A system has the input-output relation \(\frac{{dc\left( t \right)}}{{dt}} + 2c\left( t \right) = r\left( t \right)\), where c(t) is the output and r(t) is the input to the system. Determine the unit step response of the system.

c(t) = 0.5(1 – e-2t), -∞ < t < ∞

A proportional controller with transfer function, Kp is used with a first—order system having its transfer function as \(G(s)=\frac{K}{(1+sτ)}\) in unity feedback structure. For step inputs, an increase in Kp will

Decrease the time constant and increase the steady state error

Increase the time constant and decrease the steady state error

Decrease the time constant and decrease the steady state error

Decrease the time constant and increase the steady state error

Increase the time constant and increase the steady state error

70 + Mcqs in Time Response Analysis in Control Systems Page 2 McqOptions

51.	A unity feedback control system has a forward path transfer function equal to\(\frac{{42.25}}{{s\left( {s + 6.5} \right)}}\)The unit step response of this system starting from rest, will have its maximum value at a time equal to
A.	0 sec.
B.	0.56 sec.
C.	5.6 sec.
D.	infinity
Answer» E.

Discussion

52.	A system has the input-output relation \(\frac{{dc\left( t \right)}}{{dt}} + 2c\left( t \right) = r\left( t \right)\), where c(t) is the output and r(t) is the input to the system. Determine the unit step response of the system.
A.	c(t) = 0.5(1 + e-2t), t > 0
B.	c(t) = 0.5(1 – e-2t), -∞ < t < ∞
C.	c(t) = 0.5(1 – e-2t), t > 0
D.	c(t) = 0.5(1 – e2t), t > 0
Answer» D. c(t) = 0.5(1 – e2t), t > 0

Discussion

53.	A control system has \(G\left( s \right) = \frac{{10}}{{s\left( {s + 5} \right)}}\) and H(s) = K. What is the value of K for which the steady-state error for unit-step input is less than 5%?
A.	0.913
B.	0.927
C.	0.953
D.	1.05
Answer» E.

Discussion

54.	If the characteristic equation of a closed-loop system is 2s2 + 6s + 6 = 0 then the system is
A.	Overdamped
B.	Crtically damped
C.	Underdamped
D.	Undamped
Answer» D. Undamped

Discussion

55.	For a second-order system 2d2y/dt2 + 4 dy/dt + 8y = 8x, what is the damping ratio?
A.	0.1
B.	0.25
C.	0.33
D.	0.5
Answer» E.

Discussion

56.	For the function \(F\left( s \right) = \frac{1}{{s\left( {{s^2} + 2s + 2} \right)}}\) the initial and final values are:
A.	0, 0.5
B.	0, 2
C.	1, 0.5
D.	1, 2
Answer» B. 0, 2

Discussion

57.	A system having T.F. \(\frac{1}{{s + 1}}\) is excited by a step function of magnitude ‘3’. The time required by output to reach up to 96% of its steady state value is
A.	0.54 sec
B.	1.23 sec
C.	2.08 sec
D.	3.22 sec
Answer» E.

Discussion

58.	Peak time tp, is the time required for the response to reach the ______ peak of the over shoot
A.	1st
B.	2nd
C.	3rd
D.	none of these
Answer» B. 2nd

Discussion

59.	In the transient response of a second order system, delay time td is the time required for the response to reach the ____________ of the final value
A.	half
B.	1/√2
C.	25%
D.	10%
Answer» B. 1/√2

Discussion

60.	A second order pressure transducer has a natural frequency of 30 rad/sec, static sensitivity K = 1.0 μV/Pa. When a step pressure input of 8 × 103 N/m2 is applied, damped frequency of 29.85 rad/sec is observed. The damping ration of the transducer is
A.	Zero
B.	0.707
C.	1.0
D.	0.1
Answer» E.

Discussion

61.	A unit-step input to a first-order system G(s) yields a response as shown in the figure. This can happen when the values of K and a, respectively, are
A.	10 and 10
B.	50 and 10
C.	10 and 5
D.	50 and 5
Answer» C. 10 and 5

Discussion

62.	For a Type-1 System with ramp input, the steady state error is ________.
A.	Infinity
B.	Zero
C.	\(\frac{A}{{1 + {k_p}}}\)
D.	\(\frac{A}{{{k_v}}}\)
Answer» E.

Discussion

63.	For a second order system settling time is Ts = 7 s and peak time is Tp = 3 s. The location of poles are
A.	– 0.97 ± j0.69
B.	– 0.69 ± j0.97
C.	– 1.047 ± j0.571
D.	– 0.571 ± j1.047
Answer» E.

