Question: 16 -

The unit step response of a second order system is = 1-e^-5t-5te^-5t . Consider the following statements:
1. The under damped natural frequency is 5 rad/s.
2. The damping ratio is 1.
3. The impulse response is 25te^-5t.
Which of the statements given above are correct?

Only 1 and 2

Only 2 and 3

1,2 and 3

Only 1 and 3

Answer:

1,2 and 3

Solution:

C(s) = 1/s-1/s+5-5/(s+5)^2
C(s) = 25/s(s²+10s+25)
R(s) = 1/s
G(s) = 25/(s²+10s+25 )
w= √25
w = 5 rad/sec
G = 1.

Question: 17 -

As unity feedback system has a forward path transfer function G(s) = K/s(s+8) where K is the gain of the system. The value of K, for making this system critically damped should be

4

8

16

32

Answer:

16

Solution:

Overall transfer function M(s) = K/K+s(s+8)
Therefore the characteristic equation is s²+8s+K
w = √K , 2Gw = 8
w = 4 and K = 16.

Question: 18 -

The unit impulse response of a second order system is 1/6e^-0.8tsin(0.6t). Then the natural frequency and damping ratio of the system are respectively.

2 and 0.4

1 and 0.8

1 and 0.6

2 and 0.3

Answer:

1 and 0.8

Solution:

1/10[1/(s²+1.6s+1)] w = 1 rad/s
2Gw = 1.6
G = 0.8.

Question: 19 -

Consider a second order all-pole transfer function model, if the desired settling time(5%) is 0.60 sec and the desired damping ratio 0.707, where should the poles be located in s-plane?

-5+j5

-5+j4√2

-4+j7

-4+j5√2

Answer:

-5+j5

Solution:

G = 1/√2
Gw = 5
s = -5+j5.

Question: 20 -

The standard second order system to a unit step input shows the 0.36 as the first peak undershoot, hence its second overshoot is:

0.216

0.116

0.1296

0.135

Answer:

0.216

Solution:

Overshoot and undershoot are calculated from the formula of peak time as odd peaks denote the overshoot and even denotes the under shoot.