Transcript Chapter 9

Chapter 12
Cascade, Ratio, and
Feedforward Control
Overall Course Objectives
• Develop the skills necessary to function as
an industrial process control engineer.
– Skills
•
•
•
•
Tuning loops
Control loop design
Control loop troubleshooting
Command of the terminology
– Fundamental understanding
• Process dynamics
• Feedback control
Cascade, Ratio, and Feedforward
Control
• Each of these techniques offers advantages
with respect to disturbance rejection:
– Cascade reduces the effect of specific types of
disturbances.
– Ratio reduces the effect of feed flow rates
changes
– Feedforward control is a general methodology
for compensating for measured disturbances.
Compensating for Disturbances
Reduces Deviations from
Setpoint and Settling Time
6
FB-only
T' (K)
3
0
-3
Compensating
for disturbances
-6
0
10
20
30
Time (seconds)
40
50
Level Controller on a Tank With
and Without Cascade Control
Lsp
Fin
Fout
LC
Lsp
LT
Fin
Fout
LC
LT
FT
RSP
FC
Analysis of Cascade Example
• Without a cascade level controller, changes
in downstream pressure will disturb the tank
level.
• With cascade level controller, changes in
downstream pressure will be absorbed by the
flow controller before they can significantly
affect tank level because the flow controller
responds faster to this disturbance than the
tank level process.
Key Features for Cascade
Control to be Successful
• Secondary loop should reduce the effect of
one or more disturbances.
• Secondary loop must be at least 3 times faster
than master loop.
• The CV for the secondary loop should have a
direct effect on the CV for the primary loop.
• The secondary loop should be tuned tightly.
Cascade Reactor Temperature
Control
Fe e d
TC
C ool in g
wate r
TT
Produ ct
Fe e d
TT
TC
RS P
C ool in g
wate r
TT
TC
Produ ct
Analysis of Example
• Without cascade, changes in the cooling
water temperature will create a significant
upset for the reactor temperature.
• With cascade, changes in the cooling water
temperature will be absorbed by the slave
loop before they can significantly affect the
reactor temperature.
Multiple Cascade Example
TT
TC
RS P
AC
RS P
FC
FT
AT
• This approach works because the flow control
loop is much faster than the temperature control
loop which is much faster than the composition
control loop.
Example
PT
S te am
TT
Fe e d
C on de nsate
• Draw schematic: A temperature controller on the
outlet stream is cascaded to a pressure controller
on the steam which is cascaded to a control valve
on the condensate.
Solution
TC
RS P
PC
PT
S te am
TT
Fe e d
C on de nsate
Ratio Control
• Useful when the manipulated variable scales
directly with the feed rate to the process.
• Dynamic compensation is required when the
controlled variable responds dynamically
different to feed rate changes than it does to
a changes in the manipulated variable.
Impurity Concentration
Typical Performance
Improvements using Ratio Control
w/o ratio control
w/ ratio control
Time
Ratio Control for Wastewater
Neutralization

RS P
FC
FT
FT
NaO H
S olu tion
Acid
W aste wate r
pHC
pHT
Effl u e nt
Analysis of Ratio Control
Example
• The flow rate of base scales directly with
the flow rate of the acidic wastewater.
• The output of the pH controller is the ratio
of NaOH flow rate to acid wastewater flow
rate; therefore, the product of the controller
output and the measured acid wastewater
flow rate become the setpoint for the flow
controller on the NaOH addition.
Ratio Control Applied for Vent
Composition Control
×
AC
FT
AT
FC
Fe e d
FT
S te am
Ve nt
Produ ct
TT
Ratio Control Requiring
Dynamic Compensation
FT
DC
Fe e d

AC
RS P
FC
FT
AT
Example
FT
TT
Fl ue
Gas
FT
Proce ss
Fl ui d
Fu e l
• Draw schematic: For a control system that adjusts
the ratio of fuel flow to the flow rate of the process
fluid to control the outlet temperature of the process
fluid. Use a flow controller on the fuel.
Solution
×
Ratio
FT
TC
TT
Fl ue
Gas
RS P
FC
FT
Proce ss
Fl ui d
Fu e l
Feedforward and Feedback Level
Control
To Ste am
Use rs
To Ste am Use rs
FT
LC
FF
LT
LT
Mak e -u p
W ate r
Mak e -up
W ate r
FT
To S team
Users
FF
LC
+
LT
Make-up Water
Analysis of Feedforward and
Feedback Level Control
• Feedback-only must absorb the variations in
steam usage by feedback action only.
• Feedforward-only handle variation in steam
usage but small errors in metering will
eventually empty or fill the tank.
• Combined feedforward and feedback has
best features of both controllers.
Derivation of FF Controller
D(s)
Gff(s)
Gds (s)
Gd(s)
Cff (s)
Ga(s)
Gp(s)
+
+
Y(s)
Y ( s)  D( s) Gds ( s) G ff ( s) Ga ( s ) G p ( s )  D( s ) Gd ( s )  0
Solving for G ff ( s)
 Gd ( s )
G ff ( s) 
Gds ( s) Ga ( s) G p ( s )
Lead/Lag Element for
Implementing FF Control
Gds ( s) Ga ( s) G p ( s ) 
Kp e
 p s
 ps  1
K d e  d s
Gd ( s) 
ds  1
G ff ( s )  
K d ( p s  1) e
 d s
K p ( d s  1) e
 p s

