Transcript powerpoint

CBE / MET 433
22 Feb 12
(Transfer functions and
Block Diagrams)
Professor Douglas Cooper, author Loop Pro-Trainer
1
What are Valve Characteristics
Inherent Characteristics
• The three most common valve characterizations are
equal percentage, linear, and quick opening
Professor Douglas Cooper, author Loop Pro-Trainer
2
What are Valve Characteristics
Installed Characteristics
•
In many process applications the pressure drop across a valve varies
with the flow. In these instances an equal percentage valve will act to
linearize the process.
Equal percentage valves are the most commonly used control valves.
•
How do you know what inherent valve characteristic to choose to get a linear
installed characteristic?
– The correct selection of valve characteristic to linearize the process gain
will ease the tuning process and make for a robust system.
– Most times this selection is through experience, guesswork or the valve
manufacturer’s recommendation.
Professor Douglas Cooper, author Loop Pro-Trainer
3
Feedback Block Diagram
Transmitter
Transducer
Valve
Energy Transfer
Controller
Process
4
Feedback Block Diagram
i  s 
1
 s 1
R s 
E s 
+
-
Kc
M s 
M
y
s 
KV
W s 

Q s 
K1
+
+
 s 
 s 1
C s 
or M T  s 
KT
5
Feedback Block Diagram (simplified)
i  s 
1
 s 1
R s 
E s 
+
Kc
M s 
W s 
KV
K
+
+
 s 
 s 1
-
C s 
KT
6
Closed Loop Transfer Function
(let R(s)=0)
i  s 
1
 s 1
R s 
E s 
+
Kc
M s 
W s 
KV
K
+
+
 s 
 s 1
-
C s 
KT
 1 
K
 s   
K V K c   K T   s 
 i  s  
 s 1
 s  1 
 1 



s

1


 s



K
i  s 
1
KV K cKT
 s 1
7
Closed Loop Transfer Function
(let R(s)=0)
i  s 
1
 s 1
R s 
E s 
+
Kc
M s 
W s 
KV
output  s 
input  s 
+
+
 s 
 s 1
-
 1 



s

1
 s 



K
i  s 
1
KV K cKT
 s 1
K
C s 
KT
all blocks


on direct
path from input to ouput
1   all blocks in the loop


8
Open Loop vs Closed
Loop Transfer
R s  +
Function (R(s)=0)
Open Loop:
 s 

 
i  s   
i  s 
 s 1
E s 
M s 
Kc
 1 



s

1
 s 



K
i  s 
1
KV K cKT
 s 1
W s 
KV
K
 s 1
-
t


1   t   A  1  e  



s  1
Closed Loop:
1
+
+
 s 
C s 
KT
t
* 

 t   K A  1  e  


*


1
1

 s  1  K K V K c K T
K

1  K K V K c K T
s 1
*
 s 1
*
1  K K V K c K T
K

*
*
1

 t
e

*
vs e
t

9
2
A
1.8
1.6
Open - loop
1.4
Closed - loop
1.2
Y(t)
 t 
*
1
K A
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
time
tim e (t)
10
i  s 
Transfer Functions
(Chap 3-5)
Define: G  T .F .
1
 s 1
R s 
E s 
+
Kc
M s 
W s 
KV
K
 s 1
-
+
+
 s 
For heated, stirred tank:
GL 
GP 
C s 
1
KT
 s 1
i  s 
1
G
 s L1
K
 s 1
R s 
E s 
+
GK c
M s 
W s 
GKV
V
c
K
G
 s P1
-
GV  K V
C s 
Gc  K c
+
+
 s 
GK T
T
GT  K T
(s)
i ( s )

(s)

R (s)
11
12
W s 
W s s 
kg
s
kg
s
Ti  s  C

1

1

1

G
 s L1
C
G
 s s1
G
 s Ti1
To  s 
C
To  s 
C
To  s 
13
set
To
s 
G SP
R s 
14
To  s 

W (s)
To  s 

Ti ( s )
To  s 
set

To ( s )
15