MATLAB

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m b l I F

對一階倒立擺系統中的小車和擺桿進行受力分析，其中，N

把這個等式代入式(1-1)中，就得到系統的第一個運動方程：

,

d

把上式代入方程組（2-1）的第二個方程，得：

..

I

I

],

4.實際系統的模型參數如下:

M

m

b

l I

:den

=

=10

系統的開環極點為（s):

lili

sys

sys

(sec):

sys

(sec):

0.5

(sec)

1.5

11>>

A

=

A

= >>

B

=>>

=

=

12

MATLAB

I

r

(

)

(

)e

r

13

K

K

e

e

dt

dt

I

de

K

K

E

()

()

P

IK

P I E

E

K

K

I

K

K

K

K

P I

(

)

I I

r

14dendennum

F

F

num

dennum F

dennum num

den

q num bI

M

m bmgl den

q q q q

[(M

m)(

I

)(

)]

K

K

K

K

K

K

I

I

15

r

num

den

F

F

num

den

numden

Fden

den

num

den

num

den

num

den

I

g

16

bI

bI

M

m bmglI

q q

q q q

q

[(M

m)(

I

)(

)]den =den

=den

()

(num)()()(den

)

()(num

)

F

()

MATLAB

17

(sec)

=

18

ititm

(sec)

19

(sec)

(sec)

20

(sec)

lili

(sec)

21

m

=

m

=

b

=

I

=

g

=

q

=

=

=

=

=

=

Ki

=

=

=

Ki];

=

num

=

den

=

));

=

=

p

Kp=150，Ki=50，Kd=50，階躍響應仿真曲線如下圖所示

=22

23

M

m

b

l

I

C

24

仿真程序如下：

[

]

[C

]

K

r

J

25

ii i ii i

rirr

,26

=

m

=

b

=

I

=

g

=

l

=

p

=

A

=

B

=

];

=

=

p

=

K

=

=

=

R

=

K

=

LQR

=

[(A-B*K)];