K ff ( ld s  1) e
( lg s  1)
Lead/Lag parameters: K ff , ld , lg , ff
 ff s
Effect of Lead/Lag Ratio
 ld/ lg = 2
cff
 ld/ lg = 1
 ld/ lg = ½
Time
Static Feedforward Controller
G ff (s)  K ff
• A static feedforward controller make a correction
that is directly proportional to the disturbance
change.
• A static feedforward controller is used when the
process responds in a similar fashion to a change
in the disturbance and the manipulated variable.
Feedforward When p«d
TT
C ool an t
In l e t
FF
FC
FT
FT
Fe e d
C ool an t
O u tl e t
G ff ( s) 
K ff e
 ff s
 ld s  1
Example of Feedforward Control
for d<p
Q
Ti
To
To
To
10ºC
10ºC
2
10 kW
0
2
4
6
Time (minutes)
Ti
Q
8
10
0
2
10ºC
4
6
Time (minutes)
8
10
Static Feedforward Results
12
T' (ºC)
8
4
6.5 ºC
0
-4
0
2
4
6
8
10
Time
• When the inlet temperature drops by 20ºC, Q is
immediately increased by 20 kW.
• Deviations from setpoint result from dynamic
mismatch
Perfect Feedforward Control
30
FF Effect
T' (ºC)
15
Net result
0
Ti effect
-15
-30
0
2
4
6
Time (minutes)
8
10
• FF correction is mirror image of disturbance effect.
• Net effect is no change in controlled variable.
Required Dynamic Compensation
• Since the Q affects the process slower than Ti ,
initially overcompensation in Q is required
followed by cutting back on Q to 20 kW.
Results with Dynamic
Compensation
12
T' (C)
8
w/o DC
4
w/ DC
0
-4
0
2
4
6
Time (minutes)
8
10
Feedforward Control Action
Q
w/o DC
w/ DC
0
5
10
15
Time (minutes)
20
Effect of Lead/Lag Ratio
 ld/ lg = 2
cff
 ld/ lg = 1
 ld/ lg = ½
Time
Tuning a FF Controller
y
• Make initial estimates of lead/lag parameters based
on process knowledge.
• Under open loop conditions, adjust Kff until steadystate deviation from setpoint is minimized.
Time
Tuning a FF Controller
y
• Analyzing the dynamic mismatch, adjust ff.
Time
Tuning a FF Controller
y
• Finally, adjust (ld - lg) until approximately equal
areas above and below the setpoint result.
Time
Demonstration: Visual Basic
Simulator
Tuning a FF Controller
Feedback Control
• Can effectively eliminate disturbances for
fast responding processes.
• But it waits until the disturbance upsets the
process before taking corrective action.
• Can become unstable due to nonlinearity
and disturbance upsets.
Feedforward Control
• Compensates for d’s before process is affected
• Most effective for slow processes and for
processes with significant deadtime.
• Can improve reliability of the feedback
controller by reducing the deviation from
setpoint.
• Since it is a linear controller, its performance
will deteriorate with nonlinearity.
Combined FF and FB Control
Cff (s)
D(s)
Gff (s)
Gd(s)
Ysp(s)
+-
Gc(s)
Cfb (s)
+
+
Gp(s)
+
+
Y(s)
Combined FF and FB for the
CSTR
TC
+
FF
RS P
TT
FC
Fe e d
FT
S te am
TT
Produ ct
Results for CSTR
6
FB-only
T' (K)
3
0
-3
FF-only
FF+FB
-6
0
10
20
30
Time (seconds)
40
50
Analysis of Results for CSTR
• FB-only returns to setpoint quickly but has
large deviation from setpoint.
• FF-only reduces the deviation from setpoint
but is slow to return to setpoint.
• FF+FB reduces deviation from setpoint and
provides fast return to setpoint.
Example
S te am
PT
TT
TT
Fe e d
C on de n sate
• Draw schematic: For a combined feedforward and
feedback controller in which the inlet feed temperature
is the feedforward variable and the outlet temperature
is the feedback variable. The combined controller
output is the setpoint for a steam pressure controller.
Solution
+
RS P
TC
FF
S te am
PC
PT
TT
TT
Fe e d
C on de n sate
Overview
• Cascade can effectively remove certain
disturbances if the slave loop is at least 3
times faster than the master loop.
• Ratio control is effective for processes that
scale with the feed rate.
• Feedforward can be effective for measured
disturbances for slow responding processes
as long as the process nonlinearity is not too
great.