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Файл:Автоматизация процессов химических производств. Учебное пособие
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ɍɪɚɜɧɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɜɟɪɯɧɟɣ (ɭɤɪɟɩɥɹɸɳɟɣ) ɱɚɫɬɢ ɤɨɥɨɧɧɵ:
x
f
f
f
f
R
yx
R1 R1
ɞ
, (285)
ɝɞɟ y, x – ɫɨɫɬɚɜɵ ɩɚɪɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡ ɜɟɪɯɚ ɤɨɥɨɧɧɵ, ɦɨɥɹɪɧɵɟ ɞɨɥɢ;
– ɫɨɫɬɚɜ ɞɢɫɬɢɥɥɹɬɚ.
x
ɞ
x
ɞ
Ɉɛɨɡɧɚɱɢɦ:
ɍɪɚɜɧɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɧɢɠɧɟɣ (ɢɫɱɟɪɩɵɜɚɸɳɟɣ) ɱɚɫɬɢ ɤɨɥɨɧɧɵ:
btg
11
;
R1 R1
G
fG .
ɝɞɟ
ɞ
1
bx
Ɉɛɨɡɧɚɱɢɦ:
2
R1
k
R
D
yxx
;
tg
D
.
R1
R1 R1
R
2
R1
f
k
, (286)
ɉɨɫɬɪɨɟɧɢɟ ɪɚɛɨɱɢɯ ɥɢɧɢɣ ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ (ɪɢɫ. 92).
Ɋɢɫ. 92. ɉɨɫɬɪɨɟɧɢɟ ɪɚɛɨɱɢɯ ɥɢɧɢɣ ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ:
1 – ɪɚɜɧɨɜɟɫɧɚɹ ɥɢɧɢɹ ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ, 2 – ɥɢɧɢɹ ɪɚɜɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɩɚɪɨɜɨɣ
ɢ ɠɢɞɤɨɣ ɮɚɡ ɤɨɦɩɨɧɟɧɬɚ Ⱥ ɜ ɤɨɥɨɧɧɟ
ɋɨɫɬɚɜɵ ɩɚɪɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡ ɜ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɱɚɫɬɹɯ ɤɨɥɨɧɧɵ ɪɚɜɧɵ,
ɬ. ɟ. ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɥɢɧɢɢ 2.
ɧɚɯɨɞɹɬ ɬɨɱɤɭ ɋ.
ɉɨ x
ɞ
ɧɚɯɨɞɹɬ ɬɨɱɤɭ Ⱥ.
ɉɨ x
ɤ
101
ɉɨ xf ɩɪɨɜɨɞɹɬ ɜɟɪɬɢɤɚɥɶ.
x
f
f
f
K
ɞ
ɉɨ ɨɫɢ y ɨɬɤɥɚɞɵɜɚɸɬ ɜɟɥɢɱɢɧɭ
b
1
ɉɨɥɭɱɚɸɬ ɬɨɱɤɭ Ɇ ɧɚ ɩɟɪɟɫɟɱɟɧɢɢ ɋD ɫ ɜɟɪɬɢɤɚɥɶɸ ɨɬ x
ɉɨɥɭɱɚɸɬ ɋɆ
ɉɪɨɜɨɞɹɬ ɆȺ
– ɪɚɛɨɱɭɸ ɥɢɧɢɸ ɜɟɪɯɚ ɤɨɥɨɧɧɵ.
– ɪɚɛɨɱɭɸ ɥɢɧɢɸ ɧɢɡɚ ɤɨɥɨɧɧɵ.
ɢ ɩɨɥɭɱɚɸɬ ɬɨɱɤɭ D.
R1
.
f
Ⱦɢɚɝɪɚɦɦɚ «Ɋɚɛɨɱɚɹ ɥɢɧɢɹ – ɥɢɧɢɹ ɪɚɜɧɨɜɟɫɢɹ» ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ
(ɪɢɫ. 93).
