Multiple Choice Questions and Answers on Process Dynamics and Control

1. A non-linear system will have __________ steady state values.

a) One

b) More than one

c) Two   

d) Three

Answer: More than one

2. Bode stability method uses __________ loop transfer function.

a) Open

b) Closed

c) Either a or b

d) Neither a nor b

Answer: Open

3. A negative gain margin expressed in decibels means a/an __________ system.

a) Stable

b) Unstable

c) Critically damped

d) None of these

Answer: Unstable

4. Strain gage pressure transducers are used to measure __________ pressures.

a) Gage as well as vacuum

b) Absolute as well as differential

c) Both a & b

d) Neither a nor b

Answer: Both a & b

5. __________ controller has the maximum stabilising time.

a) P

b) PD

c) PI

d) PID

Answer: PI

6. A control system is unstable, if the open loop frequency response exhibits an amplitude ratio exceeding unity at the crossover frequency. This is __________ criterion.

a) Bode stability

b) Nyquist

c) Routh stability

d) None of these

Answer: Bode stability

7. In a single tank system, the transfer function of __________ to inlet flow rate is 1/TS+1.

a) Outlet flow rate

b) Level

c) Both A & B

d) Neither A nor B

Answer: Outlet flow rate

8. Characteristic equation is the denominator of __________ loop transfer function.

a) Open

b) Closed

c) Both a & b

d) Neither a nor b

Answer: Closed

9. Routh stability method uses __________ loop transfer function.

a) Open

b) Closed

c) Either a or b

d) Neither a nor b

Answer: Closed

10. Dead zone in an instrument must be less than __________ percent of the scale.

a) 0.2

b) 1.5

c) 4

d) 8

Answer: 0.2

11. 0n-off control which is a special case of proportional control, has a band width of about __________ percent.

a) 100

b) 75

c) 25

d) 0

Answer: 0

12. A system with transfer function (2S/4S) + 1 is of __________ order.

a) Zero

b) 1st

c) 2nd

d) 3rd

Answer: 1st

13. Feed forward controller accounts for the __________ changes.

a) Set point

b) Load

c) Both a & b

d)Neither a nor b

Answer: Load

14. The root locus plot of the roots of the characteristics equation of a closed loop system having the open loop transfer function K(s + 1)/2(2s + 1)(3s + 1) will have a definite number of loci for variation of K from 0 to ∞. The number of loci is

a) 1

b) 3

c) 4

d) 2

Answer: 3

15. Phase lag of the frequency response of a seco nd  order system to a sinusoidal forcing function

a) Is 30°

b) Is 90° at the most

c) Approaches 180° asymptotically

d) Is 120°

Answer: Approaches 180° asymptotically

16. Response of a linear control system for a change in set point is called

a) Frequency response

b) Transient response

c) Servo problem

d) Regulator problem

Answer: Servo problem

17. The inverse Laplace transform of the function f(s) = 1/S(1 + S) is

a) 1 + et

b) 1 - et

c) 1 + e-t

d) 1 - e-t

Answer: 1 - e-t

18. The open loop transfer function of a control system is KR/(1 + TS) . This represents

a) A first order system

b) Dead time system

c) A first order time lag

d) A second order system

Answer: A first order system

19. Select the correct statement from the following.

a) The frequency response of a pure capacity process is unbounded

b) The phase lag of a pure time delay system decreases with increasing frequency

c) The amplitude ratio of a pure capacity process  is  inversely proportional to frequency

d) The amplitude ratio of a pure time delay system increases with frequency

Answer: The amplitude ratio of a pure capacity process  is  inversely proportional to frequency

