SYSTEM IDENTIFICATION OF A FALLING-FILM EVAPORATOR IN THE DAIRY INDUSTRY

SYSTEM IDENTIFICATION OF A FALLING-FILM EVAPORATOR IN THE DAIRY INDUSTRY


Peter Cunningham1, Niel Canty2, Tom O’Mahony2, Barry O’Connor1, Donal O’Callaghan3


1AMT - Ireland, Process & Chemical Engineering Department, University College Cork,
Cork, Ireland.
2 Advanced Control Group, Dept. Electronic Engineering, Cork Institute of Technology,
Cork, Ireland.
3Teagasc, Dairy Products Research Centre, Moorepark, Fermoy, Co. Cork, Ireland.




Abstract: A falling film evaporator is the most commonly used evaporator type in the
dairy industry for the concentration of products such as milk, skim-milk and whey. This
concentration often takes place under vacuum to reduce the boiling point of water and
reduce any heat damage that may be caused to the product. From an economic perspective
the critical operational units are the evaporator effects and the pasteurisation process. In
this paper linear models of these units are identified from experimental data. These
models are shown to be accurate over the standard operating range of the process and will
be considered for PID controller optimisation and model predictive controller design.
Copyright © 2006 USTARTH

Keywords: Industrial Control, System Identification, PID, Pasteurisation, Evaporation




1. INTRODUCTION
within the overall process. The performance of the

identified models is analysed and the models are
The industrial process considered in this study is
validated on real operating data. These models will
located at the Teagasc-Moorepark Research Centre,
be initially used to optimise the existing PI(D)
Fermoy, Co. Cork. Within this centre, one of the
controllers and subsequently to design a model
ongoing projects has focused on upgrading the large
predictive control scheme.
pilot scale evaporation and drying facilities to
Section 2 briefly introduces the reader to evaporator
SCADA level process control operation. The final
technology and, subsequently, focuses on the falling
stage - moving to the use of model predictive control
film evaporator - as it is the focus of this study.
- is being carried out in collaboration with AMT-
Section 3 presents a brief account of the
Ireland, UCC and the Advanced Control Group in
pasteurisation process that is used while section 4
CIT. The objective of this collaboration is to
presents the model structure and the results of the
demonstrate to the indigenous food industry the
system identification experiments. Finally, in section
benefits of advanced control in terms of energy
5 some general conclusions and possible avenues for
saving, waste minimisation and product quality
future work are explored.
improvement.

While examples of successful applications of
2. THE FALLING-FILM EVAPORATOR
advanced process control to evaporators are reported

(Crosland, 2003), the details of the models used in
Evaporation is used by the dairy industry in the
such applications are usually omitted (Quaak et al.,
concentration of products such as milk, skim-milk
1994 and Bakker et al., 2006). Typically, they are
and whey (Kessler, 1981 and Písecký, 1997).
just referred to as either white or black-box models.
Concentration involves the removal of a solvent,
The main contribution of this paper is the
usually water, from a liquid. It is distinguished from
identification of simple linear models for two critical
drying by the fact that the final product (the
loops – the evaporation and pasteurisation units -
concentrate) is still a liquid. Some reasons for the

---

Fig. 1. Piping and instrumentation diagram for the evaporator operating in split effect mode.

concentration of a liquid are
(SISO) PID controllers, only three loops are
1. to reduce the cost of drying
considered to be critically (from an economic
2. to induce crystallisation
perspective) important. These loops are the two PID
3. to reduce costs of storage and transportation
controllers that regulate the evaporation temperature
4. to increase microbiological and chemical and the PID controller that dictates the pasteurisation
stability
temperature.
5. to recover by-products from waste streams
In this process, evaporation is performed using a

