Modern Control Engineering

(Chris Devlin) #1
aa

256 Chapter 5 / Transient and Steady-State Response Analyses

where

Similarly, subtracting from the fourth row a 0 /a 1 times the third row yields

where

Next, subtracting from the third row a 1 /a 22 times the second row yields

where

Finally, subtracting from the last row times the third row yields

where

a 44 =aˆ 44 -


aˆ 43


a 33

a 34

¢ 4 = 4


a 11
0
0
0

a 3
a 22
0
0

a 5
a 23
a 33
0

a 7
a 24
a 34
a 44

4


aˆ 43 a 33


a 34 =a 5 -

a 1
a 22

a 24

a 33 =a 3 -

a 1
a 22

a 23

¢ 4 = 4


a 11
0
0
0

a 3
a 22
0
0

a 5
a 23
a 33

aˆ 43


a 7
a 24
a 34

aˆ 44


4


aˆ 44 =a 4 -


a 0
a 1

a 5

aˆ 43 =a 2 -


a 0
a 1

a 3

¢ 4 = 4


a 11
0
0
0

a 3
a 22
a 1
0

a 5
a 23
a 3

aˆ 43


a 7
a 24
a 5

aˆ 44


4


a 24 =a 6 -

a 0
a 1

a 7

a 23 =a 4 -

a 0
a 1

a 5

a 22 =a 2 -

a 0
a 1

a 3

a 11 =a 1

Openmirrors.com

Free download pdf