20. The unit of 'time constant' of a system is the same as that of

a) Velocity

b) Time

c) (time)⁻¹

d) None of these

Answer: Time

21. The time constant of a unity gain, first order plus time delay process is 5 min. If the phase lag at a frequency of 0.2 rad/min is 60°, then the dead time (in minutes) is

a) 5π/12

b) π/6

c) π/12

d) π/3

Answer: 5π/12

22. Which of the following controllers has the least maximum deviation?

a) P-controller

b) P-I controller

c) P-I-D controller

d) P-D controller

Answer: P-D controller

23. Which of the systems having following transfer functions is stable?

a) 1/(s²+ 2)

b) 1/(s²-2s + 3)

c) 1/(s² + 2s + 2)

d) Exp(-20s)/(s² + 2s-l)   

Answer: 1/(s² + 2s + 2)

24. For an input forcing function, X(t) = 2t², the Laplace transform of this function is

a) 2/s²

b) 4/s²

c) 2/s³

d) 4/s³

Answer: 4/s³

25. Bode diagram are generated from output response of the system subjected to which of the following input?

a) Impulse

b) Step

c) Ramp

d) Sinusoidal

Answer: Sinusoidal

26. Find the ultimate gain and frequency for a proportional controller in the case of a process having the transfer function Gp(s) = 1/(4s + 1)(2s + 1)(s + 1).

a) W = 1/√14, Kc = 45/7√14

b) W = √(7/6), Kc = 46/3

c) W = 1, Kc = 13

d) W = √(7/8), Kc = 45/4

Answer: W = √(7/6), Kc = 46/3

27. A proportional controller with a gain of Kc is used to control a first order process. The offset will increase, if

a) Kc is reduced

b) Kc is increased

c) Integral control action is introduced

d) Derivative control action is introduced

Answer: Kc is increased

28. The second order system with the transfer function 4/(S² + 2S + 4) has a damping ratio of

a) 2.0

b) 0.5

c) 1.0

d) 4.0

Answer: 0.5

29. Liquid argon level in a pressurised storage tank (at 3 kg/cm² ) is measured by a/an

a) Gage glass

b) External float gage

c) Differential pressure gage

d) None of these

Answer: Differential pressure gage

30. A stable system is the one

a) For which the output response is bounded for all bounded input

b) Which exhibits an unbounded response to a bounded input

c) Which satisfies the conditions for a servo problem

d) None of these

Answer: For which the output response is bounded for all bounded input

31. Bode diagram is a plot of

a) Log (AR) vs. log (f) and (Φ) vs. log (f)

b) Log (AR) vs. f and log Φ vs.f

c) AR vs. log (f) and Φ vs. log (f)

d) None of these

Answer: Log (AR) vs. log (f) and (Φ) vs. log (f)

32. Cascade control means

a) Feed forward control

b) More than one feed-back loop

c) On-off control

d) One feed-back loop

Answer: More than one feed-back loop

33. In second order underdamped system,

a) Decay ratio = overshoot

b) Decay ratio = (overshoot)²

c) Overshoot increases for increasing damping co-efficient

d) Large damping co-efficient means smaller damping

Answer: Decay ratio = (overshoot)²

34. A control system has the following transfer function F(s) = (s - 1)(s + 1)/s(s - 2)(s + 4)

The initial value of the corresponding time function is

a) 1

b) 1/8

c) 7/8

d)   - 1

Answer: 1

35. Transfer function of transportation lag is

a) ETS

b) E-TS

c) 1/(TS + 1)

d) None of these

Answer: E-TS

36. Dead zone is the

a) Same as time constant

b) Same as transportation lag

c) Maximum change in the variable that does not change the reading of the instrument

d) None of these

Answer: Maximum change in the variable that does not change the reading of the instrument

37. In a feed-back control system G and H denote open loop and close loop transfer functions respectively. The output-input relationship is

a) G/(1 + H)

b) H(1 + G)

c) G/H

d) H/G

Answer: H(1 + G)

