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 
Rs  +
Es 
-
Kc
M s 
M y s 
KV
W s 
Cs 
or M T s 

Qs 
1
 s 1
K1
 s 1
+
+
s 
KT
5
Feedback Block Diagram (simplified)
i s 
Rs  +
Es 
Kc
M s 
W s 
KV
-
Cs 
1
 s 1
K
 s 1
+
+
s 
KT
6
Closed Loop Transfer Function
(let R(s)=0)
i s 
Rs  +
Es 
Kc
M s 
W s 
KV
-
Cs 
1
 s 1
K
 s 1
+
+
s 
KT
 1 
K
s   
i s  
KV K c  KT s 

 s 1
 s  1
 1 
 s  1
s 



i s  1  K  K K K
 s 1 V c T
7
Closed Loop Transfer Function
(let R(s)=0)
i s 
Rs  +
Es 
Kc
M s 
W s 
KV
-
 1 
 s  1
s 



i s  1  K  K K K
 s 1 V c T
Cs 
1
 s 1
K
 s 1
+
+
s 
KT
all blocks on direct path from input to ouput 


s 
1   all blocks in the loop 
output s 
input
8
Open Loop vs Closed
Loop Transfer
Rs  +
Function (R(s)=0)
Open Loop:
i s 
Es 
Kc
M s 
KV
K
 s 1
-
t

s   1  t   A1  e  




i s   s  1
Closed Loop:
W s 
1
 s 1
Cs 
+
+
s 
KT
t
* 

t   K A1  e  


*
 1 
1
 s  1
1
1  K KV K c KT
s 







 s  1  K KV K c KT
i s  1  K K K K
s 1
V
c T
1  K KV K c KT
 s 1
K*
 *
 s 1
K*
1
*

e
t
*
vs e
t

9
A
2
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.
Rs 
Es 
+
Kc
M s 
W s 
KV
-
1
 s 1
K
 s 1
+
+
s 
+
+
s 
For heated, stirred tank:
Cs 
1
GL 
 s 1
K
GP 
 s 1
GV  KV
KT
i s 
Rs  +
Es 
GKc
c
M s 
W s 
GKV
V
Cs 
Gc  K c
1
G
s L1
K
 s P1
G
GKT
T
GT  KT
( s)

i ( s )
( s )

R( s )
11
12
W s 
kg
Ws s 
kg
s
s
Ti s  C
To s 
1
 s L1

1
 s s1

C
To s 
1
 s Ti1

C
To s 
G
G
G
C
13
Toset s 
GSP
Rs 
14
To s 

W (s)
To s 

Ti (s )
To s 

Toset (s )
15