2214
.pdfПереходная характеристика
h(t) = Kо*1(t),
где Ко = K1/(1+K1*K2) – коэффициент передачи.
Встречно – параллельное соединение интегрирующего W1(p) = K1/р и пропорционального W1(p) = K2 звеньев.
K1/р
Kо/(То*р + 1)
_
K2
Переходная характеристика
h(t) = Kо(1 – e-t/T )*1(t),
где Ко = K1/(1+K1*K2) – коэффициент передачи; То = Т1/(1+К1*К2) – постоянная времени.
Встречно – параллельное соединение дифференцирующего W1(p) = K1*р и пропорционального W1(p) = K2 звеньев.
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K1*р/(То*р +1) |
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Переходная характеристика
h(t) = K1/То*( e-t/Tо)*1(t),
где То = К1*К2 – постоянная времени.
61
На рис. 27 представлены переходные характеристики ПХ соединения с обратной связью в виде пропорционального звена.
h(t) |
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Рис. 27. ПХ соединения с обратной связью в виде пропорционального звена
Встречно – параллельное соединение пропорционального звена и дифференцирующего или интегрирующего звена в цепи обратной связи позволяет получить подобные выше рассмотренным системам переходные процессы.
Однако параметры коэффициент передачи Ко и постоянная времени То системы определяются по другим зависимостям.
Встречно – параллельное соединение пропорционального W1(p)=K1 и интегрирующего W1(p) = K2/р звеньев.
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Kо*р/(То*р + 1) |
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K2/р |
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1 W1*W2 |
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T0 p 1 |
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p
где K0 = 1/K2, Т0 = 1/K1*K2
62
Переходная характеристика
h(t) = Kо/То *е-t/T.
Встречно – параллельное соединение пропорционального W1(p) = K1 и дифференцирующего W1(p) = K2*р звеньев.
K1
_
К1/(То*р+1)
K2*р
W |
W1 |
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K1 |
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(1 K1* p*K2) |
T p 1 |
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Переходная характеристика
h(t) = K1(1 – е-t/T0),
где То = К1*К2 – постоянная времени.
Переходные характеристики этих структурных схем такие же, как на рисунке 25.
Все рассмотренные структурные схемы с отрицательной
обратной связью (ООС), |
то есть передаточная функция со- |
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единения с ООС определяется |
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Передаточная |
функция соединения с положительной |
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обратной связью (ПОС) определяется |
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Wпос = |
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X 1 W1*W2
63
Методические указания к выполнению контрольной работы
1.Варианты заданий последовательного, параллельного
ивстречно-параллельного соединения и параметров типовых динамических звеньев приведены в табл.7- 9.
2.Изменение параметров задания приведены в табл. 10. В табл. 7 - 10 используются следующие обозначения: П1, П2 – пропорциональные П – звенья; И1, И2 – интегрирующие И – звенья; Д1, Д2 – дифференцирующие Д – звенья;
А – апериодическое А – звено 1-го порядка; Ф – форсирующее Ф - звено 1-го порядка;
П, И и Д звенья с индексом ”1” расположены в прямой
цепи, а эти же звенья с индексом ”2” – в обратной цепи схемы с ООС. Звенья А или Ф располагаются с учетом звеньев П,
И и Д.
К11 – коэффициент передачи 1-го П – звена; К12 – коэффициент передачи 2-го П – звена; К21 – коэффициент передачи 1-го И – звена; К22 – коэффициент передачи 2-го И – звена; К31 – коэффициент передачи 1-го Д – звена; К32 – коэффициент передачи 2-го Д – звена; К4 – коэффициент передачи А – звена; Т1 – постоянная времени А – звена; К5 – коэффициент передачи Ф – звена; Т2 – постоянная времени Ф – звена.
3.Представить последовательное, параллельное и встречно-параллельное соединение.
4.Представить передаточные функции для преобразования трех видов соединений в типовое звено 1-го порядка.
5.Построить в выбранном масштабе переходную характеристику для заданных параметров трех видов соединений h(t) и для измененных параметров трех видов соединений
h*(t).
