# Control Systems (Test 5)

## Gate Exam : Ec Electronics And Communication Engineering

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Q.1
The frequency response of a linear system G(jw) is provided in the tubular form below A. B. C. D. Explaination / Solution: Workspace
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Q.2
The phase cross-over frequency of the transfer function is
A. √3
B. 1/√3
C. 3
D. 3√3
Explaination / Solution: Workspace
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Q.3
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 ? 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
Explaination / Solution:

Given the feedback system and the Nyquist plot of G (s)is For the given system, we have the open loop transfer function as
G (s) = KG (s)
Considering the open loop system G (s) is stable, we have no open loop poles in right half plane
P = 0
From Nyquist theorem, we know that
N = P - Z
Where N is the number of encirclements of (-1 + j0), P is number of open loop poles in right half plane, Z is number of closed loop poles in right half plane. For stability, we must have
Z = 0
N = 0,   if closed loop system is stable
≠ 0,   if closed loop system is unstable
observing the Nyquist plot, we conclude that the plot of KG(s) encircles (-1 + j0)
if  K> 1
Hence, N ≠ 0 for sufficient large and positive value of K . Thus, the closedsystem is unstable for sufficiently large and positive K .

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Q.4
The unilateral Laplace transform of f (t) is . The unilateral Laplace transform of t f (t) is
A. B. C. D. Explaination / Solution: Workspace
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Q.5
The transfer function of a compensator is given as Gc(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
Explaination / Solution: both option (A) and (C) satisfier but option (C) will pot polar and zero as RHS of s-plane thus not possible option (A) is right

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Q.6
The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by A. B. C. D. Explaination / Solution:

For given plot root locus exists from -3 to , So there must be odd number of poles and zeros. There is a double pole at s = - 3
Now poles = 0, -2, -3, -3
zeros = - 1
Thus transfer function Workspace
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Q.7
The signal flow graph for a system is given below. The Transfer function, Y(s)/U(s) for the system is A. B. C. D. Explaination / Solution:
No Explaination.

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Q.8
The input-output transfer function of a plant 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

A. 0 dB
B. 20 dB
C. 26 dB
D. 46 dB
Explaination / Solution:  Workspace
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Q.9
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 A. B. C. D. Explaination / Solution: Workspace
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Q.10
If the closed-loop transfer function of a control system is given as then It is
A. an unstable system
B. an uncontrollable system
C. a minimum phase system
D. a non-minimum phase system