Ɋɢɫ. 93. Ⱦɢɚɝɪɚɦɦɚ «Ɋɚɛɨɱɚɹ ɥɢɧɢɹ-ɥɢɧɢɹ ɪɚɜɧɨɜɟɫɢɹ» ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ:
1 – ɪɚɜɧɨɜɟɫɧɚɹ ɥɢɧɢɹ ɩɪɨɰɟɫɫɚ ɛɢɧɚɪɧɨɣ ɪɟɤɬɢɮɢɤɚɰɢɢ, 2 – ɥɢɧɢɹ ɪɚɜɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ
ɜ ɩɚɪɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɚɯ
Ʌɢɧɢɹ ɋɆ – ɪɚɛɨɱɚɹ ɥɢɧɢɹ ɜɟɪɯɚ ɤɨɥɨɧɧɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ:
x
ɞ
btg
11
;
R1 R1
R
D
G
;
ɮɥ
R
.
G
ɞ
Ʌɢɧɢɹ ɆȺ – ɪɚɛɨɱɚɹ ɥɢɧɢɹ ɧɢɡɚ ɤɨɥɨɧɧɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ:
1
bx
2
R1
;
tg
D
k
2
R
R1
;
fG .
G
ɞ
Ⱥɧɚɥɢɡ ɞɢɚɝɪɚɦɦɵ «Ɋɚɛɨɱɚɹ ɥɢɧɢɹ – ɥɢɧɢɹ ɪɚɜɧɨɜɟɫɢɹ»
ɉɨ ɞɢɚɝɪɚɦɦɟ ɨɩɪɟɞɟɥɹɸɬ ɫɥɟɞɭɸɳɢɟ ɩɚɪɚɦɟɬɪɵ:
ɑɢɫɥɨ ɫɬɭɩɟɧɟɣ ɪɚɡɞɟɥɟɧɢɹ, ɱɢɫɥɨ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɬɚɪɟɥɨɤ n
n
ɬ
ɚɥɶɧɵɯ ɬɚɪɟɥɨɤ
n
, ɝɞɟ Ș – ɄɉȾ ɬɚɪɟɥɤɢ.
ɢ ɱɢɫɥɨ ɪɟ-
ɬ
102
Ⱦɜɢɠɭɳɭɸ ɫɢɥɭ ɩɪɨɰɟɫɫɚ ɜ ɥɸɛɵɯ ɬɨɱɤɚɯ ɤɨɥɨɧɧɵ:
x
x
f
*x
x' ,
i
GGo , ɢ ɫɪ' .
y
Ⱦɜɢɠɭɳɢɟ ɫɢɥɵ
ɨɬ ɪɟɠɢɦɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɰɟɫɫɚ, ɨɩɪɟɞɟɥɹɸɳɢɯ ɩɨɥɨɠɟɧɢɟ ɪɚɜɧɨ-
*
y
i
,
yy' ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɫɫɨɩɟɪɟɞɚɱɢ
ɢ
''ɡɚɜɢɫɹɬ:
ɫɪ
i
ɜɟɫɧɨɣ ɤɪɢɜɨɣ (Ɋ ɢ ș);
ɨɬ x
, xɞ, xɤ – ɨɩɪɟɞɟɥɹɸɳɢɯ ɩɨɥɨɠɟɧɢɟ ɪɚɛɨɱɟɣ ɥɢɧɢɢ ɩɪɨɰɟɫɫɚ;
f
G
ɨɬ R = G
ɨɬ ɬɟɩɥɨɜɵɯ ɩɚɪɚɦɟɬɪɨɜ G
/ Gɞ ɢ
ɮɥ
fG , ɬ. ɟ. ɨɬ G
ɞ
.