64
Таблица 7
Варианты заданий параметров типовых динамических звеньев для последовательного соединения
В |
П1 |
П2 |
И1 |
И2 |
Д1 |
Д2 |
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А |
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Ф |
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К11 |
К12 |
К21 |
К22 |
К31 |
К32 |
К |
Т |
К |
|
Т |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
11 |
1 |
4 |
1 |
– |
– |
– |
– |
– |
– |
– |
|
– |
2 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
|
– |
3 |
5 |
4 |
– |
– |
– |
– |
– |
– |
– |
|
– |
4 |
4 |
2 |
– |
– |
– |
– |
– |
– |
– |
|
– |
5 |
10 |
5 |
– |
– |
– |
– |
– |
– |
– |
|
– |
6 |
2 |
4 |
– |
– |
– |
– |
– |
– |
– |
|
– |
7 |
5 |
4 |
– |
– |
– |
– |
– |
– |
– |
|
– |
8 |
2 |
5 |
– |
– |
– |
– |
– |
– |
– |
|
– |
9 |
– |
– |
2 |
2 |
– |
– |
– |
– |
– |
|
– |
10 |
– |
– |
2 |
4 |
– |
– |
– |
– |
– |
|
– |
11 |
– |
– |
1 |
2 |
– |
– |
– |
– |
– |
|
– |
12 |
– |
– |
4 |
1 |
– |
– |
– |
– |
– |
|
– |
13 |
– |
– |
2 |
1 |
– |
– |
– |
– |
– |
|
– |
14 |
– |
– |
5 |
2 |
– |
– |
– |
– |
– |
|
– |
15 |
– |
– |
3 |
5 |
– |
– |
– |
– |
– |
|
– |
16 |
– |
– |
3 |
6 |
– |
– |
– |
– |
– |
|
– |
17 |
– |
– |
– |
– |
2 |
4 |
– |
– |
– |
|
– |
18 |
– |
– |
– |
– |
4 |
2 |
– |
– |
– |
|
– |
19 |
– |
– |
– |
– |
2 |
2 |
– |
– |
– |
|
– |
20 |
– |
– |
– |
– |
5 |
1 |
– |
– |
– |
|
– |
21 |
– |
– |
– |
– |
3 |
1 |
– |
– |
– |
|
– |
22 |
– |
– |
– |
– |
1 |
2 |
– |
– |
– |
|
– |
23 |
– |
– |
– |
– |
2 |
3 |
– |
– |
– |
|
– |
24 |
– |
– |
– |
– |
1 |
3 |
– |
– |
– |
|
– |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
11 |
25 |
5 |
– |
– |
2 |
– |
– |
– |
– |
– |
|
– |
26 |
– |
4 |
2 |
– |
– |
– |
– |
– |
– |
|
– |
27 |
6 |
– |
– |
2 |
– |
– |
– |
– |
– |
|
– |
28 |
– |
2 |
5 |
– |
– |
– |
– |
– |
– |
|
– |
29 |
8 |
– |
– |
4 |
– |
– |
– |
– |
– |
|
– |
65
Продолжение табл. 7
30 |
– |
5 |
3 |
– |
– |
– |
– |
– |
– |
– |
31 |
3 |
– |
– |
2 |
– |
– |
– |
– |
– |
– |
32 |
– |
4 |
4 |
– |
– |
– |
– |
– |
– |
– |
33 |
2 |
– |
– |
– |
– |
3 |
– |
– |
– |
– |
34 |
– |
6 |
– |
– |
4 |
– |
– |
– |
– |
– |
35 |
– |
5 |
– |
– |
4 |
– |
– |
– |
– |
– |
36 |
3 |
– |
– |
– |
– |
5 |
– |
– |
– |
– |
37 |
– |
2 |
– |
– |
4 |
– |
– |
– |
– |
– |
38 |
7 |
– |
– |
– |
– |
2 |
– |
– |
– |
– |
39 |
– |
2 |
– |
– |
3 |
– |
– |
– |
– |
– |
40 |
3 |
– |
– |
– |
– |
6 |
– |
– |
– |
– |
41 |
– |
– |
5 |
– |
– |
4 |
– |
– |
– |
– |
42 |
– |
– |
