Chapter 2
Traditional Advanced Control
Approaches – Feedforward, Cascade
and Selected Control
2-1 Feed Forward Control (FFC)




Block Diagram
Design of FFC controllers
Examples
Applications
Why Feedforward ?

Advantages of Feedback Control




Corrective action is independent of sources of
disturbances
No knowledge of process (process model) is required
Versatile and robust
Disadvantages



No corrective action until disturbance has affected the
output. Perfect control is impossible.
Nothing can be done about known process disturbance
If disturbances occur at a frequency comparable to the
settling time of the process. Then process may never
settle down.
Feedforward Control
Feedforward
Controller
Disturbance
Output
Process
Manipulated
Variable
Feedforward Control

Advantages




Corrective action is taken as soon as disturbances
arrives.
Controlled variable need not be measured.
Does not affect the stability of the processes
Disadvantages



Load variable must be measured
A process model is required
Errors in modeling can result in poor control
EXAMPLES
steam
FI
steam
LI
Boiler
Feed control
FI
LI
FB
Feedback control
FFC
steam
Feedforward control
FI
LI
FB
FFC
Σ
Combined feedforward-feedback control
Design Procedures (Block diagram
Method)
Load transfer function

Load
GL(s)
L
FF
Controller
GF(s)
Process
M
Manipulated
Variable
Gp(s)
X2
∑
C
Outp
ut
Derivation
C ( s )  GL ( s ) L ( s )  GP ( s ) M ( s )
 GL ( s ) L( s )  GP ( s )GF ( s ) L( s )
 GL s   GP s GF ( s )L( s )
We want C ( s )  0 for all L( s ). Hence
GL s   GP s GF ( s )  0
or
G F s   
GL s 
GP s 
need : (1)GL ( s ), load transfer function
(2)GP s , process transfer function
Examples

Example 1




Let Gp(s)=Kp/τps+1, GL(s)=KL/τLs+1
Then, GF(s)=-(KL/Kp)(τps+1)/(τLs+1)
Therefore, feedforward controller is a “lead-lag” unit.
Example 2



Let Gp(s)=Kpe-Dps/τps+1, GL(s)=KLe-DLs/τLs+1
Then, GF(s)=-(KL/Kp)(τps+1)/(τLs+1)e(-DL+DP)s
If -DL+DP is positive, then this controller is unrealizable.
However, an approximation would be to neglect the
delay terms, and readjusting the time constants. In this
case, perfect FF compensation is impossible.
Tuning feedforward controllers




 1s  1
GF ( s )  K
 2s 1
Let
This has three adjustable constants, K, τ1, τ2
Tuning K, K is selected so that for a persistent
disturbance, there is no steady state error in
output.
Adjustingτ1, τ2 can be obtained from transfer
functions. Fine tune τ1, τ2 such that for a step
disturbance, the response is somewhat
symmetrical about the set point.
Example: A simulated disturbed plant
Disturbed
flow rate
DV
Chemicals
Waste water
treatment
MV
BOD (CV)
Simulated Block Disgram
Disturbed flow
rate
1
 s  1 s  2 s  3
+
Chemicals
1
 s  1
3
Feedforward v.s. Feedback Control
0.15
FB
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
FF
0
5
10
15
20
25
30
Example: Distillation Column

Example: Distillation Column




Mass Balance: F=D+B
Fz=Dy+Bx
D=F(z-x)/(y-x)
In practice
D

F ( z  xset )
yset  xset
For example: If light key increase in feed, increase
distillate rate.
Design of Feedforward Control Using
Material and Energy Balances

Consider the hear exchanger
Ws
Steam
T2
w, T1
Condensate



Energy Balance yields Q=WC(T2-T1)=Wsλ
Where λ=hear of vaporization Ws=WC(T2-T1)/λ
This equation tells us the current stream demand based on (1)
current flow rate, W, (2) current inlet temperature, T1, (3) desired
value of outlet temperature T2.
Control Law and Design

Implementation:
Tset
measured
T1
Σ
+
-
K
measured
Gain
X
w

Note no dynamics are incorporated
Ws
When to use Feedforward ?





Feedback control is unsatisfactory
Disturbance can be measured and
compensated for
Frequency of disturbance variations are
comparable to frequency of oscillation of the
system
Output variable cannot be measured.
There are large time delays in the system
2-2 Cascade Control



Block Diagram
Design Considerations
Applications
Illustrative Example : Steam Jacket
TC
PT
PC
Illustrative Example: Steam Jacket Continued

Energy Balance of the Tank:
dT
V
 hATJ  T   Heat Loss
dt

Energy Balance of Jacket:
dTJ d  PJVJ
 
dt
dt  ns R

 VJ d PJ / ns 
 
dt
 R
Material Balance of the Jacket
dns
 nin  condensate
dt
Illustrative Example: Steam Jacket Continued

