# Control Systems (Test 3)

## Gate Exam : Ee Electrical Engineering

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Q.1
An open loop system represented by the transfer function is
A. Stable and of the minimum phase type
B. Stable and of the non - minimum phase type
C. Unstable and of the minimum phase type
D. Unstable and of non-minimum phase type
Explaination / Solution:

Open loop system stability is depends only on pole locations ⇒ system is stable There is one zero on right half of s-plane so system is non – minimum phase

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Q.2
The transfer function of a system is The steady state output y(t) is A cos(2t + φ) for the input cos(2t). The values of A and φ, respectively are
A. B. C. D. Explaination / Solution: Workspace
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Q.3
The pole-zero given below correspond to a A. Law pass filter
B. High pass filter
C. Band filter
D. Notch filter
Explaination / Solution: Workspace
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Q.4
A certain system has transfer function where α is a parameter. Consider the standard negative unity feedback configuration as shown below Which of the following statements is true?
A. The closed loop systems is never stable for any value of α.
B.  For some positive value of α, the closed loop system is stable, but not for all positive values.
C. For all positive values of α, the closed loop system is stable.
D. The closed loop system stable for all values of α, both positive and negative.
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. The gain and phase margins of G(s) for closed loop stability are
A. 6 dB and 180◦C
B. 3 dB and 180◦C
C. 6 dB and 90 dB an
D. 3 dB and 90
Explaination / Solution:

The Nyzuist plot intersect the real axis ate - 0.5. Thus
G. M. =- 20 log x =- 20 log 0.5 = 6.020 dB
And its phase margin is 90c

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Q.6
An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is ________ bits / second.
A. 1
B. 2
C. 3
D. 4
Explaination / Solution:

Quantized 4 level require 2 bit representation i.e. for one sample 2 bit are required. Since 2 sample per second are transmitted we require 4 bit to be transmitted per second.

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Q.7
For the transfer function G(j𝜔) = 5 + j𝜔, the corresponding Nyquist plot for positive frequency has the form
A. B. C. D. Explaination / Solution:

G(j𝜔) = 5 + j𝜔 Here σ = 5. Thus G(j𝜔) is a straight line parallel to j𝜔 axis

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Q.8
The block diagram of a system with one input it and two outputs y1 and y2 is given below A state space model of the above system in terms of the state vector and the output vector is.
A. B. C. D. Explaination / Solution: Drawing SFG as shown below  Workspace
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Q.9
The polar plot of an open loop stable system is shown below. The closed loop system is A. Always stable
B. Marginally stable
C. Unstable with one pole on the RHS s-plane
D. Unstable with two poles on the RHS s-plane
Explaination / Solution:
No Explaination.

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Q.10
Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?
A. B. C. D.  