1 cbe / met 433 24 mar 12 dead time... “dead time is the killer of control the presence of dead...
TRANSCRIPT
1
CBE / MET 433
24 Mar 12
Dead Time . . .
“Dead Time is the Killer of Control
The presence of dead time, Өp, is never a good thing in a control loop.
Think about driving your car with a dead time between the steering wheel and the tires. Every time you turn the steering wheel, the tires do not respond for, say, two seconds. Yikes.”
Professor Douglas Cooper, author Loop Pro-Trainer
2
Dead Time
Causes for dead time in a control loop:
• Control loops typically have "sample and hold" measurement instrumentation that introduces a minimum dead time of one sample time, T, into every loop. This is rarely an issue for tuning, but indicates that every loop has at least some dead time.
• The time it takes for material to travel from one point to another can add dead time to a loop. If a property (e.g. a concentration or temperature) is changed at one end of a pipe and the sensor is located at the other end, the change will not be detected until the material has moved down the length of the pipe. This is not a problem that occurs only in big plants with long pipes. A bench top process can have fluid creeping along a tube. The distance may only be an arm's length, but a low enough flow velocity can translate into a meaningful delay.
• Sensors and analyzers can take precious time to yield their measurement results. For example, suppose a thermocouple is heavily shielded so it can survive in a harsh environment. The mass of the shield can add troublesome delay to the detection of temperature changes in the fluid being measured.
(Cooper, Practical Process Control E-book)
3
Dead Time: Measurement
At SS T1 = T
So if step change in Ti (t), what is response (open loop) of T1 or T ??
t
eAt 1
)(tuAti
1
1
ss
s
i
4
Sketch Response: Open Loop
• Transportation delay; time delay (lag); pure dead time• What does this look like in a Transfer Function?
)(
01
0
1tt
eAttt
?1 t
st
i
ess
s0
1
11
t
0
0
)(tuAti
t
ot velocity
distances
f
Acs*L
v
L][
5
Exercise: Write Open Loop T.F.
1
1
s
11
sK
s+
+
si
sQ
sWVK
sMcK sM y-
sE+ sR
TK sC
sMor T
sQ
s1
1)(
)( 0
s
eK
sX
sY st
1st Order Plus Dead Time (FOPDT)
6
Example:
??0 t
For L = 0, 1, 12.5, 25, and 50 m long pipes
cmID
vel
CA
sm
o
54.2
5.2
5
sec20
0 10 20 30 40 50 60 70 80 90 100-1
0
1
2
3
4
5
First Order Response Plus Dead Time
G(t) [oC]
G1(t) [oC] - 12.5
G1(t) [oC] - 25
G1(t) [oC] - 50
Time (s)
De
via
tion
Te
mp
era
ture
[o
C]
7
Normal Block Diagram
)(1 sG
sY++
sL
)(2 sGcG-
sE+ sR
TK sC
8
)(sGL
++
sL
)(sGPcG-
sE+ sR sC
Normal Block Diagram (simplified)
sVp
)(
)(
sG
sG
P
L
2 types of changes to system:
• Load change (disturbance)
• Setpoint change
9
10
11
12
13
14
15
16
Problem Solving Exercise:
17