Modern Control Engineering

aa

254 Chapter 5 / Transient and Steady-State Response Analyses

The first term in the first column of the Routh array is 1. The next term in the first column is a 1 ,

which is equal to The next term is b 1 , which is equal to

The next term in the first column is c 1 , which is equal to

In a similar manner the remaining terms in the first column of the Routh array can be found.

The Routh array has the property that the last nonzero terms of any columns are the same;

that is, if the array is given by

then

and if the array is given by

then

In any case, the last term of the first column is equal to an,or

an=

¢n- 1 an

¢n- 1

=

¢n

¢n- 1

a 6 =b 3 =d 2 =f 1

a 0

a 1

b 1

c 1

d 1

e 1

f 1

a 2

a 3

b 2

c 2

d 2

0

a 4

a 5

b 3

0

a 6

0

a 7 =c 3 =e 2 =g 1

a 0

a 1

b 1

c 1

d 1

e 1

f 1

g 1

a 2

a 3

b 2

c 2

d 2

e 2

a 4

a 5

b 3

c 3

a 6

a 7

=

¢ 3

¢ 2

=

a 1 a 2 a 3 - a^23 - a^21 a 4 +a 1 a 5

a 1 a 2 - a 3

b 1 a 3 - a 1 b 2

b 1

=

c

a 1 a 2 - a 3

a 1

da 3 - a 1 c

a 1 a 4 - a 5

a 1

d

c

a 1 a 2 - a 3

a 1

d

a 1 a 2 - a 3

a 1

=

¢ 2

¢ 1

¢ 1.

Openmirrors.com