– |
3 |
2 |
– |
– |
– |
– |
– |
43 |
– |
– |
10 |
– |
– |
2 |
– |
– |
– |
– |
44 |
– |
– |
– |
10 |
4 |
– |
– |
– |
– |
– |
45 |
– |
– |
3 |
– |
– |
4 |
– |
– |
– |
– |
46 |
– |
– |
– |
3 |
2 |
– |
– |
– |
– |
– |
47 |
– |
– |
4 |
– |
– |
2 |
– |
– |
– |
– |
48 |
– |
– |
– |
4 |
5 |
– |
– |
– |
– |
– |
49 |
– |
2 |
– |
– |
– |
– |
4 |
0.5 |
– |
– |
50 |
7 |
– |
– |
– |
– |
– |
2 |
0.1 |
– |
– |
51 |
– |
4 |
– |
– |
– |
– |
– |
– |
1 |
0.5 |
52 |
10 |
2 |
– |
– |
– |
– |
– |
– |
– |
– |
53 |
– |
1 |
10 |
– |
– |
– |
– |
– |
– |
– |
54 |
5 |
– |
– |
4 |
– |
– |
– |
– |
– |
– |
55 |
– |
4 |
5 |
– |
– |
– |
– |
– |
– |
– |
56 |
– |
– |
2 |
5 |
– |
– |
– |
– |
– |
– |
57 |
2 |
– |
– |
5 |
– |
– |
– |
– |
– |
– |
58 |
2 |
5 |
– |
– |
– |
– |
– |
– |
– |
– |
59 |
10 |
– |
– |
2 |
– |
– |
– |
– |
– |
– |
60 |
– |
2 |
– |
– |
– |
– |
10 |
0.2 |
– |
– |
66
Таблица 8 Варианты заданий параметров типовых динамических зве-
ньев для параллельного соединения
В |
П1 |
П2 |
И1 |
И2 |
Д1 |
Д2 |
|
А |
|
Ф |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
К11 |
К12 |
К21 |
К22 |
К31 |
К32 |
К |
Т |
К |
|
Т |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
11 |
1 |
– |
– |
3 |
4 |
– |
– |
– |
– |
– |
|
– |
2 |
4 |
– |
– |
– |
– |
– |
– |
– |
4 |
|
0.1 |
3 |
– |
– |
5 |
– |
– |
2 |
– |
– |
– |
|
– |
4 |
– |
4 |
4 |
– |
– |
– |
– |
– |
– |
|
– |
5 |
– |
– |
– |
– |
2 |
2 |
– |
– |
– |
|
– |
6 |
– |
2 |
– |
– |
– |
– |
10 |
1 |
– |
|
– |
7 |
2 |
– |
– |
– |
– |
4 |
– |
– |
– |
|
– |
8 |
5 |
– |
– |
2 |
– |
– |
– |
– |
– |
|
– |
9 |
– |
– |
5 |
4 |
– |
– |
– |
– |
– |
|
– |
10 |
– |
– |
– |
– |
2 |
2 |
– |
– |
– |
|
– |
11 |
5 |
– |
– |
– |
– |
– |
– |
– |
2 |
|
0.1 |
12 |
2 |
5 |
– |
– |
– |
– |
– |
– |
– |
|
– |
13 |
– |
2 |
– |
– |
– |
– |
5 |
1 |
– |
|
– |
14 |
2 |
– |
– |
6 |
– |
– |
– |
– |
– |
|
– |
15 |
– |
– |
– |
– |
– |
– |
10 |
0.1 |
– |
|
– |
16 |
5 |
– |
– |
– |
– |
2 |
– |
– |
– |
|
– |
17 |
5 |
– |
– |
– |
– |
– |
– |
– |
1 |
|
0.1 |
18 |
– |
– |
4 |
2 |
– |
– |
– |
– |
– |
|
– |
19 |
– |
4 |
– |
– |
2 |
– |
– |
– |
– |
|
– |
20 |
2 |
– |
– |
– |
5 |
– |
– |
– |
– |
|
– |
21 |
– |
– |
2 |
– |
– |
4 |
– |
– |
– |
|
– |
22 |
– |
3 |
2 |
– |
– |
– |
– |
– |
– |
|
– |
23 |
5 |
4 |
– |
– |
– |
– |
– |
– |
– |
|
– |
24 |
– |
2 |
4 |
– |
– |
– |
– |
– |
– |
|
– |
25 |
3 |
2 |
– |
– |
– |
– |
– |
– |
– |
|
– |
26 |
3 |
– |
– |
– |
– |
3 |
– |
– |
– |
|
– |
27 |
– |
– |
– |
– |
4 |
3 |