f
, Gɞ, Gf;
ɮɥ
Ɍɪɟɛɭɟɦɭɸ ɞɜɢɠɭɳɭɸ ɫɢɥɭ ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ ɦɨɠɧɨ ɨɛɟɫɩɟɱɢɬɶ:
ɫɬɚɛɢɥɢɡɚɰɢɟɣ ɪɟɠɢɦɧɵɯ ɩɚɪɚɦɟɬɪɨɜ Ɋ ɢɥɢ ș;
ɫɬɚɛɢɥɢɡɚɰɢɟɣ ɩɚɪɚɦɟɬɪɨɜ ɩɨɬɨɤɚ ɩɢɬɚɧɢɹ G
ɫɬɚɛɢɥɢɡɚɰɢɟɣ ɢɥɢ ɢɡɦɟɧɟɧɢɟɦ ɮɥɟɝɦɨɜɨɝɨ ɱɢɫɥɚ R = G
ɢ șf;
f
ɮɥ
Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ
ɋɯɟɦɚ ɪɟɤɬɢɮɢɤɚɰɢɨɧɧɨɣ ɭɫɬɚɧɨɜɤɢ (ɪɢɫ. 94).
/ Gɞ.
Ɋɢɫ. 94. ɋɯɟɦɚ ɪɟɤɬɢɮɢɤɚɰɢɨɧɧɨɣ ɭɫɬɚɧɨɜɤɢ:
1 – ɪɟɤɬɢɮɢɤɚɰɢɨɧɧɚɹ ɤɨɥɨɧɧɚ, 2 – ɩɨɞɨɝɪɟɜɚɬɟɥɶ ɩɨɬɨɤɚ ɩɢɬɚɧɢɹ, 3 – ɤɢɩɹɬɢɥɶɧɢɤ,
4 – ɤɨɧɞɟɧɫɚɬɨɪ (ɞɟɮɥɟɝɦɚɬɨɪ), 5 – ɮɥɟɝɦɨɜɚɹ ɟɦɤɨɫɬɶ
103
Ɉɩɢɫɚɧɢɟ ɭɫɬɚɧɨɜɤɢ
x
Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ – ɪɟɤɬɢɮɢɤɚɰɢɨɧɧɚɹ ɭɫɬɚɧɨɜɤɚ ɞɥɹ ɜɵɞɟɥɟɧɢɹ ɢɡ ɢɫ-
ɯɨɞɧɨɣ ɠɢɞɤɨɣ ɫɦɟɫɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɫɨɫɬɚɜɟ ɞɢɫɬɢɥɥɹɬɚ.
ɉɪɨɰɟɫɫ ɦɚɫɫɨɩɟɪɟɞɚɱɢ ɩɪɨɢɫɯɨɞɢɬ ɧɚ ɬɚɪɟɥɤɚɯ ɭɤɪɟɩɥɹɸɳɟɣ (ɜɟɪɯɧɟɣ) ɢ
ɢɫɱɟɪɩɵɜɚɸɳɟɣ (ɧɢɠɧɟɣ) ɱɚɫɬɟɣ ɤɨɥɨɧɧɵ ɜ ɪɟɡɭɥɶɬɚɬɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɠɢɞɤɨɣ
ɢ ɩɚɪɨɜɨɣ ɮɚɡ, ɞɜɢɠɭɳɢɯɫɹ ɜ ɤɨɥɨɧɧɟ ɩɪɨɬɢɜɨɬɨɤɨɦ.
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ – ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɪɚɜɧɨɜɟɫɧɨɣ ɢ ɪɚɛɨɱɟɣ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ
ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ
ɜ ɠɢɞɤɨɣ ɢɥɢ ɩɚɪɨɜɨɣ ɮɚɡɟ:
*
xx' ɢ *yyy' , ɫɨ-
ɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɋɚɛɨɬɚ ɭɫɬɚɧɨɜɤɢ
ɂɫɯɨɞɧɚɹ ɫɦɟɫɶ G
ɬɟɦɩɟɪɚɬɭɪɵ ɤɢɩɟɧɢɹ ș
) ɧɚɝɪɟɜɚɟɬɫɹ ɜ ɩɨɞɨɝɪɟɜɚɬɟɥɟ ɩɨɬɨɤɚ ɩɢɬɚɧɢɹ 2 ɞɨ
ɩ (Gxf
ɢ ɩɨɞɚɟɬɫɹ ɜ ɤɨɥɨɧɧɭ 1 ɧɚ ɬɚɪɟɥɤɭ ɩɢɬɚɧɢɹ (i = f).
