Post on 05-Jun-2018
transcript
Non-zero input
1 2
1 1 2
1 2
2
1
1
( )
1
( 1) 1
1, 1
( ) 1
lim ( ) 1
t
t t
t
t
t
x x
x t K e K
x x K e K e K
K e K
K
x t K e
x t
1
1
(0) 1
(0) 1
( ) (0) 1 1
if : (0) 0
( ) 1
t
t
x K
K x
x t x e
x
x t e
Complete response = natural response + forced response
Natural response(homogeneous solution):
Forced response(particular solution), steady state:
Complete response = natural response + forced response
Natural response(homogeneous solution):
Forced response(particular solution), steady state:
0
11 0
( )t
RC
dvRC v
dt
RCs sRC
v t Ke
1 1
ss
ssss ss
v V
dVRC V V
dt
Complete response = natural response + forced response
( ) 1
(0) 1 0 1
( ) 1
t
RC
t
RC
v t Ke
v K K
v t e
Complete response = natural response + forced response
Natural response(homogeneous solution):
Forced response(particular solution), steady state:
0
1 0
( )L
tR
L dvv
R dt
L Ls s
R R
v t Ke
1 1
ss
ssss ss
v V
dVLV V
R dt