# Control Systems Questions and Answers – Root Contours and Systems with Transportation Lag

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This set of Control Systems online test focuses on “Root Contours and Systems with Transportation Lag”.

1. Consider the points s1 =-3+4j and s2 = -3-2j in the s-plane. Then, for a system with the open loop transfer function G(s)H(s) =K/(s+1)4.
a) S1 is on the root locus but s2 is not
b) S2 is on the root locus but s1 is not
c) Both s1 and s2 are not on the root locus
d) Neither s1 nor s2 is on the root locus

Explanation: Roots lying on the root locus which is the locus traced by the gain of the system with respect to the frequency and depends upon the open loop poles and their position.

2. The characteristic equation of a control system is given by s(s+4)(s2+2s+s) +k(s+1) =0. What are the angles of the asymptotes for the root loci
a) 60°, 180°, 300°
b) 0°, 180°, 300°
c) 120°, 180°, 240°
d) 0°, 120°, 240°

Explanation: P-Z = 3
Angle of asymptote = (2q+1)180°/P-Z
Hence the angles are 60°, 180°, and 300°.

3. The characteristic equation of a feedback control system is given by s3+5s2+(K+6)s+K=0. In the root loci diagram, the asymptotes of the root loci for large K meet at a point in the s plane whose coordinates are:
a) (2,0)
b) (-1,0)
c) (-2,0)
d) (-3,0)

Explanation: The point of meeting of the asymptotes are is calculated by using Routh Hurwitz table and then equating the S^0 term equal to zero.
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4. The root locus diagram has loop transfer function G(s)H(s) = K/ s(s+4)(s2+4s+5) has
a) No breakaway points
b) Three real breakaway points
c) Only one breakaway points
d) One real and two complex breakaway points

Explanation: The breakaway points are the points at which the root locus branches are broken and are calculated by differentiating the value of K with respect to s and equating it with zero.

5. For asymptotes passing from breakaway point then this point is also centroid
a) True
b) False

Explanation: For asymptotes which are the tangents to the root locus and extending from the minus infinite to plus infinite and if passing from breakaway point then this point is also centroid.

6. Transportation lag is seen in systems:
a) Amount to be transferred in large
b) Time take to transfer is large
c) Inefficiency of the process
d) Errors

Explanation: Transportation lag refers to the lag where the output does not follow the input and is seen in systems where the time taken to transfer is very large.

7. Mediums responsible for transportation lag are:
a) Lines
b) Pipes
c) Belt conveyors
d) All of the mentioned

Explanation: Transportation lag is mainly seen in the practical mediums where the time of transfer is very large and accurate results are not possible in these type of the systems. Lines, pipes and belt conveyors are the mediums responsible for transportation lag.

8. Linear lumped parameter models are not valid under situations as:
a) Transmission pipe between the hydraulic pump and the motor causes a time lag in transportation of oil from pump to motor
b) Transmission of heat by conduction or convection produces serious transportation lag
c) Both of the mentioned
d) None of the mentioned

Explanation: Linear lumped parameter models are the models used in the electrical circuits that are used to store energy and not valid when the pure time lags are negligible compared to other lags in the system.

9. Practically all the systems have transportation lag :
a) True
b) False

Explanation: Not all systems have transportation lag but whose transmission time is more ha the transmission lag and for these type of the systems the output is not accurate.

10. Transportation lag causes :
a) Instability in system
b) Stability in system
c) System remains unaffected
d) Bandwidth increases

Explanation: Transportation lag is the delay in the generation of the output where for the input given output is not present and causes instability in the system.

Sanfoundry Global Education & Learning Series – Control Systems.
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