ɩ0
ɂɫɯɨɞɧɚɹ ɫɦɟɫɶ ɫɬɟɤɚɟɬ ɩɨ ɬɚɪɟɥɤɚɦ ɧɢɠɧɟɣ ɱɚɫɬɢ ɤɨɥɨɧɧɵ ɜ ɜɢɞɟ ɠɢɞ-
ɤɨɫɬɧɨɝɨ ɩɨɬɨɤɚ G
ɜɵɦ ɩɨɬɨɤɨɦ G
ɂɡ ɤɭɛɚ ɤɨɥɨɧɧɵ ɜɵɜɨɞɢɬɫɹ ɤɭɛɨɜɵɣ ɩɪɨɞɭɤɬ G
ɩɨɞɚɟɬɫɹ ɜ ɤɢɩɹɬɢɥɶɧɢɤ 3, ɝɞɟ ɢɫɩɚɪɹɟɬɫɹ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɚɪɨɜɨɝɨ ɩɨɬɨɤɚ G
ɜ ɤɭɛ ɤɨɥɨɧɧɵ, ɭɱɚɫɬɜɭɹ ɜ ɦɚɫɫɨɨɛɦɟɧɧɨɦ ɩɪɨɰɟɫɫɟ ɫ ɩɚɪɨ-
x
.
y
. ɑɚɫɬɶ ɤɭɛɨɜɨɝɨ ɩɪɨɞɭɤɬɚ
ɤɭɛ
y0
ɤɨɬɨɪɵɣ ɩɨɞɚɟɬɫɹ ɜ ɧɢɡ ɤɨɥɨɧɧɵ.
ɉɚɪɨɜɨɣ ɩɨɬɨɤ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɤɨɥɨɧɧɵ, ɤɨɧɬɚɤɬɢɪɭɹ ɫ ɠɢɞɤɢɦ ɩɨɬɨ-
ɤɨɦ ɢ ɨɛɨɝɚɳɚɹɫɶ ɰɟɥɟɜɵɦ ɤɨɦɩɨɧɟɧɬɨɦ.
Ɉɛɨɝɚɳɟɧɧɵɣ ɰɟɥɟɜɵɦ ɤɨɦɩɨɧɟɧɬɨɦ ɩɚɪɨɜɨɣ ɩɨɬɨɤ G
ɜɵɜɨɞɢɬɫɹ ɢɡ ɜɟɪ-
yn
ɯɚ ɤɨɥɨɧɧɵ ɢ ɩɨɞɚɟɬɫɹ ɜ ɞɟɮɥɟɝɦɚɬɨɪ 4, ɝɞɟ ɤɨɧɞɟɧɫɢɪɭɟɬɫɹ.
Ʉɨɧɞɟɧɫɚɬ ɫɨɛɢɪɚɟɬɫɹ ɜɨ ɮɥɟɝɦɨɜɨɣ ɟɦɤɨɫɬɢ 5. ɂɡ ɫɛɨɪɧɢɤɚ ɮɥɟɝɦɵ ɨɬɛɢ-
ɪɚɟɬɫɹ ɞɜɚ ɩɨɬɨɤɚ:
ɩɨɬɨɤ ɞɢɫɬɢɥɥɹɬɚ G
ɩɨɬɨɤ ɮɥɟɝɦɵ G
– ɰɟɥɟɜɨɣ ɩɪɨɞɭɤɬ;
ɞ
– ɠɢɞɤɚɹ ɮɚɡɚ, ɢɫɩɨɥɶɡɭɟɦɚɹ ɞɥɹ ɨɪɨɲɟɧɢɹ ɜɟɪɯɚ
ɮɥ
ɤɨɥɨɧɧɵ.
