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Control Engineering Practice 9 (2001) 1215–1220
The Blend stationFa new ratio control structure
Tore H. gglund* a
Department of Automatic Control, Lund Institute of Technology, Box 118, S-221 00 Lund, Sweden Received 6 April 2001; accepted 6 April 2001
Abstract The paper treats the problem of ratio control. Previous solutions based on simple Ratio stations perform poorly during transients caused by setpoint changes. A new solution, the Blend station, that improves control during transients, is

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Control Engineering Practice 9 (2001) 1215–1220
The Blend station
F
a new ratio control structure
Tore H
.
aagglund*
Department of Automatic Control, Lund Institute of Technolo
g
y, Box 118, S-221 00 Lund, Sweden
Received 6 April 2001; accepted 6 April 2001
Abstract
The paper treats the problem of ratio control. Previous solutions based on simple Ratio stations perform poorly during transientscaused by setpoint changes. A new solution, the Blend station, that improves control during transients, is proposed. Both aconstant-gain and an adaptive version are presented.
r
2001 Elsevier Science Ltd. All rights reserved.
Keywords:
Ratio control; Ratio station; Blending; In-line blending; Mixing
1. Introduction
Process control problems are traditionally solvedusing PID controllers that are connected through well-known couplings such as cascade control, feedforwardcontrol, ratio control, split-range control, etc. SeeSeborg, Edgar, and Mellichamp (1989);
(
AAstr
.
oom andH
.
aagglund (1995); and Dumdie (1996). Logic, selectorsand sequence functions are also used to obtain thedesired overall control function. This distributedapproach was previously accomplished using single-station controllers, function modules, relays etc. Nowa-days, most functions are incorporated in DCS systems.The use of the basic PID controller has beenimproved since the introduction of computers in processcontrol. Facilities such as automatic tuning, adaptation,gain scheduling, anti-windup, back-calculation, alarmsand supervisory functions, are examples of suchimprovements. See
(
AAstr
.
oom and H
.
aagglund (1995).However, very little research and development hasbeen devoted to the basic couplings. These are oftenperformed in the same way as before the computerimplementations, i.e. when function modules and hardwiring had to be used. In modern DCS systems, there isa potential for improvement of these functions as well.This paper treats ratio control. Ratio control isapplied when the control objective is to keep the ratiobetween two variables, often ﬂows, at a certain ratio
a
:
In combustion, e.g., it is desired to control the fuel to airsupply ratio, in order for the combustion to be aseﬃcient as possible. Blending of chemicals is anotherexample where it is desired to keep the ratio betweendiﬀerent ﬂows constant. In in-line blending systems,when there are no downstream mixing tanks, this is of special importance. If the composition is not main-tained, quality problems may occur.Ratio control is traditionally obtained using simpleRatio stations. See Shinskey (1981); Shinskey (1996);and Seborg et al. (1989). These are explained in the nextsection. Using Ratio stations, the desired ratio may bekept during a steady-state operation. However, duringtransients the Ratio station fails to retain the desiredratio
a
:
This is a serious problem, since ratio control isnormally applied to problems where the ﬂows aresupposed to vary and where steady-state conditionsare uncommon.This paper suggests a new ratio control structure. TheRatio station is replaced by a Blend station thatimproves the ratio control during transients. The papersuggests both a constant-gain and an adaptive Blendstation where no parameter tuning is required from theuser.
2. Ratio control
Ratio control is normally solved in the way shown inFig. 1. There are two control loops. The main loopconsists of process
P
1
and controller
C
1
:
Output
y
1
is the
*Tel.: +46-46-2228798, fax: +46-46-138118.
