Homework 4 Answer

1

t

h(t)

1

0

1.3

0.1

Homework 4 Answer

Problem 1

The unit-step response of a linear control system is showed in Fig.problem1 .

1. Find the transfer function of a second-order prototype system to model the

system.

2. Find the open transfer function(or the forword-path transfer function) If the

system is a unity feedback system.

Fig.problem1

Answer

21 1.3 1% 100% % 30%

1e

0.36

20.1

1p

n

t

s 33.6n rad/s

2

2 2 2

1130

2 24.2 1130

n

n n

ss s s s

A unit feedback system ( )

( )1 ( )

G ss

G s

The open transfer function 2

2 2

1130 46.6

2 24.2 (0.041 1)

n

n

G ss s s s s s

Homework 4 Answer

2

Problem 2

1. Determine the value of K so that 0.6 in a second-order prototype

system showed in Fig.problem 2.

2. Find the settling time st ( 5% criterion), percent overshoot % ,

and peak time pt .

2

sK

)1(

5

ss

R C

__

Fig.problem 2

Answer

2

( ) 10( )

( ) (1 5 ) 10

C ss

R s s K s

Compare with the prototype second order modern 2

2 22

n

n n

ss s

2 10n 2 1 5n K

10n 1 5

2 10

K

In order to 0.6 0.56K

3.51.84s

n

t

(s) ( 5% criterion)

21.24

1p

n

t

(s)

21% 100% 9.84%e