《自动控制原理》5章课后习题参考答案

习题

5.1246K=,T=1

5.2

5,3(163

(d(2

(1(0.51

Gss$$s==

++++

(2

(3

T

coTxl=x(GjKCOT=-oo-+-=-ljTKjG(0(T

((

(20.5sin302.86

sin27.14ssc111=+-=+Re

Im

3=00

3+

=0(0

(T+-TKRe

ImO

(o=oo

1

X(0=+

=0co25

-1(]

1(([(222+-=(I)(OTO)(OTWTTjTKjG+-22

ll==

TTycoj

TTTTKj

jGy4.1

((2121-=+-=o)Rc

Im

00

CO=(D=oc(O-1

31.4

5.4(110010((1(10

(1(0.11

Gsssss=

++++

0204120

040

-20

-40

2104100

2040dB

L(cos

rad

co[-4O]

[-20]

[0]

(2

0.20.4120

040

-20

-40

210420

dB

L(o)s

rad

co

[-60]

1-20]

2

2

12112O.25O.94radsrn(o0^

2

2

11

201g201g

201g

6.142120.2510.25

rMdB运

(3

0.2

0.4

1

20

040

-20

-40

2

10

4

100

20

40

dB

L(cos

rad

co

[MO]

[-201

[-40]

200

5.5

5.6题号开环极点穿越负实轴次数

奈氏判据闭环极点闭环系统（1P=0Z=P-2N=2不稳定（2P=0Z=P-2N=0稳定

（3P=0Z=P-2N=2不稳定（4P=0

Z=P-2N=0

稳定（5P=1Z=P-2N=0稳定（6P=0Z=P-2N=0稳定（7P=0Z=P-2N=0稳定（8

P=1

Z=P-2N=2

不稳定

5.7（1

（2

（3

00=-=.=-+NNN110-=-=-=-+NNNO

00=-=-=-+NNN

1

10-=-=-=-+NNN011=-=-=-+NNNO

1-NNN

2

12

10=-=-=-+NNN2

1210-=-=-=-+NNN

1(1(1(100(100101.01101

+++=

SSSSGa

K

1(10(40

1

2

c++=

SSSSG

l(l(1.0(1001401f++=

SSS

SGb100((0.11

GSSS=

+

1(

10000(6

.311

2e+=

SSSG

1001.0(11.0(l(1.0(d+++=

SSSSSG61

.054

.0154.0,

11(2

2

=+==+=

KK

Aw

CDCDOIO

s

900.257.31802.16rad

tg(0(0(0--•

5

.1,

1211(2

2

==++=

KK

Aco

3

3

COS

tgtg

rad

2

20

1

1

707

.0,180290==

cowcoO

1

1

180

22.0290-=+---cowtgtg

大于零，系统稳定。

只要K,00

>Y

00.020.040.060.080.10.12

0.2

0.4

0.6

0.8

1

1.2

1.4

StepResponse

Time(sec

Amplitude

00.20.40.60.811.2

0.2

04

0.6

0.8

1

1.2

1.4

StepResponse

Time(sec

Amplitude

5.8(1

(2

(3

5.9g2

2(0.05

10(0.010.011

nK

Gssss^(o(o=

===++,

(201g20.0520nLdBw=-=210

(10201g

40,

0.05KLdBK==-=

5.10

由sc

Kt兀

(0二

可知了快速性提高。

1

1

10

5

.86142.687.7890

025.05.25.090

180

=.■+

cctg

tg

tg

(oocoyO

1

95

.89001.090180,LO=-==-tg

sradcyco55.7,78.1=Ksradcco414.1,l==Ks

rad

0)708

.0,

1==Ksradc

co

5.11707.04==^(os

rad

n

(1

I型系统,r(t=l(2

I型系统,r(t=t(3(4

(5

(6(7

5.12

K增大和T减少

KssTsTsK

sTsK

<D=

+++++

K

Tm21=

，，不变(稳定裕度不变

2

22

(12(121bn0)3坛=-+

■+

5.13

11=+=

P

ssrKe35

.01

12

416==

v

ssrKe%

8.4%100%2

1=X=・&

岐

oe05

.006J3

.4J，

团

co,Stnss

radnnc8.2707.0707.02==o(oo)=0

63

=ydBKgsradgoo=x=co0,l==rrM(os

radnb4==co(o0