# Control Systems (Test 4)

## Gate Exam : Ee Electrical Engineering

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Q.1
The unit step response of a system with the transfer function is given by which one of the following waveforms?
A. B. C. D. Explaination / Solution:  Workspace
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Q.2
Negative feedback in a closed-loop control system DOES NOT
A. reduce the overall gain
B. reduce bandwidth
C. improve disturbance rejection
D. reduce sensitivity to parameter variation
Explaination / Solution:

Negative feedback in closed-loop control system does not reduce bandwidth.

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Q.3
If then the region of convergence (ROC) of its Z-transform in the Z-plane will be
A. B. C. D. Explaination / Solution: Workspace
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Q.4
The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has theses properties ?
A. B. C. D. Explaination / Solution:

For under-damped second order response Workspace
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Q.5
The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: A. B. C. D. Explaination / Solution:  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. The number of quantization levels required to reduce the quantization noise by a factor of 4 wo
A. 1024
B. 512
C. 256
D. 64
Explaination / Solution:
No Explaination.

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Q.7
The transfer function of the circuit shown below is A. B. C. D. Explaination / Solution:
No Explaination.

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Q.8
Two systems H1(Z) and H2(Z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H2(Z)is A. B. C. D. Explaination / Solution: Workspace
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Q.9
The first two rows of Routh's tabulation of a third order equation are as follows.
s3    2    4
s2    4    4.
This means there are

A. two roots at s= ± j and one root in right half s-plane
B. two roots at s = ± j2 and one root in left half s-plane
C. two roots at s= ± j2 and one root in right half s-plane
D. two roots at s = ± j and one root in left half s-plane
Explaination / Solution:
No Explaination.

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Q.10
Consider a stable system with transfer function Where b1, ---, band a1, ---, aare real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB/decade as 𝜔 ⟶ ∞. A possible pair of values for p and q is
A. p = 0 and q = 3
B. p = 1 and q = 7
C. p = 2 and q = 3
D. p = 3 and q = 5 