《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

Gsssss==

++++

(2

(3

T

3Tx1=x(GjKCOT=-oo-+-=+jTKjG(0(T

((

(20.5sin302.86

sin27.14ssc111=-+-=+Re

Im

C0=cO

co+

=0(n

(T+-TKRe

ImO

CD=OO

1

X3=+

=0325

-KI

1(([(222+-=(O(OT(O(OTCDTTjTKjG+-22

11==

TTycoj

TTTTKj

jGy4.1

((2121-=+-=(oRe

Im

00

3=3=83-1

31.4

5.4(110010((1(10

(1(0.11

Gsssss

++++

0.20.4120

040

-20

-40

2104100

2040dB

L(cos

rad

(o[-40]

[-20]

[0]

(2

0.20.4120

040

-20

-40

210420

dB

L(cos

rad

co

[-601

[-20]

2

2

121120.250.94radsrncoco^

=_=_•=

2

2

11

201g201g

201g

6.142120.2510.25

rMdB

(3

0.2

0.4

1

20

040

-20

-40

2

1()

4

10()

20

40

dB

L(ws

rad

co

[-40]

[-20]

[-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=()Z=P-2N=2不稳定(4P=()

Z=P-2N=0

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

P=1

Z=P-2N=2

不稳定

5.7(1

(2

(3

()0=-=-=-+NNN110-=-=-=-+NNNO

00=_=_=_+NNN

1

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

ll=-=-=_+NNN

2

12

10=.==+NNN2

1210-=-=-=-+NNN

1(1(1(100(100101.01101

4-4-4-=

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

Aco

cocoO10

s

900.257.31802.16rad

tgCDCDCD-——•

5

.1,

1211(2

2

==++=

KK

Aco

CD

3

COS

tgtg

rad

2

20

1

1

707

.0,180290=

(DttXoO

1

18()

22.0290-=+-----cocotgtg

大于零，系统稳定。

只要K,00

为

00.020.040.060.080.10.12

0.2

0.4

0.6

().8

1

1.2

1.4

StepResponse

Time(sec

Amplitude

00.20.40.60.811.2

0.2

0.4

0.6

().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(33=

===++,

(201g20.0520nLdBco=-=210

(10201g

40,

0.05KLdBK==-=

5.10

由sc

Kt71

3=

可知:快速性提高。

1

1

10

5

.86142.687.7890

025.05.25.090

180

二一十二一一+-二—c

CCtg

tg

tg

cococoyO

1

95

.89001.090180,1.0=-=-tg

sradcyo)55.7,78.1=Ksradcco414.1,l=Ks

radc

co708

.(),

1==Ksradc

co

5.11707.04=^cos

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

((KKlmK

KssTsTsK

sTsK

①二

+++++

K

Tm21=

，，不变(稳定裕度不变

2

22

(12(121bn33殳=-+

-+

5.13

11=+=

P

ssrKe35

.01

12

416==

v

ssrKe%

8.4%100%2

l=x=一4

A

oe05

.006.13

co,Stnss

radnnc8.2707.0707.02=-=cococo=0

63

=ydBKgsradgoo=oo=(D0,l==rrMo)s

radnb4==CDCO0

1

1

110