????????????????(Stability)?????(Steady-State Error)?????(Transient Response)

1
???????
2
??

• ????????????????(Stability)?????(Steady-State
  Error)?????(Transient Response)
• ?????,?????????????
• ?????????(Stability Criterion)?????(Root Locus
  Method)????(Frequency Method)
• ??

3
3.1. ??????????????

• ????
• ??????????????r(t)?????,???????,?????????
• ????????????
• 1??????
• 2??????
• 3???????

4
3.1.1. ??????

• ????????????? ??????

• ?????????????????????,???????????

• ??????????????????

5
(?)???? (Step Signal)
A1?,????????,?1(t)??
6
(?)????(Ramp Signal)
?A1?,?????????
7
(?)????? (Parabolic Signal)
?A1?,??????????
8
(?)???? (Impulse Signal)
?e ???????????????(??d(t) ??)?
9
(?)????(Sin Signal)
A???
T???,w 2p/T????
10
3.1.2. ???????

• ????????????

• ???????????????????????????

• ?????????

11
????
????
2?????td (time delay)?????????50?????
3?????tr (rise time)????
4?????tp (peak time)????????????????
5?????ts(settling time)
12
??????
?????sp
????td
????tp
????tr
????ts
13
??????

• ????,????

????????,??????????????????????????
14
3.1.3. ???? (Transient Response )
(?)?????????
?????????????,??t ????????
15
????????
??????
16
(?)?????????
17
(?)?????????

• ????,
• wn??????????

18
??(2-2)?R-L-C????
?R0??????
19
??????????
20
?????????????
???

• 0ltzlt1,?????
• z 1,??????
• z gt1,?????

21
? 0ltzlt1 ,?????
??r(t)1(t)
22
0ltzlt1 ,?????(?)
?t?8?,????e (8)0?
23
z0,?????
?????????????s1,2 jwn
24
? z 1,??????
??????????s1 s 2 -wn
???,???,??????
25
? z gt1,?????
26
?????(?)
???,????? z 1??
27
??z????????????????
28
???????????
????????d(t),?R(s)1
29
??z ???????????
30
(?)?????????????
??????????? ????? ?????? ?????
31
????tr (rise time)
c(tr)?1
32
????tp (peak time)
????????wd tp p
????
33
?????sp (percent overshot)
??t tp
34
????ts (settling time)
?z 0.69(?0.77),ts????,??ts?z ???????????
T1/zwn
??????????z ????????????ts????
35
????ts(????)
36
??

• ?wn??,???tr?tp,????z ?,???ts????zwn?,??z
  ??????,????
• ??wn,??tr,tp?ts???
• ?????sp??z ??,z ??,sp???

37
3.1.4. ???????????
?????????????
38
???????????(2)
?????????????
39
??

• ??????????????????????????????????????????????????
  ??????????
• ????????????????????????????????
• ?????????????????,??????????????

40
3.2. ???????????????
41
??????????
???????
42
??????
43
????
??
????????????????,???????????1/10???,?????????,????
???????????(???????)??,??????????????????????????,
?????????
44
????example
????
???????????????????
45
????example(?)
???????????????????????????(?????)????
????????????,?????????????????c1(t)??????????,????
????
46
????
?z 0.45?,????????????????????????
t ???0.9,??????-1.11,??????????12,?????8.8?
?t 2.25?,?????-1/t -0.444,?????????
-0.45,??????,???????,??????
47
?????
???????????,????????????,??????????????
??????????
48
?????????
49
?3.1
1????????????,???????(?????)?1,????????????????
?
50
?3.1(?)
2? ??MATLAB???????,??????? ???
A ?????,???sp37,????ts1.6?

• ??????????

• ??????????????????????,??????

• ??????????????????????,??????

51
3.3. ???????????
????????
????

• ???????????????

• ?????????????,??????????

• ???????????????????????????????

52
3.3.1. ??????? (Steady-State Error)
53
????e(t)?????r(t)???????
????
????????????????????
54
3.3.2. ???????
???N????????????????????????????????????,???????N?
???????,????????,???????,?????N2
55
(?)????????????
??????
56
(?)????????????
??????
57
(?)???????(??????)????????
???????
58
??????
????????????????,?????????????,N??????????????
59
?3.2
60
3.3.3. ????????????
?????,?????????????,??????????????,?????????,?????
?????,????????
??
???
61
????????????(?)
R(s)0
????????????
?????????n(t)1(t)
62
3.3.4. ??????????