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɫ
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ – ɨɛɟɫɩɟɱɟɧɢɟ ɫ
– ɤɨɧɰɟɧɬɪɚɰɢɹ ɞɢɫɬɢɥɥɹɬɚ.
ɞ
= ɫ
.
ɞ
ɞɡɞ
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɰɟɫɫɚ ɪɟɤɬɢɮɢɤɚɰɢɢ (ɱ. 2)
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɪɟɤɬɢɮɢɤɚɰɢɨɧɧɨɣ ɭɫɬɚɧɨɜɤɢ (ɪɢɫ. 95).
,
104
Ɋɢɫ. 95. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɪɟɤɬɢɮɢɤɚɰɢɨɧɧɨɣ ɭɫɬɚɧɨɜɤɢ
U
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɧɢɡɚ ɤɨɥɨɧɧɵ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɤɭɛɚ ɢ ɤɢɩɹɬɢɥɶɧɢɤɚ (ɪɢɫ. 96).
Ɋɢɫ. 96. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɤɭɛɚ ɢ ɤɢɩɹɬɢɥɶɧɢɤɚ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɧɢɡɚ ɤɨɥɨɧɧɵ (șɧ = ș0 ).
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
d
T
VC G r G C G r GC
kk pk x px x y k k pk
ɧ
. (287)
ɝɪ ɝɪ 111 0 ɧ
dt
TT
105
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
x
M
G
ɇɚ ɨɫɧɨɜɚɧɢɢ (287) ɢ (288) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
șɧ = f (Gɝɪ, Gɤ).
ɝɪ rɝɪ
+ Gɯ1 C
șɯ1 = Gy0 rk + GkCpkșɧ. (288)
1
ɪɯ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ Gɝɪ.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɜɫɟɦɭ ɜɟɳɟɫɬɜɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
G
dh
U
k
. (289)
SGGG
kk x k y
dt
10
= Gk + Gy0, (290)
x1
ɝɞɟ ȡk – ɩɥɨɬɧɨɫɬɶ ɤɭɛɨɜɨɣ ɠɢɞɤɨɫɬɢ, ɤɝ/ɦ3;
– ɫɟɱɟɧɢɟ ɤɭɛɚ ɤɨɥɨɧɧɵ, ɦ2;
S
k
h
– ɭɪɨɜɟɧɶ ɤɭɛɨɜɨɣ ɠɢɞɤɨɫɬɢ, ɦ;
k
, Gk, Gy0 – ɦɚɫɫɨɜɵɟ ɪɚɫɯɨɞɵ ɩɨɬɨɤɨɜ ɜ ɤɭɛɟ ɤɨɥɨɧɧɵ.
G
x1
ɇɚ ɨɫɧɨɜɚɧɢɢ (289) ɢ (290) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
h
= f (Gk, Gy0).
k
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ Gk.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɥɟɝɤɨɥɟɬɭɱɟɦɭ ɤɨɦɩɨɧɟɧɬɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dC
0
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
G
x
GC GC G C
. (291)
011000
dt
x1Cx1
xkx yy
= Gk Cɤ + Gy0 Cy0. (292)
Ɉɫɧɨɜɧɵɟ ɞɨɩɭɳɟɧɢɹ:
Ʉɢɩɹɬɢɥɶɧɢɤ ɫ ɩɨɥɧɵɦ ɢɫɩɚɪɟɧɢɟɦ, ɬ. ɟ. C
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɤɢɩɹɬɢɥɶɧɢɤɚ:
Gr Gr .
0 ɝɪ ɝɪyk
= Cx0.
y0
Ɉɛɨɡɧɚɱɟɧɢɹ:
– ɦɚɫɫɚ ɠɢɞɤɨɫɬɢ ɜ ɧɢɠɧɟɣ ɱɚɫɬɢ ɤɨɥɨɧɧɵ, ɤɝ;
Ɇ
0
r
– ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɤɨɧɞɟɧɫɚɰɢɢ ɩɚɪɚ, Ⱦɠ/ɤɝ;
ɝɪ
– ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɤɭɛɨɜɨɣ ɠɢɞɤɨɫɬɢ, Ⱦɠ/ɤɝ.
r
k
ɇɚ ɨɫɧɨɜɚɧɢɢ (293) ɢ (294) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
(,, (),)
cfGGGGc .
kxky x
10ɝɪ 1
106
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ Gɝɪ.