– |
– |
– |
|
– |
28 |
3 |
– |
– |
– |
– |
– |
– |
– |
2 |
|
0.2 |
29 |
– |
– |
4 |
6 |
– |
– |
– |
– |
– |
|
– |
30 |
4 |
– |
– |
3 |
– |
– |
– |
– |
– |
|
– |
67
Продолжение табл. 8
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
31 |
– |
– |
5 |
– |
– |
8 |
– |
– |
– |
– |
32 |
– |
2 |
– |
– |
– |
– |
10 |
1 |
– |
– |
33 |
4 |
10 |
– |
– |
– |
– |
– |
– |
– |
– |
34 |
5 |
– |
– |
10 |
– |
– |
– |
– |
– |
– |
35 |
– |
3 |
– |
– |
7 |
– |
– |
– |
– |
– |
36 |
3 |
– |
– |
– |
– |
5 |
– |
– |
– |
– |
37 |
– |
– |
3 |
2 |
– |
– |
– |
– |
– |
– |
38 |
– |
2 |
7 |
– |
– |
– |
– |
– |
– |
– |
39 |
4 |
– |
– |
– |
– |
7 |
– |
– |
– |
– |
40 |
– |
0.5 |
– |
– |
– |
– |
– |
– |
2 |
0.5 |
41 |
5 |
4 |
– |
– |
– |
– |
– |
– |
– |
– |
42 |
– |
– |
– |
– |
4 |
1 |
– |
– |
– |
– |
43 |
– |
4 |
– |
– |
2 |
– |
– |
– |
– |
– |
44 |
5 |
– |
– |
– |
– |
– |
4 |
0.2 |
– |
– |
45 |
– |
– |
3 |
2 |
– |
– |
– |
– |
– |
– |
46 |
3 |
– |
– |
2 |
– |
– |
– |
– |
– |
– |
47 |
– |
– |
– |
4 |
2 |
– |
– |
– |
– |
– |
48 |
– |
4 |
– |
– |
– |
– |
– |
– |
5 |
0.1 |
49 |
– |
5 |
4 |
– |
– |
– |
– |
– |
– |
– |
50 |
2 |
– |
– |
– |
– |
– |
– |
– |
2 |
0.4 |
51 |
5 |
1 |
– |
– |
– |
– |
– |
– |
– |
– |
52 |
– |
2 |
4 |
– |
– |
– |
– |
– |
– |
– |
53 |
– |
– |
2 |
4 |
– |
– |
– |
– |
– |
– |
54 |
5 |
4 |
– |
– |
– |
– |
– |
– |
– |
– |
55 |
– |
– |
2 |
1 |
– |
– |
– |
– |
– |
– |
56 |
1 |
2 |
– |
– |
– |
– |
– |
– |
– |
– |
57 |
– |
4 |
2 |
– |
– |
– |
– |
– |
– |
– |
58 |
– |
– |
8 |
2 |
– |
– |
– |
– |
– |
– |
59 |
– |
4 |
6 |
– |
– |
– |
– |
– |
– |
– |
60 |
– |
– |
1 |
2 |
– |
– |
– |
– |
– |
– |
68
Таблица 9 Варианты заданий параметров типовых динамических зве-
ньев для встречно-параллельного соединения
В |
П1 |
П2 |
И1 |
И2 |
Д1 |
Д2 |
|
А |
|
Ф |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
К11 |
К12 |
К21 |
К22 |
К31 |
К32 |
К |
Т |
К |
|
Т |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
11 |
1 |
– |
0.5 |
– |
– |
2 |
– |
– |
– |
– |
|
– |
2 |
10 |
– |
– |
– |
– |
1 |
– |
– |
– |
|
– |
3 |
– |
1 |
– |
– |
– |
– |
– |
– |
10 |
|
1 |
4 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
|
– |
5 |
– |
1 |
5 |
– |
– |
– |
– |
– |
– |
|
– |
6 |
1 |
– |
– |
2 |
– |
– |
– |
– |
– |
|
– |
7 |
– |
2 |
– |
– |
– |
– |
5 |
1 |
– |
|
– |
8 |
– |
– |
– |
– |
– |
1 |
10 |
1 |
– |
|
– |
9 |
5 |
– |
– |
– |
– |
1 |
– |
– |
– |
|
– |
10 |
– |
2 |
– |
– |
5 |
– |
– |
– |
– |
|
– |
11 |
2 |
4 |