falling film evaporator (other varieties include
If evaporation is performed as a preliminary step to
circulation evaporators, tubular type evaporators and
drying then the milk is normally concentrated from
plate type evaporators). For simplicity, a single effect
an initial solids content of 9-13% to a final
falling film evaporator (Fig. 2) will be used to outline
concentration of 40-50% total solids before the
the operational principles. A typical single effect
product is pumped to the dryer. However, as milk is
evaporator consists of: a balance tank, a condenser, a
heat sensitive it is important to reduce the impact of
preheater, an evaporator calandria, a separator, and a
the heat treatment process. The solution usually
vacuum pump. The process can be decomposed into
employed is to perform the evaporation under
a product route (steps Pa-Pf), a steam route (steps Sa-
vacuum, thereby reducing the boiling point of water.
Sc) and a product vapour route (steps Va-Vd).
This method allows temperatures as low as 40oC to
Firstly, we will consider the path the product takes
be utilised. Evaporators should also be designed to
through the evaporator.
minimise product residence time.
Pa. From the balance tank the concentrate flows
A large amount of energy is required to boil water
through the condenser where it gets its first
from a solution. This energy is usually provided in
injection of heat - see (Vc) overleaf.
the form of steam. To minimise cost, evaporation is
Pb. The product then flows through the preheater
normally performed in multiple effect evaporators
where it gets a second injection of heat (see Sc).
where two or more effects operate at progressively
Pc. The product is then pasteurised via the Direct
lower pressures and thus progressively lower boiling
Steam Injection (DSI) pasteurisation unit and
points. In this arrangement the vapour produced in
passes through the holding tubes.
the previous effect can be used as the heating
Pd. From the DSI the product enters the evaporator
medium in the next effect. The result is that the
calandria. A nozzle and spreader plate form a
amount of steam required is approximately equal to
distribution system at the top of the evaporator
the total amount of water evaporated divided by the
that ensures a uniform product distribution.
number of effects.
Pe. Upon leaving the distribution plate the product
The evaporator considered in this study consists of
flows through stainless steel tubes. The product
four falling-film effects and has a water evaporation
forms a thin film on the inside of the tube while
capacity of 800 kg/h. The evaporator can be
the outside of the tube is surrounded by steam.
configured in a number of different modes. One of
Pf. The product from the tubes reaches the bottom of
the more common modes is called the split effect
the calandria where it is collected along with
mode. In this mode only the third effect and the
product from the separator (see Va).
finishing effect are used, a schematic diagram of this

mode is shown in Fig. 1. While the split effect mode
is controlled via six single-input single-output

---

Fig. 3. Simplified illustration of the vapour path
through the evaporator.



Fig. 2. Block diagram of a single effect falling-film
evaporator showing the critical units.

Next, consider the steam’s path through the process.
Sa. Typically, but not always, the steam enters the

calandria at the bottom and surrounds the tubes
Fig. 4. Effect of a decrease in Tw on Q1 and Q2.
through which the product is flowing.

Sb.
Q
Heat is then transferred from the steam to the
1 = U1A1(Ts-T)

Eq.
(1)
product. This transfer of heat causes the water in
Q2 = U2A2(T-Tw)

Eq.
(2)
the product to boil and produce vapour inside the

tubes.
where U1, U2 are the heat transfer coefficients
Sc.
between (i) steam and product and (ii) vapour and
Some steam from the calandria shell enters the
preheater and is used as the heating medium in
cold water, respectively. A1, A2 are the contact areas
the preheater (see Pb).
between (i) steam and product and (ii) vapour and

cold water, respectively. Ts, Tw and T are the
Finally, consider the route of the product vapour
temperatures of the steam, cold water and vapour
through the process.
respectively. P is the pressure in the box
Va.
(evaporator).
The product vapour exits the bottom of the
calandria and enters the separator where

product is removed from the vapour and
2.1 The effect of the cold water temperature (Tw) on
returned to the product stream.
the vapour temperature (T)
Vb.

The vapour then enters the condenser.
Vc.
Consider the case where initially Q
In the condenser the vapour acts as a heating
1 = Q2 and,
medium for the product (see Pa).
subsequently, Tw decreases. The resulting changes
Vd.
are described below, while Fig. 4 illustrates the effect
The vapour then passes the cold water pipes
and condenses.
on Q1 and Q2.

a. When Tw decreases, Q2 will increase according to
A vacuum pump sets the initial vacuum pressure in
Eq. (2).
the evaporator; this determines the initial temperature
b. This increase in Q2 results in an increase in the
of evaporation. However, when the plant is operating
volume of vapour that is condensed.
it is the condenser that plays the key role in
c. As a consequence, there is less vapour in the box
controlling the vacuum. This role of the condenser
(Fig. 3) and the pressure reduces.
can be explained by considering the product vapour
d. If P decreases then T also decreases.
path (points Va to Vd above). While the product also
e. The decrease in T causes Q2 to reduce. At the
helps in condensing the vapour, it will be assumed
same time, according to Eq. (1), Q1 will increase.
that this effect is constant. Therefore the path of the
f. Q2 decreases and Q1 increases until a new
vapour can be represented by the simple box shown
equilibrium is reached.
in Fig. 3.
g. A new evaporation temperature is also achieved.
Consider the case where the plant is operating in

equilibrium; the vapour is at a fixed temperature and
An opposite effect occurs when Tw increases. The
therefore the pressure is constant. Then Q
effect of the steam temperature, Ts, on evaporation
1 (the
energy received from the steam) is equal to Q
temperature can also be deduced from equations 1
2 (the
energy transferred from the vapour to the cold
and 2, and for brevity, the description will be
water). Q
omitted.
1 and Q2 can be defined as follows

---

Fig 6: Two-input single-output block diagram for the
evaporation temperature.

