2015


12. Consider the Bode plot shown in figure.

Assume that all the poles and zeros are real valued. The value of f_H – f_L (in Hertz) is ____________________

Answer:8970

Solution : https://www.youtube.com/watch?v=R95T4ztuNQo