• ?????????????????????????????????????????????????
  ????????
• ????????????,???????,????????????????
• ????????????????,?????????
• ?????????????,??????

63
?????????????????
??????????
64
??????????????
65
????????
66
3.4. ??-?????????
??????????

• ??-????(Routh-Hurwitz)??,??????
• ????,?????????
• ????(Nyquist)??,???????????
• ??????? ,?????????????

67
3.4.1. ???(Stability)???
??????????,????????,?????????,?????????????,??????
??
??
?????????,????????????????????????,????BIBO??
68
????
????k???-pi(i1,2,,k),r??????(-s ijw i )
(i1,2,,r),k2rn
69
??

• -pi lt0,-s i lt0(?????????),????????????????wi?0,???
  ?????????wi 0,?????????????
• ?-pi?-s i????????????,???????
• ??-pi??????,?-s i??????(??????),???????????

70
?????????????
??????????,?????????

?????,??????????

???????S???????
71
??????????
72
3.4.2. ????(Routh Criterion)
(?)??????????
73
??
?????n??,??k???- p j (j1,2,,k),r???-s ijw i
(i1,2,,r),n k2r??????????
????????????,?- p j lt0,-s ilt0,?p j gt0,s
igt0?????????????,?????????????
74
(?) ????
?????????,????, ????????,?????????????????????????

75
?3.3
?
1????????????????,???????????
2???????? s4 1
12 6 s3
6 11 0
s2 61/6 6
s1 455/61 0
s0 6
3???????????,?????
76
?3.4
1???????? s5 1 2
5 s4 3
1 6 s3 5
9 (??????3)
s2 -11 15 (??????5/2)
s1 174
(??????11) s0
15
?
2???????,?????????????????????(5?-11?
174),???????????????
77
???? (1)
?????????????????,????????(??????)
?
1?????? s 3 1 1
s
2 2 2
s 1 e
s 0 2
????????e ????
2?e ???????(2?2)????,?????????? ,????????
78
???? (2)
?????????(???k?)????????,????????????????,????????
??
????
???k-1???????????,?????????
???????s???,????????,???k?
?????????
??????????????????????
79
?3.6
?
1???????? s 3 1 16
s 2 10 160 ?????10s 2
160 s 1 0 0
???? 20
0 ???? 20s 0
s 0 160
2???????????,?????????????
80
?3.7
?
1???????? s 5 1 3 -4
s 4 2 6 -8 ????? 2s 4 6s 2 -
8 s 3 0 0 0
???? 8 12 0
???? 8s 3 12s s 2
3 -8 s 1 100/3
s 0 -8
2????????,?????????? ,?????
81
(?) ???????1???????
?????????????,??????????s 1
82
?3.8
?
1?????? s 3
2 13 s
2 10 4
s 1 12.2 s
0 4
2?????????,?????s???????
83
?3.8(?)
4???????? z 3 2
-1 z 2 4
-1 z 1 -1/2
z 0 -1
5??????????,????????s -1???,????????1
84
2. ?????????????
85
?3.9
?
86
3. ??????????
??
?????????????????,???????????
???????
87
(1)???????????????
?n????
??????????,n ?????,?????? ????
88
(2)???????
????????p(s)/q(s)???e-t s??(pade)??
???m?,???n? ,m?n???,???????????????,??????????????

89
?3.5
90
K?????1.13
91
3.4.3. ??????
???????? ansnan-1sn-1a1s
a0 0
92
??????(Hurwitz Criterion)
???????????????????angt0????,???????????i
(i1,2,,n)?????
n1
a1gt0,?1 a0gt0
n2
93
n3
n4
94
?3.10
?
1????????????????,?????????
??????
95
3.5. ????????? (sensitivity)
G(s)H(s)gtgt1
????????G(s)H(s)??????G(s)???????
96
????
?C(s)?G(s)R(s)
G(s)?G(s)
????
G(s)H(s)gtgt?G(s)H(s)
97
?????????
?????????????????????????
??
GB(s)C(s)/R(s)
98
??????????1
?????????????????????????,??????????????????
99
??????????????
k R1/Rf
100
Agtgt1?
????????????(??????Rf )?,?????A???????1
A104??k 0.1
101
????
??????????????
?????????????
???????????,????????
???????,???????????????,???????,????????
?? ???????G(s)????????????
??????????????? ?????????????
? ?????????????