# Control Systems (Test 2)

## Gate Exam : Ec Electronics And Communication Engineering

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Q.1
An open loop transfer function G(s) of a system is For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,
A. -0.42
B. -1.58
C. -0.42 and -1.58
D. None of the above
Explaination / Solution:

1+ G= ( Workspace
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Q.2
The state space representation of a separately excited DC servo motor dynamics is given as where ω is the speed of the motor, ia is the armature current and u is the armature voltage. The transfer function ω(s)/U(s) of the motor is
A. B. C. D. Explaination / Solution:  Workspace
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Q.3
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h = 1, we can conclude A. h[n] is real for all n
B. h[n] is purely imaginary for all n
C. h[n] is real for only even n
D. h[n] is purely imaginary for only odd n
Explaination / Solution:

From the pole-zero plot, we obtain the transfer function as Workspace
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Q.4
The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function is
A. 1
B. 2
C. 5
D. 9
Explaination / Solution: Workspace
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Q.5
The Nyquist plot of a stable transfer function G(s) is shown in the figure are interested in the stability of the closed loop system in the feedback configuration shown. 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
Explaination / Solution:

The plot has one encirclement of origin in clockwise direction. Thus G(s) has a zero is in RHP.

Workspace
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Q.6
A speed signal, band limited to 4 kHz and peak voltage varying between +5 V and -5 V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is
A. 16 dB
B. 32 dB
C. 48 dB
D. 4 kHz
Explaination / Solution: Workspace
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Q.7
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is A. u(t)
B. tu(t)
C. D. Explaination / Solution:
No Explaination.

Workspace
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Q.8
The residues of a complex function at its poles are
A. 1/2, -1/2 and 1
B. 1/2, -1/2 and -1
C. 1/2, -1 and 3/2
D. 1/2, -1 and 3/2
Explaination / Solution:  Workspace
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Q.9
Assign output of each integrator by a state variable The transfer function of the system is
A. B. C. D. Explaination / Solution:

By masson’s gain formula  Workspace
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Q.10
A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function
A. encircles the s-plane point (−1 + j0) in the counterclockwise direction as many times as the number of right-half s-plane poles.
B. encircles the s-plane point (0 − j1) in the clockwise direction as many times as the number of right-half s-plane poles.
C. encircles the s-plane point (−1 + j0) in the counterclockwise direction as many times as the number of left-half s-plane poles.
D. encircles the s-plane point (−1 + j0) in the counterclockwise direction as many times as the number of right-half s-plane zeros.