: 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