38. The closed loop pole of a stable second order system could be

a) Both real and positive

b) Complex conjugate with positive real parts

c) Both real and negative

d) One real positive and the other real negative

Answer: Both real and positive

39. The initial value (t=0) of the unit step response of the transfer function [(s + 1)/(2s + 1)] is

a) 0

b) 1/2

c) 1

d) 2

Answer: 1/2

40. Gain margin is equal to the

a) Amplitude ratio

b) Reciprocal of amplitude ratio

c) Gain in P controller   

d) Gain in P-I controller

Answer: Reciprocal of amplitude ratio

41. Which of the following judges the accuracy of an instrument?

a) Dead zone

b) Drift

c) Static error

d) None of these

Answer: Static error

42. The transfer function of a first order system is

a) 1/(Ts + 1)

b) 1/Ts

c) S/(Ts + 1)

d) None of these

Answer: 1/(Ts + 1)

43. The time constant of a first order process with resistance R and capacitance C is

a) R + C

b) R - C

c) RC

d) 1/RC

Answer: RC

44. The transfer function of a pure dead time system with dead time τd is

a) 1/(τds + 1)

b) Τds + 1

c) E-τds

d) Eτds

Answer: E-τds

45. A first order system with unity gain and time constant τ is subjected to a sinusoidal input of frequency w = 1/τ. The amplitude ratio for this system is

a) 1

b) 0.5

c) 1/√2

d) 0.25

Answer: 1/√2

46. The transfer function for a P-D controller is

a) Kc(1+τD s)

b) Kc(1 +1/τD s)

c) Kc τD s

d) Kc/τD s

Answer: Kc(1+τD s)

47. Phase lag of the sinusoidal response of a first order system is

a) 120°

b) 30°

c) 180°

d) 90°

Answer: 90°

48. The unit step response of the transfer function 1/(s² + 2s + 3)

a) Has a non-zero slope at the origin

b) Has a damped oscillatory characteristics

c) Is overdamped

d) Is unstable

Answer: Has a damped oscillatory characteristics

49. When the damping co-efficient (ξ) is unity, the system is

a) Overdamped

b) Critically damped

c) Underdamped

d) Highly fluctuating

Answer: Critically damped

50. For a feed back control system to be stable, the

a) Roots of the characteristic equation should be real   

b) Poles of the closed loop transfer function should lie in the left half of the complex plane

c).Bode plots of the corresponding open loop transfer function should monotoni-cally decrease

d) Poles of the closed loop transfer function should lie in the right half of the complex plane

Answer: Poles of the closed loop transfer function should lie in the left half of the complex plane

51. In a closed loop system, the process to be controlled is an integrating process with transfer function l/2s. The controller proposed to be used in an integral controller with transfer function 1/T₁s. When a step change in set point is applied to such a closed loop system, the controlled variable will exhibit

a) Overdamped response

b) Underdamped response

c) Undamped response

d) Unstable response

Answer: Underdamped response

52. Which of the following controllers has maximum offset?

a) P-controller

b) P-I controller

c) P-D controller

d) P-I-D controller

Answer: P-controller

53. In a single tank system, the transfer function of level to inlet flow rate is

a) R/TS

b) R/(TS + 1)

c) L(TS + l)

d) 1/TS

Answer: R/(TS + 1)

54. The root locus method, a pole of a transfer function G(s) is the value of s for which G(s) approaches

a)   - 1

b) 0

c) 1

d) ∞

Answer: ∞

55. Use of I-control along with P-control facilitates

a) Elimination of offset

b) Reduction of offset

c) Reduction of stability time

d) None of these

Answer: Option A

56. Positioning controllers are used for

a) Low loads

b) Temperature changes

c) High loads

d) Flow rate changes

Answer: High loads

57. The offset introduced by proportional controller with gain Kc in response of first order system can be reduced by

a) Reducing value of Kc

b) Introducing integral control

c) Introducing derivative control

d) None of the above

Answer: Introducing integral control

58. In a second order under damped system, the

a) Time required for the response of first reach its ultimate value is called the response time

b) Overshoot (which is a measure of how much the response exceeds the ultimate value) increase with the decrease of damping co-efficiente

c) Decay ratio (which is the ratio of the sizes of successive peaks) is equal to the reciprocal of overshoot

d) None of these

Answer: Overshoot (which is a measure of how much the response exceeds the ultimate value) increase with the decrease of damping co-efficiente