Assume:
T s 
1

PJ ( s ) 30 s  13s  1
PJ s 
1

X s  10 s  1s  12

Where X=valve position
Block Diagram
Steam
supply
pressure
Tset
Feed back
Controller
Valve
position
Steam
Valve
secondary
Tset
Primary
Controller
secondary
Jacket
Pressure
Controller
Jacket
steam
pressure
supply
pressure
Jacket
Steam
Valve
Secondary loop
Primary loop
pressure
Stirred
Tank
Tank
Temp.
primary
Stirred
Tank
Tank
Temp.
Principal Advantages and Disadvantages

Advantages




Disturbances in the secondary loop are corrected by
secondary controllers
Response of the secondary loop is improved, thus
increasing the speed of response of the primary loop
Gain variations in secondary loop are compensated by
secondary loop
Disadvantages



Increased cost of instrumentation
Need to tune two loops instead of one
Secondary variable must be measured
Design Considerations

Secondary loop must be fast responding otherwise
system will not settle



Time constant in the secondary loop must be smaller than primary
loop
Since secondary loop is fast, proportional action
alone is sufficient, offset is not a problem in
secondary loop
Only disturbances within the secondary loop are
compensated by the secondary loop. Hence,
cascading improves the response to these
disturbances
Applications: 1. Valve Position Control
Air Pressure to
Valve Motor
Desired
position

Control
Valve
Motor
Valve
position
Secondary
loop


Valve motion is affected by friction and pressure
drop in the line. Friction causes dead band. High
pressure drop also causes hysteresis in the valve
response
Useful in most loops except flow and pressure
Application 2. Cascade Flow Loop
Output From
Primary Controller
“ no cascade “
Output From
Fset
Primary Controller
FC
DP
FT
“ cascade “
Primary
controller
cset
Σ
mset
GC2
Secondary
controller
GC1
Secondary
process
e2
GP1
primary
process
m2
c
GP2
Secondary loop
Primary loop
GC1GP1
m2

 GC 2
mset 1  GC1GP1
cset
Σ
GC2
mset
GCL
GC 2GCL GP 2
c

cset 1  GC 2GCL GP 2
m2
GP2
c
θc
+
-
Σ
Gc
Primary
+
Σ
-
GC2
G2(S)
G3(S)
12
1
( S  1) (10S  1)
1
(30 S  1)(3S  1)
2
Secondary
For a cascade system
(open-loop)
 12 G2G3

 c 1  12 G2
Without cascade control

 G2G3
c
θ
Illustrative Example: Steam Jacket –
Continued – Cascade Case

Wu = 0.53
Mag = 20*log10(AR) = -30 (dB)
 AR = 0.0316

 Ku 
1
 31.6228
AR
Illustrative Example: Steam Jacket –
Continued – No Cascade Case

Wu = 0.25
Mag = 20*log10(AR) = 0 (dB)
 AR = 1

 Ku 
1
1
AR
Illustrative Example: Steam Jacket –
Continued – No Cascade Case




Ku = 1;wu = 0.25;Pu = 2*Pi / wu = 25.1327
 Kc = Ku/1.7 = 0.5882
 Taui = Pu / 2 = 12.5664
 Taud = Pu /8 = 3.1416
Illustrative Example: Steam Jacket –
Continued – Cascade Case



Ku = 20;wu = 0.53;Pu = 2*Pi / wu = 12
 Kc = Ku/1.7 = 11.8
 Taui = Pu / 2 = 6
2-3 Selective Control Systems



Override Control
Auctioneering Control
Ratio Control

Change from one controlled (CV) or manipulated variables
(MV) to another
1. Override Control – Example Boiler Control
steam
PC
water
LT
LC
LSS
Normal
loop
LSS: Low Selective Switch – Output a lower of two inputs
Prevents: 1. Level from going too low, 2. Pressure from
exceeding limit (lower)
Example: Compressor Surge Control
Normal loop
HSS
SC
PC
FC
Gas in
Gas out
motor
Example: Steam Distribution System
High Pressure Line
PC
HSS
PC
Low Pressure Line
2. Auctioneering Control Systems
Hot spot
Temperate
T1
T2
Length of reactor
Temperature profiles in a tubular reactor
Auctioneering Control Systems
TT
TT
TT
HSS
TC
Cooling flow
TT
Temperature Control
Split Range Control: More than one manipulated variable is
adjusted by the controller
TC
Bypass
Exchanger
T2
Steam
Example: Steam Header: Pressure Control
Boiler 2
PC
Boiler 2
Boiler 2
Steam Header
3. Ratio Control – Type of feedforward control
A
Wild stream
FA
Disadvantage:
Ratio may go
To erratic
FT
Desired
Ratio
ε
Driver
Gc
FT
B
FB
Controlled Stream
However, one stream in proportion to another. Use if the ratio
must be measured and displayed
Another implementation of Ratio Control
A
Wild stream
FA
FT
Multiplier
Desired Ratio
+
-
ε
FC
FT
FB
Controlled stream