E-mail address:
tore@control.lth.se (T. H
.
aagglund).0967-0661/01/$-see front matter
r
2001 Elsevier Science Ltd. All rights reserved.PII: S 0967 -0661(01 )0 0067-3
main ﬂow and the external setpoint
r
1
is the desiredmain ﬂow. In the second loop, consisting of process
P
2
and controller
C
2
;
it is attempted to control the ﬂow
y
2
so that the ratio
y
2
=
y
1
is equal to ratio
a
:
In Fig. 1 this isobtained using a Ratio station where setpoint
r
2
isdetermined by
r
2
ð
t
Þ¼
ay
1
ð
t
Þ ð
1
Þ
i.e. simply by multiplying the main ﬂow
y
1
with thedesired ratio
a
:
In Eq. (1), parameter
a
is assumed to be constant.This is not necessary. The desired ratio
a
is often time-varying. In combustion, e.g., the ratio
a
is often adjustedbased on
O
2
measurements in the exhaust.Provided the controllers have an integral action, thesolution given in Fig. 1 will work in a steady-state, i.e.
y
1
¼
r
1
and
y
2
¼
ay
1
:
However, using the simple Ratiostation to form the secondary setpoint
r
2
according toEquation (1) is not eﬃcient during transients. Thesecond ﬂow
y
2
will always be delayed compared to thedesired ﬂow
ay
1
:
The length of this delay is determinedby the dynamics in the second loop.When setpoint
r
1
is increasing, the delay causes anunder-supply of the media corresponding to ﬂow
y
2
;
andconversely when
r
1
is decreasing there is an excess of themedia corresponding to ﬂow
y
2
:
There are cases when it is important never to get anyunder-supply of one of the two media. In the combus-tion case, one gets an under-supply of air during thetransient part when the external set point increases, butan excess of air when the set point decreases. To preventthe fuel from being fully burnt by an under-supply of air, the solution in Fig. 1 has to be complemented withsome logic using MAX
=
MIN selectors. See
(
AAstr
.
oom andH
.
aagglund (1995).A suggested approach to overcome the transientproblems is to apply the Ratio station to setpoint
r
1
instead of measurement signal
y
1
;
see Fig. 2. Here,setpoint
r
2
is determined by
r
2
ð
t
Þ¼
ar
1
ð
t
Þ
:
ð
2
Þ
Now, the second ﬂow is not necessarily delayedcompared to the main ﬂow as in the previous approach.The transient behaviour is determined by the dynamicsin both loops. By tuning the controllers so that the loopsget the same closed-loop dynamics, the ratio
y
2
=
y
1
maybe kept equal to
a
even during setpoint changes.There are, however, some severe drawbacks with thesolution proposed in Fig. 2. The procedure is a kind of open-loop approach. If the dynamics in one of the loopschange, so may the ratio
y
2
=
y
1
:
Process dynamics oftenchange in process control, mostly due to nonlinearities.To obtain the same closed-loop dynamics in the twoloops, one of the loops in Fig. 2 has to be detuned.Normally, the secondary loop is the fastest, andconsequently the one that has to be detuned. Therefore,this loop will give unnecessarily slow responses to loaddisturbances.An advantage with the solution in Fig. 1, where thetrue main ﬂow
y
1
is used to form the setpoint, is that theratio will be kept even if the main ﬂow cannot be keptclose to the setpoint
r
1
:
If e.g. a load disturbance causesthe primary ﬂow
y
1
to deviate from set-point
r
1
;
thesecondary loop will try to keep the ratio
y
2
=
y
1
close to
a
even during the load transient. There are situationswhen this feature is important from a security point of view.So, even if the approach given in Fig. 2 has somedesirable features at setpoint changes, the approachgiven in Fig. 1 is normally preferred and has become anindustrial practice.
3. The Blend station
The main drawback with the simple Ratio stationapproach shown in Fig. 1 is that the secondary ﬂow
y
2
isdelayed compared to the desired ﬂow
ay
1
:
This problemcan be solved if not only
y
1
is used to form thesecondary setpoint, but also the main setpoint
r
1
:
Thestructure, called the Blend station, is shown in Fig. 3.
Fig. 1. Ratio control using a Ratio station
ð
RS
Þ
applied to mainﬂow
y
1
:
Fig. 2. Ratio control using a Ratio station
ð
RS
Þ
applied to setpoint
r
1
:
T. H
.
aa
gg
lund / Control Engineering Practice 9 (2001) 1215–1220
1216
In the Blend station, the secondary setpoint isdetermined according to
r
2
ð
t
Þ¼
a
ð
g
r
1
ð
t
Þþð
1
À
g
Þ
y
1
ð
y
ÞÞ
:
ð
3
Þ
Gain
g
is a weighting factor that determines the relationbetween setpoint
r
1
and main ﬂow
y
1
when formingsecondary setpoint
r
2
:
Choosing
g
¼
0 means that thestandard Ratio station given in Fig. 1 is obtained.Choosing
g
¼
1 means that the structure given in Fig. 2is obtained. The Blend station provides the possibility of combining the advantages of two approaches.The following example illustrates the beneﬁts of usingthe Blend station instead of the simple Ratio station.
