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Piping and Instrumentation Diagrams (P&IDs)
GEL-2005
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Piping and Instrumentation Diagrams (P&IDs)
GEL-2005
Pas à l’examen.
• Ne pas confondre PID et P&ID.
• Introduction aux P&IDs:
http://www.cpdee.ufmg.br/~seixas/PaginaII/Download/DownloadFiles/P&IDs.PDF
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Cascade Control
GEL-2005
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Cascade ControlSingle feedback loop:
Cascade loops:
Better rejection of dyi when Gpo(s) is slower than Gpi(s). yi must be measured.
Gc(s)u yGpi(s)
r+ -
dyi
Gpo(s)
dy
yiProcess
+ +
Gco(s)u y
+ -Gpi(s)
r+ -
dyi
Gci(s) Gpo(s)
dy
yiriProcess
+ +
Inner loop
Master
Outer loop
Slave
GEL-2005
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5GEL-2005
Cascade Control
Most common cascade control: inner-loop = flow control. Tuning:
o Gci(s): based on Yi(s)/U(s) = Gpi(s)o Gco(s): based on Y(s)/Ri(s)
Gco(s)u y
+ -Gpi(s)
r+ -
dyi
Gci(s) Gpo(s)
dy
yiriProcess
+ +
Inner loop
Master
Outer loop
Slave
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Single Feedback Control
LT
Cold Water
Hot Water
LC
LevelSetpointr
100%
y
Gc(s)
Gpi(s)
Gpo(s)
Gc(s)u yGpi(s)
r+ -
dyi
Gpo(s)
dy
yiProcess
+ +
GEL-2005
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Cascade Control
LT
Cold Water
Hot Water
LC
LevelSetpointr
100%
FT FC
y
yi
ri
Gco(s)
Gci(s)
Gpi(s)
Gpo(s)
Gco(s)u y
+ -Gpi(s)
r+ -
dyi
Gci(s) Gpo(s)
dy
yiriProcess
+ +
Inner loop
Master
Outer loop
Slave
GEL-2005
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Cascade Control
GEL-2005
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Cascade Control WithoutCascade
10% Pressure Drop
0 200 400
50
52
54y 1/r
1: Lev
el &
Set
poin
t (%
)
Time [s]0 200 400
46
48
50
52
y 2: Tem
pera
ture
(%
)
Time [s]
0 200 40040
50
60
70
u 1: Col
d W
ater
Val
ve
Ope
ning
(%
)
Time [s]0 200 400
49
50
51
u 2: Hot
Wat
er V
alve
Ope
n. (
%)
Time [s]
GEL-2005
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Cascade Control WithCascade
0 200 400
50
52
54y 1/r
1: Lev
el &
Set
poin
t (%
)
Time [s]0 200 400
46
48
50
52
y 2: Tem
pera
ture
(%
)
Time [s]
0 200 40040
50
60
70
u 1: Col
d W
ater
Val
ve
Ope
ning
(%
)
Time [s]0 200 400
49
50
51
u 2: Hot
Wat
er V
alve
Ope
n. (
%)
Time [s]
GEL-2005
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Cascade Control WithCascade
0 100 200 300 4000.25
0.3
0.35
y 3/r3: C
old
Wat
er F
low
rate
& S
etpo
int (
%)
Time [s]
GEL-2005
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Exemple
GEL-2005
Voir le fichier cascade.mdl.
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Implantation numérique
GEL-2005
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Implantation numérique
GEL-2005
• Connaissant GC(s), on désire une équation récurrente du régulateur pour l’implanter sur un calculateur numérique:
u(k) = a1u(k-1) + a2u(k-2) + … + b0e(k) + b1e(k-1) + …
où u(k) = valeur de u à l’instant présent ku(k-1) = valeur de u à l’instant d’échantillonnage précédentetc.
• Cette équation est calculée à chaque période d’échantillonnage Te.
• Choix de Te: temps de réponse (et non constante de temps) de la boucle fermée (Y/R) / a, avec 10 < a < 25
• Étapes: GC(s) GC(z) a1, a2, …, b0, b1, …
GC GP+
-
u yr e
Pas à l’examen.
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Implantation numérique
GEL-2005
1
1
1 1
1
( ) 3.15 2.85 3.15 2.85( )
( ) 1 1
( ) ( ) 3.15 ( ) 2.85 ( )
: retard d'une période d'échantillonnage
( ) ( 1) 3.15 ( ) 2.85 ( 1)
C
U z z zG z
E z z z
U z z U z E z z E z
z
u k u k e k e k