Dead time compensation of Control Chapter 3_507.ppt

Chapter 3
Dead Time Compensation – Smith
Predictor, A Model Based Approach

1. Effects of Dead-Time (Time
Delay)
 Process with large dead time (relative
to the time constant of the process)
are difficult to control by pure
feedback alone:
 Effect of disturbances is not seen by controller
for a while
 Effect of control action is not seen at the
output for a while. This causes controller to
take additional compensation unnecessary
 This results in a loop that has inherently built
in limitations to control

Example – A Bode Plot Example
 3
1
)
(



s
e
s
G
s
h=tf(1,[1 3 3 1],'inputdelay',1);

Example- continued, case without
time delay
 3
1
1
)
(


s
s
G

PID Control Results- Case with dela
y (Kc=1,Ki=1,Kd=1)

PID Control Results- Case without d
elay (Kc=1,Ki=1,Kd=1)

2. Causes of Dead-Time
 Transportation lag (long pipelines)
 Sampling downstream of the process
 Slow measuring device: GC
 Large number of first-order time
constants in series (e.g. distillation
column)
 Sampling delays introduced by
computer control

3. The Smith Predictor
 
S
Gc
Controller
＋
－
Process
 
S
G s
td
e
 
S
ysp
 
S
y
 
S
y
 
S
Gc
Controller
＋
－
Process
 
S
G s
td
e
 
S
ysp
 
S
y
 
S
y*
 
S
Gc
Controller
＋
－
Process
 
S
G s
td
e
 
S
ysp  
S
y
 
S
y
 
S
G
e s
td
)
1
( 

＋
＋  
S
y'
 
S
y*
Dead-time compensator
Controller mechanism

Control with Smith Predictor: (K
c=1,Ki=1,Kd=1)

Alternate form
 
S
G
 
S
G
 
S
Gc
＋
－
d
 
S
G
s
td
e
sp
y y
＋
－＋
－
s
td
e
d

Example 2: Long time delay
-10
-8
-6
-4
-2
0
Magnitude
(dB)
10
-2
10
-1
10
0
-360
-270
-180
-90
0
Phase
(deg)
Bode Diagram
Frequency (rad/sec)
1
G(s)=
s^3 + 3 s^2 + 3 s +
1
exp(-3*s) * ---------------------
Mag=-3.3dB=20log10(AR);
AR=0.6839;
Wu=0.5;Pu=2π/0.5=12.5664
Ku=1/0.6839=1.4622
Kc=0.8601
Taui=Pu/2=6.2832
Taud=Pu/8=1.5708

Load Disturbance Response
0 5 10 15 20 25 30
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1

Gc(s) G(s)
(1-e-td’s
)G’(s)
e-tds
Process
)
(s
ysp
)
(s
y
)
(s
y
+
-
+
-
)
(s
y
a
)
(
' s
y
The Effect of Modeling Error
 
 
  sp
s
t
s
t
c
sp
c
s
t
s
t
c
y
e
G
Ge
G
G
s
y
or
y
G
G
e
Ge
G
s
y
d
d
d
d
'
'
'
'
)
(
*
'
1
)
(
*










Errors in td’,G’ both cause the control system to degrade

Smith Predictor with Modeling Error
Model=e-s
/(s3
+s2
+s+1)
Plant=e-s
/(s3
+3s2
+3s+1)
Model=e-0.5s
/(s3
+s2
+s+1)

Analytical Predictor
GC(s)
GPe-DS
Analytical
Predictor
ySP
y(t+D)
y(s)
Analytical Predictor is a model that projects what y will be
D units into the future (on-line model identification)

y(t)
time
Step response to manipulate
variable
Processes with inverse response
The output goes to the wrong way first
Example:
This can occurs in (1) reboiler level response to change in heat
input to the reboiler. (2) Some tubular reactor exist temperature
To inlet flow rate .
Inverse response is caused by a RHP zero
1
1
)
(
2
2
1
1




s
K
s
K
s
y



Example: Inverse response of concentration and t
emperature to a chanbe in process flow of 0.15 ft3
/min

Gc(s)
Process with inverse response
)
(s
ysp
)
(s
y
)
(s
y
+
-
1
1
1

s
k

Controller
1
2
2

s
k

+
-

Gc(s)
Process with inverse response
)
(s
ysp
)
(s
y
)
(s
y
+
-
+
-
)
(s
y
a
)
(
' s
y
)
1
1
1
1
(
1
2 

 s
s
k


1
1
1

s
k

Controller
1
2
2

s
k

+
-

Open Loop Response Analysis
  
  
 
s
y
s
s
K
K
s
K
K
s
G
s
y sp
c
1
1
)
(
2
1
2
1
1
2
2
1










 
 
         
   
  
LHP
in the
is
zero
the
if
and
1
1
)
(
'
*
then
1
1
1
1
)
(
response
loop
open
the
to
add
we
If
positive
is
then
,
1
:
at
zero
RHP
2
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
2
1
2
1
1
2
2
1
2
1















































K
K
K
y
s
s
K
K
s
K
K
K
s
G
s
y
s
y
s
y
s
y
s
s
K
G
s
y'
s
K
K
if
Note
K
K
K
K
s
s
c
sp
c

Dead time compensation of Control Chapter 3_507.ppt

More Related Content

Similar to Dead time compensation of Control Chapter 3_507.ppt (20)

Recently uploaded (20)

Dead time compensation of Control Chapter 3_507.ppt