Discussion

64.	For the unit step response of second order system following statements are given:(A) Delay time is the time required for the response to reach 60% of the final value in first attempt(B) Settling time is the time required for the response to reach and stay within (2% or 5%) tolerance band of its final value(C) Delay time is the time required for the response to reach 50% of the final value in first attempt(D) Settling time is the time required for the response to reach and stay withing 15% of the final valueWhich of the above are correct?Choose the correct answer from the options given below:
A.	(A) and (B) only
B.	(B) and (C) only
C.	(C) and (D) only
D.	(A) and (D) only
Answer» C. (C) and (D) only

Discussion

65.	If the characteristic equation of a closed loop system is s2 + 2s + 2 = 0, then the system is
A.	overdamped
B.	critically damped
C.	underdamped
D.	undamped
Answer» D. undamped

Discussion

66.	If transfer function of a system is 1 / (τs + 1), then steady state error to unit step input is
A.	0.5
B.	zero
C.	infinite
D.	none of these
Answer» B. zero

Discussion

67.	An undamped system has a ________ response.
A.	Oscillatory
B.	Sustained Oscillation
C.	Non-Oscillatory
D.	Undeterminable
Answer» C. Non-Oscillatory

Discussion

68.	A proportional controller with transfer function, Kp is used with a first—order system having its transfer function as \(G(s)=\frac{K}{(1+sτ)}\) in unity feedback structure. For step inputs, an increase in Kp will
A.	Increase the time constant and decrease the steady state error
B.	Decrease the time constant and decrease the steady state error
C.	Decrease the time constant and increase the steady state error
D.	Increase the time constant and increase the steady state error
Answer» C. Decrease the time constant and increase the steady state error

Discussion

69.	A unity feedback system with open loop transfer function \({\rm{G}}\left( {\rm{s}} \right) = \frac{9}{{{\rm{s}}\left( {{\rm{s}} + {\rm{P}}} \right)}}\) is critically damped. The value of the parameter ‘P’ is
A.	6
B.	3
C.	2
D.	9
Answer» B. 3

Discussion

70.	Consider the following statements regarding the steady-statete error due to a step function input.(a) Type ‘0’ system \({e_{ss}} = \frac{R}{{1 + {K_p}}}\) (b) Type ‘0’ system ess = 0(c) Type ‘1’ system ess = 0(d) Type ‘1’ system ess = ∞Which of the above statements are correct?
A.	(a) and (b)
B.	(b) and (c)
C.	(a) and (c)
D.	(a) and (d)
Answer» D. (a) and (d)

Discussion

Explore topic-wise MCQs in Control Systems.

A unity feedback control system has a forward path transfer function equal to\(\frac{{42.25}}{{s\left( {s + 6.5} \right)}}\)The unit step response of this system starting from rest, will have its maximum value at a time equal to

A system has the input-output relation \(\frac{{dc\left( t \right)}}{{dt}} + 2c\left( t \right) = r\left( t \right)\), where c(t) is the output and r(t) is the input to the system. Determine the unit step response of the system.

A control system has \(G\left( s \right) = \frac{{10}}{{s\left( {s + 5} \right)}}\) and H(s) = K. What is the value of K for which the steady-state error for unit-step input is less than 5%?

If the characteristic equation of a closed-loop system is 2s2 + 6s + 6 = 0 then the system is

For a second-order system 2d2y/dt2 + 4 dy/dt + 8y = 8x, what is the damping ratio?

For the function \(F\left( s \right) = \frac{1}{{s\left( {{s^2} + 2s + 2} \right)}}\) the initial and final values are:

A system having T.F. \(\frac{1}{{s + 1}}\) is excited by a step function of magnitude ‘3’. The time required by output to reach up to 96% of its steady state value is

Peak time tp, is the time required for the response to reach the ______ peak of the over shoot

In the transient response of a second order system, delay time td is the time required for the response to reach the ____________ of the final value

A second order pressure transducer has a natural frequency of 30 rad/sec, static sensitivity K = 1.0 μV/Pa. When a step pressure input of 8 × 103 N/m2 is applied, damped frequency of 29.85 rad/sec is observed. The damping ration of the transducer is

A unit-step input to a first-order system G(s) yields a response as shown in the figure. This can happen when the values of K and a, respectively, are

For a Type-1 System with ramp input, the steady state error is ________.

For a second order system settling time is Ts = 7 s and peak time is Tp = 3 s. The location of poles are

If the characteristic equation of a closed loop system is s2 + 2s + 2 = 0, then the system is

If transfer function of a system is 1 / (τs + 1), then steady state error to unit step input is

An undamped system has a ________ response.

A proportional controller with transfer function, Kp is used with a first—order system having its transfer function as \(G(s)=\frac{K}{(1+sτ)}\) in unity feedback structure. For step inputs, an increase in Kp will

A unity feedback system with open loop transfer function \({\rm{G}}\left( {\rm{s}} \right) = \frac{9}{{{\rm{s}}\left( {{\rm{s}} + {\rm{P}}} \right)}}\) is critically damped. The value of the parameter ‘P’ is

Consider the following statements regarding the steady-statete error due to a step function input.(a) Type ‘0’ system \({e_{ss}} = \frac{R}{{1 + {K_p}}}\) (b) Type ‘0’ system ess = 0(c) Type ‘1’ system ess = 0(d) Type ‘1’ system ess = ∞Which of the above statements are correct?