Example 1
(The Blend station). Consider two pro-cesses,
P
1
and
P
2
;
both with structures given by thetransfer function1
ð
1
þ
sT
Þ
2
:
ð
4
Þ
The main process,
P
1
;
has the time constants
T
¼
10
;
and the secondary process,
P
2
;
has the time constants
T
¼
2
:
The processes are controlled using the Blendstation conﬁguration in Fig. 3. The controllers
C
1
and
C
2
are both PI controllers with settings:
K
1
¼
1
T
i
1
¼
7
:
0
;
K
2
¼
1
T
i
2
¼
2
:
8
:
ð
5
Þ
For simplicity, the desired ratio
a
is chosen to be
a
¼
1
;
which means that it is desired to keep the two ﬂowsequal,
y
1
¼
y
2
:
Fig. 4 shows responses using diﬀerent values of
g
:
Thecase
g
¼
0 corresponds to the standard use of the Ratiostation given in Fig. 1. The delay of the second ﬂow
y
2
during transients causes a signiﬁcant deviation from thedesired ratio
a
:
The case
g
¼
1 corresponds to use of the Ratio stationgiven in Fig. 2, but without detuning the second loop toobtain the same closed-loop dynamics.The optimum choice of
g
seems to be somewherearound
g
¼
0
:
4
:
The choice of
g
is treated in the nextsubsection. Even better results would have beenobtained by ‘‘shaping’’ the setpoint
r
2
:
This is of lessimportance when setpoint
r
1
is changing smoothlyinstead of stepwise. This is demonstrated in the nextsection.
3.1. Choice of
g
Assume that the two
closed
loops can be approxi-mated by ﬁrst-order systems with time constants
T
1
and
T
2
;
respectively. This means that
Y
1
ð
s
Þ¼
11
þ
sT
1
R
1
ð
s
Þ
;
Y
2
ð
s
Þ¼
11
þ
sT
2
R
2
ð
s
Þ
:
ð
6
Þ
From Eq. (3), the second setpoint is given by
R
2
ð
s
Þ¼
a
ð
g
R
1
ð
s
Þþð
1
À
g
Þ
Y
1
ð
s
ÞÞ¼
a
g
þð
1
À
g
Þ
11
þ
sT
1
R
1
ð
s
Þ¼
a
1
þ
s
g
T
1
1
þ
sT
1
R
1
ð
s
Þ
:
ð
7
Þ
This means that the relation between the main setpoint
r
1
and the second ﬂow
y
2
can be approximated by
Y
2
ð
s
Þ¼
11
þ
sT
2
a
1
þ
s
g
T
1
1
þ
sT
1
R
1
ð
s
Þ
E
11
þ
sT
2
a
11
þ
s
ð
1
À
g
Þ
T
1
R
1
ð
s
Þ
E
a
11
þ
s
ðð
1
À
g
Þ
T
1
þ
T
2
Þ
R
1
ð
s
Þ
:
ð
8
Þ
The ﬁrst approximation is that the zero in
À
g
T
1
isreplaced by a pole in
g
T
1
:
The second approximation isthat the two poles are replaced by one single pole withthe time constant equal to the sum of the two timeconstants.
Fig. 3. Ratio control using the Blend station
ð
BS
Þ
:
Fig. 4. Setpoint responses for diﬀerent choices of
g
:
Flow
y
1
is shownin dashed line. Flow
y
2
is shown for
g
¼
0
;
0
:
2
;
0
:
4
;
0
:
6
;
0
:
8
;
and 1.0.
