ab ca gs s ci a b () x() x() b c x=ax+bu y=cx+du...2020/07/03 · a p a p hq hq hq a s a p a p hq...
TRANSCRIPT
: 113 14 (2020/7/03)
cb
A
( )tx( )u t ( )tx ( )y t
K
(A b) (c A)
nx R1
n
P: 2
y tu t x = Ax + bu
d(t) :
( )dG se tr t
y = cx+ dusG s
0d s pG s G s G s G s
c d sG s G s G s 1pG s sc I A b
: 3
y tu t x = Ax + bu
d(t) :
( )dG se tr t
y = cx+ dusG s
c d sG s G s G s 1pG s sc I A b
1KG s
s s52
K sG s
s s2
1 3 4 5K s
G ss s s s1 5
KG ss s s
: 4
1 2
0 1 00
uc c
x = x + x =
t t
2f
1c
1f1
2
1 2 1
1 01 0
0p
s css c c s s c
G =
1 0y = x
PI
: 5
1KG s
s s
5 12
G s K ss s
2 11 34 5 s s
K sG s
s s
51
1KG s
s s s
: 6
PID 0
Kp : TI :TD :
pK
1
IT s
DT s
c s 11p DI
G = K T sT s
1D
D
T sT s
proportional
integral
derivative
PID Controler
: 7
P D I
: 8
y tu t x = Ax + buy = cx+ du
e tr tcG s
n nRAA b c 1
1 1 01
1 1 0
nn
p n nn
h s h s hG ss a s a s a
n
1 21 2 1 0
1 22 1 0
n nn n
d n nn
q s q s q s qG ss p s p s p n-1+n = 2n-1n-1
2n 1
d(t) :
: 9
22 1 0
3 22 1 0
p
N s h s h s hG sD s s a s a s a
ux = Ax + by = cx
y tu te tdG s
3 3RA
22 1 02
1 0d
Q s q s q s qG sP s s p s p
2
1d p
d p
G G N s Q sG s
G G D s P s N s Q s3 2 2 2 2
2 1 0 1 0 2 1 0 2 1 0 0s a s a s a s p s p h s h s h q s q s q5 4 3
1 2 2 2 2 1 0 1 2 2 1 1s p h q a s a p p h q h q a s
5 4 3 24 3 2 1 0 0s d s d s d s d s d
21 1 2 0 0 2 1 1 2 0 0 0 1 1 0 0 1 1 0 0 0 0 0a p a p h q h q h q a s a p a p h q h q s a p h q
: 10
11pG s
s s
0 1 00 1 1
ux = x +
1 0y = x
y tu te tdG s 3 3 4j
0 1 1 01 1 0 1C OU U
1 1 0
0d
q s qG ss p
1 0d pG s G s2 3 2
0 1 0 0 0 1 01 0s s s p q s q s p s p q s q3 23 3 3 3 4 10 42 72s j s j s s s s
33 729d
sG ss
: 11
y tu t x = Ax + bu
d(t) :
( )dG se tr t
y = cx+ dusG s
c d sG s G s G s 1pG s sc I A b
: 12
1/sl
1/sl
l y tu t
( )dG se tr t
sG s pG s1sc I A b
r(t) e(t)1
1 p s d
E s R sG G G
0lims
e sE s
: 13
0
1) aR ss 0 0
1lim lim1 1 0s s
a ae sE s sG s G
2) 2
aR ss
20 00
1lim lim1 lims s
s
a ae sE s sG s sG s
3) 3
aR ss
3 20 00
1lim lim1 lims s
s
a ae sE s sG s s G s
0 0lims
sG s
2
0lims
s G s
0G
0
1/sl
1/sl
l
: 14
0
1
1 !lar t t
l laR ss
(l 1)
pcc p
c p
N sN s N sG s G s G s
D s D s D s
1 1
1
11
m ll l l
m
kka D aE sG s D N s s p s p s s
1 0lk k
pcl
DD a DD N s D N
ll 0
cc l
NGs
1/sl
1/sl
l
: 15
0
1
2
11 p
eK
0e
0e 0e
e e
e1
v
eK
1
a
eK
Kp :
Kv :
Ka :
Steady-state Response : 16
y tu t x = Ax + bu
d(t) :
dG se tr t
y = cx+ dusG s
d s pG s G s G s G s
F
1-1) 1-2)2)
: 17
y tu tdG se tr t
sG s
1-1) 1-2)
11 1 0
11 1 0
nn
n nn
h s h s hs a s a s a
1 21 2 1 0
1 22 1 0
n l n ln l n l
d n l n ln l
q s q s q s qG ss p s p s p
pG s
1lsdG s
Gc(s)
: 18
y tu te tr t
2) 1 2
1 2 1 01 2
2 1 0
n nn n
c l n nn
q s q s q s qG ss s p s p s p
pG s
1c dlG s G s
s
11 1 0
11 1 0
nn
n nn
h s h s hs a s a s a
: 19
y tu te tr t
sG s
1-1) 1-2)
11 2s s
pG s
1s
dG s
22 1 02
1 0
q s q s qs p s p
2) y tu te tr t
pG sdG s sG s
11 2s s
22 1 0
0
q s q s qs s p
: 20
y tu t x = Ax + bu
d(t) :
e tr t
y = cx+ duf
1z tlz t
1k
lkl
l
1 1
2 2
0 1 0 0
10 0 0l l
z zz z u
z z
0
0
x xA b
= +
c
u(t) z1 11
l ss
c I A b
11 l
l
zu k k
z
x
f x f