T
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɧɢɡɚ ɤɨɥɨɧɧɵ (ɪɢɫ. 97).
Ɋɢɫ. 97. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɧɢɡɚ ɤɨɥɨɧɧɵ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɧɢɡɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ (ɪɢɫ. 98)
,
ɩɨ h
ɢɥɢ hk, Ck.
k
ɧ
Ɋɢɫ. 98. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɧɢɡɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɜɟɪɯɚ ɤɨɥɨɧɧɵ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɞɟɮɥɟɝɦɚɬɨɪɚ ɫ ɮɥɟɝɦɨɜɨɣ ɟɦɤɨɫɬɶɸ (ɪɢɫ. 99).
Ɋɢɫ. 99. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɞɟɮɥɟɝɦɚɬɨɪɚ ɫ ɮɥɟɝɦɨɜɨɣ ɟɦɤɨɫɬɶɸ
107
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɜɫɟɦɭ ɜɟɳɟɫɬɜɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɮɥ
SGGG
U
ɮɥ ɮɥ ɮɥ ɞɢɫɬ
, (293)
dt
yn
ɝɞɟ ȡɮɥ – ɩɥɨɬɧɨɫɬɶ ɮɥɟɝɦɵ, ɤɝ/ɦ3;
– ɫɟɱɟɧɢɟ ɮɥɟɝɦɨɜɨɣ ɟɦɤɨɫɬɢ, ɦ2;
S
ɮɥ
h
– ɭɪɨɜɟɧɶ ɮɥɟɝɦɵ, ɦ;
ɮɥ
, Gɮɥ, G
G
yn
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
G
ɇɚ ɨɫɧɨɜɚɧɢɢ (293) ɢ (294) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
h
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
– ɦɚɫɫɨɜɵɟ ɪɚɫɯɨɞɵ, ɤɝ/ɫ.
ɞɢɫɬ
ɮɥ
= Gɮɥ + G
yn
. (294)
ɞɢɫɬ
= f (Gyn, Gɮɥ, Gɞ).
ɞɢɫɬ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dC
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
G
ɇɚ ɨɫɧɨɜɚɧɢɢ (295) ɢ (296) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
C
MGCGCGC
ɞɢɫɬ
1 ɮɥ 1 ɞɢɫɬ 1nynynxnxn
dt
Cyn = G
yn
ɞɢɫɬ Cx n+1
= f (Gyn, Gɮɥ, Gɞ).
ɞɢɫɬ
+ Gɮɥ C
x n+1
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ Gɮɥ.
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɜɟɪɯɚ ɤɨɥɨɧɧɵ (ș
= șɧ).
ɜ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ n-ɨɣ ɬɚɪɟɥɤɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 100.
.
. (295)
. (296)
Ɋɢɫ. 100. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ n-ɨɣ ɬɚɪɟɥɤɢ
108
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
f
d
T
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
G
MC G C GC
yn-1 Cpyn-1 șyn-1
ɜ
dt
GC GC
ɮɥ ɪɮɥ ɮɥ xn pxn ɜ
+ G
ɮɥ Cɪɮɥ șɮɥ
TT
111xn pxn yn pyn yn yn pyn ɜ
TT
= Gyn C
pyn șɜ
+ Gxn C
. (297)
. (298)
pxn șɜ
Ɉɛɨɡɧɚɱɟɧɢɹ:
Ɇ
– ɦɚɫɫɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɧɚɜɟɪɯɭ ɤɨɥɨɧɧɵ;
xn
C
pyn, Cpyn-1
, Cɪɮɥ, C
– ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ ɩɚɪɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɵ ɧɚ
pxn
n-ɨɣ ɬɚɪɟɥɤɟ;
G
, Gyn, Gxn – ɪɚɫɯɨɞɵ ɩɚɪɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɵ ɧɚ n-ɨɣ ɬɚɪɟɥɤɟ.
yn-1
ɇɚ ɨɫɧɨɜɚɧɢɢ (299) ɢ (300) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
(,, ,)
GGG G
T
.