T. H
.
aa
gg
lund / Control Engineering Practice 9 (2001) 1215–1220
1217
Since it is desired to obtain the same time constant inthe transfer function from
r
1
to
y
2
as from
r
1
to
y
1
;
thefollowing relation is desired
ð
1
À
g
Þ
T
1
þ
T
2
¼
T
1
:
ð
9
Þ
Hence, the optimal value of
g
is close to
g
¼
T
2
T
1
:
ð
10
Þ
Eq. (10) is obviously true for the case
T
1
¼
T
2
:
In thiscase, when both loops have the same dynamics, theexternal setpoint
r
1
should be applied on both loopssimultaneously in order to keep the ratio equal to
a
:
Thisis accomplished using
g
¼
1
:
Eq. (10) is also true when
T
2
¼
0
;
i.e. when the second loop lacks dynamics. Sinceno delay is present, the ratio is kept equal to
a
using thestandard Ratio station, i.e. by using
g
¼
0
:
Note thatwhen
T
1
o
T
2
;
that is when the main ﬂow dynamics isfaster than the dynamics in the second loop, Eq. (10)suggests that the gain should be chosen such that
g
>
1
:
The two closed-loop time constants
T
1
and
T
2
arenormally not known. If the controllers are properlytuned, it is, however, often possible to approximate therelation between
T
1
and
T
2
with the relation between theintegral times of the two controllers, i.e.
g
¼
T
i
2
T
i
1
:
ð
11
Þ
The ratio between the two integral times used inExample 1 gives the gain
g
¼
2
:
87
:
0
¼
0
:
4
:
ð
12
Þ
This gain is shown to be close to optimal in Fig. 4.
3.2. Load disturbances
An advantage with the original Ratio station pro-posed in Fig. 1, is that the ratio may be kept close to thedesired ratio even if the main ﬂow for some reasoncannot be kept close to the setpoint
r
1
:
This advantage islost in the Blend station when
g
a
0
:
If this is a problem,
g
may be set equal to zero during periods of constantsetpoint
r
1
:
In this way, the nonzero value of
g
is onlyused during setpoint changes.
4. The adaptive Blend station
In the previous section, guidelines for choosing thegain
g
were given. However, in process control it ishighly desirable not to introduce further parameters tobe tuned by the users. Furthermore, since the processesoften are time varying and nonlinear, optimal choices of parameters vary over time. Therefore, an adaptiveprocedure to automatically obtain gain
g
is proposedin this section. The structure of the adaptive Blendstation is given in Fig. 5.In the adaptive Blend station, gain
g
is adjusted online based on the actual values of the two ﬂows
y
1
and
y
2
:
The following adaptation mechanism is suggested:d
g
d
t
¼
S T
i
ð
ay
1
À
y
2
Þ
:
ð
13
Þ
In Eq. (13), gain
g
is adjusted based on the integral of the diﬀerence between the two ﬂows, properly scaledwith the desired ratio
a
:
Equilibrium occurs when
ay
1
¼
y
2
or
S
¼
0
:
Integral time
T
i
determines the adaptation rate. It isreasonable to determine it automatically as a factortimes the longest integral time of the two loops. In thesimulation examples shown later in this paper, the value
T
i
¼
70 is chosen, corresponding to a value that is 10times longer than the longest integral time of the twocontrollers
C
1
and
C
2
:
The sign parameter
S
takes the values +1,
À
1
;
or 0.When the main setpoint
r
1
increases, gain
g
shouldincrease if
ay
1
>
y
2
;
and decrease if
ay
1
o
y
2
:
However,when
r
1
decreases, the opposite is true. When
r
1
decreases, gain
g
should decrease if
ay
1
>
y
2
;
andincrease if
ay
1
o
y
2
:
The sign parameter
S
takes care of this in the following way:
S
¼
IF r1
>
MAX
ð
y1
;
y2
=
a
Þþ
eps then 1ELSE IF r1
o
MIN
ð
y1
;
y2
=
a
ÞÀ
eps then
À
1ELSE 0
:
A hysteresis,
eps
, is introduced to avoid adaptationwhen the signals are close to the setpoints. The mainreason is to avoid adaptation when the signal to noiseratio is small. The hysteresis
eps
can be ﬁxed once andfor all, or it may be determined from the noise levels inthe signals. The hysteresis is chosen as 0.01 in thesimulations presented in this paper.
Example 2
(The adaptive Blend station). In this exam-ple, the same processes and controllers as used in the
Fig. 5. Ratio control using the adaptive Blend station
ð
ABS
Þ
:
T. H
.
aa
gg
lund / Control Engineering Practice 9 (2001) 1215–1220
1218

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