59. The frequency response of a first order system, has a phase shift with lower and upper bounds given by

a) - ∞, π/2

b) -π/2, π/2

c) -π/2, 0

d) 0, π/2

Answer: 0, π/2

60. Phase margin is equal to

a) 180° - phase lag

b) Phase lag - 180°

c) Phase lag + 180°

d) Phase lag + 90°

Answer: 180° - phase lag

61. Pick out the wrong statement.

a) There is no transfer lag for a single first order system

b) Stirred tank with a water jacket exemplifies an interacting system

c) Transfer lag is a characteristics of all higher order systems (other than first order systems)

d) Transfer lag decreases as the number of stages decreases

Answer: Transfer lag decreases as the number of stages decreases

62. Pick out the wrong statement

a) Proportional controller is normally used for level control in industrial applications

b) CSTR can be considered as a distributed parameter system

c) Distributed parameter approach gives partial differential equation

d) Non-linear behaviour is exemplified by an on-off controller

Answer: CSTR can be considered as a distributed parameter system

63. The characteristic equation for the control system with a closed loop transfer function G₁/1 + G₂ is given by 1 + G₂ = 0. The characteristic equation for the control system

a) Depends only upon the open loop transfer function

b) Determines its stability

c) Is the same for set point or load changes

d) All of the above

Answer: All of the above

64. Temperature control of an exothermic chemical reaction taking place in a CSTR is done with the help of cooling water flowing in a jacket around the reactor. The types of valve and controller action to be recommended are

a) Air to open valve with the controller direct acting

b) Air to close valve with the controller indirect acting

c) Air to open valve with the controller indirect acting

d) Air to close valve with the controller direct acting

Answer: Air to open valve with the controller indirect acting

65. Number of poles in a system with transfer function 1/(s² + 2s² + 1) is

a) 2

b) 5

c) 3

d) 1

Answer: 3

66. Routh test

a) Criterion provides information about the actual location of roots

b) Cannot be used to test the stability of a control system containing transportation lag

c) Criterion is not applicable to systems with polynomial characteristic equation

d) Can not determine as to how many roots of the characteristics equation have positive real roots

Answer: Cannot be used to test the stability of a control system containing transportation lag

67. The transfer function of a process is 1/(16s² + 8s + 4). If a step change is introduced into the system, then the response will be

a) Under damped

b) Critically damped

c) Over damped

d) None of these

Answer: Under damped

68. Suppose that the gain, time constant and dead time of a process with the following transfer function:Gc(s) = 10 exp( - 0.1s)/(0.5s + 1) are known with a possible error of ± 20% of their values. The largest permissible gain Kc of a proportional controller needs to be calculated below taking the values of process gain, time constant and dead time as

a) 8, 0.6, 0.08

b) 12, 0.6, 0.12

c) 8, 0.6, 0.12

d) 12, 0.4, 0.08

Answer: 12, 0.6, 0.12

69. Time constant is the

a) Time taken by the controlled variable to reach 63.2% of its full change

b) Same as transportation lag

c) Same as dead time

d) Time required by the measured variable to reach 63.2% of its ultimate change

Answer: Time taken by the controlled variable to reach 63.2% of its full change

70. On-off controllers are normally used for

a) Low loads

b) Temperature changes

c) Flow rate changes

d)  None of these

Answer: Low loads

71. Concentration of sugar solution can be determined by the

a) Polarimetry

b) Flame photometry

c) Emission spectroscopy

d) Oscillometry

Answer: Polarimetry

72. The response of two tanks of same size and resistance in series is

a) Under damped

b) Critically damped

c) Over damped

d) None of the above

Answer: Critically damped