ɜɮɥyn yn xn
1
.
ɮɥ
Ȼɚɥɚɧɫ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɤɨɧɞɟɧɫɚɬɨɪɚ ɛɟɡ ɮɥɟɝɦɨɜɨɣ ɟɦɤɨɫɬɢ ɢɡɨɛɪɚɠɟɧɚ ɧɚ
ɪɢɫ. 101.
Ɋɢɫ. 101. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɤɨɧɞɟɧɫɚɬɨɪɚ ɛɟɡ ɮɥɟɝɦɨɜɨɣ ɟɦɤɨɫɬɢ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
VM dP
ɜɜ
T
Rdt
ɜ
() ( )
. (299)
GP GG
ɜ
yn ykɯɥ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
() ()
GG GP . (300)
ɯɥ ɜ
yk yn
Ɉɫɨɛɟɧɧɨɫɬɢ:
p
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɞɥɹ
ɞɚɟɬ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɢɧɬɟɝɪɚɥɶɧɨɝɨ
ɜ
ɡɜɟɧɚ.
G
ȿɫɥɢ ɭɱɟɫɬɶ ɜɵɪɚɠɟɧɢɟ
= f(pɜ), ɬɨ ɡɜɟɧɨ ɩɨɥɭɱɚɟɬɫɹ ɚɩɟɪɢɨɞɢɱɟɫɤɢɦ
yn
1 ɩɨɪɹɞɤɚ.
G
= f(Gɯɥ), ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɧɚ ɨɫɧɨɜɚɧɢɢ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɤɨɧɞɟɧɫɚɬɨɪɚ:
yɤ
Gr GC
'. (301)
109
T
ɯɥyk yk pɯɥɯɥ
ɇɚ ɨɫɧɨɜɚɧɢɢ (298), (299) ɢ (300) ɦɨɠɧɨ ɩɪɢɧɹɬɶ: Pɜ = f (Gɯɥ).
U
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɜɟɪɯɚ ɤɨɥɨɧɧɵ (ɪɢɫ. 102).
Ɋɢɫ. 102. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɜɟɪɯɚ ɤɨɥɨɧɧɵ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɜɟɪɯɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ (ɪɢɫ. 103)
ɩɨ
T
ɢ pɜ.
ɜ
Ɋɢɫ. 103. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɜɟɪɯɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ ɩɨ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɜɟɪɯɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ (ɪɢɫ. 104)
ɩɨ
h
ɢ
T
.
ɮɥ
ɜ
Ɋɢɫ. 104. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɜɟɪɯɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ ɩɨ h
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ (ɪɢɫ. 105)
ɩɨ
T
ɢ
T
.
ɜ
ɧ
T
Ɋɢɫ. 105. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɤɨɥɨɧɧɵ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɨɝɨ ɨɛɴɟɤɬɚ ɩɨ
ɢ
ɜ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɩɨɞɨɝɪɟɜɚɬɟɥɹ ɩɨɬɨɤɚ ɩɢɬɚɧɢɹ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ.
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ.
0
d
T
ɩ
VC GC G C GC GC
ɩɩ ɪɩ ɬ ɪɬɬ ɬ ɪɬɬ ɩ ɪɩɩ ɩ ɪɩɩ
. (302)
dt
TT TT
110
0ɜɯ ɜɵɯ
T
ɢ pɜ
ɜ
ɢ
T
ɮɥ
ɜ
T
ɧ
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