Time Response Analysis MCQ

51. The input-output relationship of a system is given by

$r(t)=2\frac{\mathrm{d^2}c(t) }{\mathrm{d} t^2}+3\frac{\mathrm{d} c(t)}{\mathrm{d} t}+2c(t)$

where r(t) and c(t) are input and output respectively. The transfer function of the system is equal to

1. $\frac{1}{s^2+s+2}$
2. $\frac{1}{s^2+3s+2}$
3. $\frac{2}{s^2+3s+2}$
4. $\frac{1}{s^2+5s+3}$

52. Consider the function

$F(s)=\frac{ω}{s^2+ω^2}$

where F(s) = laplace transform of f(t). The final value of f(t) is equal to

1. infinite
2. zero
3. finite constant
4. a value between -1 and +1

53. The type number of the control system with

$G(s)H(s)=\frac{K(s+2)}{s(s^2+2s+3)}$

1. two
2. one
3. four
4. three

54.  For type 2 system, the steady-state error due to ramp input is equal to

1. finite constant
2. zero
3. indeterminate
4. infinite

55. Given a unity feedback system with

$G(s)=\frac{K}{s(s+4)}$

the value of K for damping ratio of 0.5 is

1. 4
2. 1
3. 64
4. 16

56. For a unity feedback control system with forward path transfer function $G(s)=\frac{K}{s+5}$. What is error transfer function w_e(s) used for determination of error coefficients?

1. $\frac{K}{s+5}$
2. $\frac{K}{s+K+5}$
3. $\frac{s+5}{s+K+5}$
4. $\frac{K(s+5)}{s+K+5}$

57. For a second-order system, natural frequency of oscillation is 10 rad/s and damping ratio is 0.1. What is 2% settling time?

1. 10 s
2. 40 s
3. 4 s
4. 0.4 s

58. The open-loop transfer function for unity feedback system is given by

$\frac{5(1+0.1s)}{s(1+5s)(1+20s)}$

Consider the following statements:

1. The steady-state error for a step input of magnitude 10 is equal to zero.
2. The steady-state error for a ramp input of magnitude 10 is 2.
3. The steady-state error for an acceleration input of magnitude 10 is infinite.

Which of the statements given above are correct?

1. Only i and ii
2. Only i and iii
3. Only ii and iii
4. i, ii and iii

59. A particular control system yielded a steady-state error of 0.20 for unit step input. A unit integrator is cascaded to this system and unit ramp input is applied to this modified system. What is the value of steady-state error for this modified system?

1. 0.10
2. 0.15
3. 0.20
4. 0.25

60. A system function $N(s)=\frac{V(s)}{I(s)}=\frac{s+3}{4s+5}$

The system is initially at rest. If the excitation i(t) is a unit step, which of the following are the initial and steady-state values of v(t)?

	Initial value	Steady-state value
a.	0	3/5
b.	1/4	0
c.	3/5	1/4
d.	1/4	3/5