– |
– |
– |
– |
– |
– |
– |
|
– |
12 |
– |
1 |
– |
– |
– |
– |
– |
– |
5 |
|
1 |
13 |
4 |
– |
– |
2 |
– |
– |
– |
– |
– |
|
– |
14 |
2 |
2 |
4 |
– |
– |
– |
– |
– |
– |
|
– |
15 |
– |
– |
– |
– |
– |
2 |
4 |
0.1 |
– |
|
– |
16 |
– |
– |
– |
– |
– |
– |
2 |
1 |
– |
|
– |
17 |
5 |
– |
– |
– |
– |
2 |
– |
– |
– |
|
– |
18 |
4 |
2 |
– |
– |
– |
– |
– |
– |
– |
|
– |
19 |
10 |
– |
– |
2 |
– |
– |
– |
– |
– |
|
– |
20 |
– |
2 |
– |
– |
– |
– |
1 |
0.1 |
– |
|
– |
21 |
– |
2 |
4 |
– |
– |
– |
– |
– |
– |
|
– |
22 |
– |
0.5 |
– |
– |
10 |
– |
– |
– |
– |
|
– |
23 |
2 |
– |
– |
1 |
– |
– |
– |
– |
– |
|
– |
24 |
5 |
– |
– |
– |
– |
0.5 |
– |
– |
– |
|
– |
25 |
– |
1 |
2 |
– |
– |
– |
– |
– |
– |
|
– |
26 |
10 |
– |
– |
0.2 |
– |
– |
– |
– |
– |
|
– |
27 |
– |
– |
– |
– |
– |
– |
5 |
1 |
– |
|
– |
28 |
5 |
– |
– |
– |
– |
0.5 |
– |
– |
– |
|
– |
29 |
4 |
1 |
– |
– |
– |
– |
– |
– |
– |
|
– |
30 |
– |
0.2 |
– |
– |
5 |
– |
– |
– |
– |
|
– |
69
Продолжение табл. 9
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
31 |
– |
1 |
– |
– |
– |
– |
– |
– |
5 |
0.2 |
32 |
– |
– |
– |
– |
– |
5 |
5 |
0.2 |
– |
– |
33 |
– |
2 |
8 |
– |
– |
– |
– |
– |
– |
– |
34 |
– |
2 |
– |
– |
– |
– |
8 |
0.5 |
– |
– |
35 |
15 |
– |
– |
2 |
– |
– |
– |
– |
– |
– |
36 |
– |
1 |
– |
– |
– |
– |
– |
– |
6 |
0.2 |
37 |
4 |
1 |
– |
– |
– |
– |
– |
– |
– |
– |
38 |
– |
0.2 |
– |
– |
5 |
– |
– |
– |
– |
– |
39 |
10 |
– |
– |
– |
– |
0.1 |
– |
– |
– |
– |
40 |
10 |
– |
– |
– |
0.2 |
– |
– |
– |
– |
– |
41 |
– |
2 |
4 |
– |
– |
– |
– |
– |
– |
– |
42 |
– |
0.1 |
– |
– |
– |
– |
5 |
0.1 |
– |
– |
43 |
5 |
– |
– |
0.1 |
– |
– |
– |
– |
– |
– |
44 |
10 |
– |
– |
– |
– |
– |
– |
– |
0.2 |
0.2 |
45 |
5 |
2 |
– |
– |
– |
– |
– |
– |
– |
– |
46 |
– |
2 |
– |
– |
5 |
– |
– |
– |
– |
– |
47 |
– |
1 |
– |
– |
– |
– |
– |
– |
10 |
0,2 |
48 |
10 |
– |
– |
– |
– |
2 |
– |
– |
– |
– |
49 |
5 |
– |
– |
– |
– |
– |
– |
– |
2 |
0.4 |
50 |
2 |
– |
– |
– |
– |
5 |
– |
– |
– |
– |
51 |
– |
2 |
10 |
– |
– |
– |
– |
– |
– |
– |
52 |
– |
1 |
– |
– |
– |
– |
1 |
0.5 |
– |
– |
53 |
– |
4 |
5 |
– |
– |
– |
– |
– |
– |
– |
54 |
1 |
– |
– |
– |
– |
– |
– |
– |
1 |
0.5 |
55 |
– |
1 |
– |
– |
– |
– |
10 |
0.2 |
– |
– |
56 |
– |
1 |
2 |
– |
– |
– |
– |
– |
– |
– |
57 |
10 |
– |
– |
– |
– |
– |
– |
– |
10 |
0.5 |
58 |
– |
1 |
– |
– |
– |
– |
1 |
0.2 |
– |
– |
59 |
5 |
1 |
– |
– |
– |
– |
– |
– |
– |
– |
60 |
– |
1 |
4 |
– |
– |
– |
– |
– |
– |
– |
70