Fig. 5. Schematic of the DSI pasteurisation process.

3. PASTEURISATION UNIT


The pasteurisation process, illustrated in Fig. 5, is
Fig. 7. Pasteurisation process modelled as a SISO
responsible for the removal of harmful pathogens
system with a measurable disturbance input.
from the product by heating the product to 75°C and

maintaining that temperature for a desired length of
system with a single (measurable) disturbance
time (Alpha-Laval, 1986). The type of pasteurisation
variable, Fig 7.
applied in the evaporator process at Teagasc-

Moorepark is called Direct Steam Injection (DSI).

This method involves heating the product by directly
injecting steam into the product line. Product
4.1 Identification from operating data
Originally, standard operating data was investigated
contamination is avoided since most of the water is
to examine its usefulness for system identification
evaporated instantaneously.
purposes. However, it was found that, under normal
Referring to Fig. 5, the pre-pasteurisation plant operation, the set-points of all the SISO PID
temperature of the product is measured by sensor
controllers were altered simultaneously. The
2E61 located approximately one meter before the
resulting data sets were highly correlated and it was
DSI injectors. The product temperature after
virtually impossible to extract a model of, for
pasteurisation is recorded by sensor 2E34 located
example, the effect of steam on evaporation
approximately one meter after the DSI injectors. Two
temperature. Fig. 8 presents the %opening of the
PID controllers are used to control the pasteurisation
steam valve and pre-pasteurisation temperature (oC)
process. PID 12 controls the water level in the steam
for the pasteurisation process under normal operating
generator. This is a cylindrical tank containing a
conditions. These two input signals were cross-
heating element in the form of a coil. External steam
correlated using the Fast Fourier Transform (FFT)
is pumped through the coil, heating the water inside.
(Press,
The steam exits the tank and is used to indirectly
et al., 1992). The cross correlation function,
Fig. 9, reveals the highly correlated nature of the two
preheat the water supply to the steam generator tank.
signals, and hence it was not possible to reliably
Steam produced inside the steam generator is applied
identify the individual models G
directly to the product. PID 13 maintains the product
P and GD. Similar
results were obtained when the two input signals to
at the pasteurisation temperature by controlling the
the evaporation process were analysed.
amount of external steam supplied to the steam

generator.

60
4. SYSTEM IDENTIFICATION
C)

o
40
(
p
Fig. 6 presents a block diagram representation of the
m 20
falling film evaporator. As described in section two,
Te
the evaporation temperature is primarily dictated by
0
8
9
10
11
12
13
the steam temperature and cold water temperature
)
and hence represents a two-input single-output
30
%
(
system. At present, the temperatures of both these
20
variables are regulated by two independent single-
i
gnal
input single-output (SISO) PI(D) controllers that
l
S 10
r
o
manipulate the flow of water and steam pressure
ont
respectively – see Fig. 1. The DSI pasteurisation
C
8
9
10
11
12
13
process is primarily controlled by regulating the
time (hours)

steam flow, though the pre-pasteurisation Fig. 8. Normal operating input data for pasteurisation
temperature obviously has a significant influence.
unit.
Hence this process can be modelled by a SISO

---

150
55
C)
Evaporation Temp
o
50
(
n
p
i
o 100
45
m
at
Te 40
rrel
13
13.5
14
14.5
o
50
80
)
C
%
s
(
e 60
0
r
os
l
v
C
Va
Water Valve
4013
13.5
14
14.5
-50
65
)
-2
-1
0
1
2
% 60
(
Time Shift (samples)
4
e
x 10
l
v 55

Va
Steam Valve
Fig. 9. Cross correlation function.
5013
13.5
14
14.5

Time (Hours)

80
Fig. 11. System identification data for GW(z) and
70
GS(z).
C)
Set Point
o

(
T
p 60
PRE
m
T
Further open-loop tests were performed to obtain
PAST
Te 50
good models for GW(z) and GS(z). To identify GW(z)
40
the steam valve was held constant at 62% while the
10
10.5
11
11.5
12
12.5
water valve was changed. Firstly, it was changed
35
from 76.1% to 60%, next, it was changed from 60%
)
to 45%, then, from 45% to 60% and finally from
30
l
(%
a
60% to 75%. To identify GS(z) the water valve was
i
gn 25
held constant at 75% while the steam valve was
l
S
ro 20
changed. Firstly, it was changed from 62% to 57%,
nt
Co
next, it was changed form 57% to 52%, then, from
15
10
10.5
11
11.5
12
12.5
52% to 57% and finally from 57% to 62% as shown
Time (Hours)

in Fig. 11. As the tests were performed in open loop,
Fig. 10. System identification data for GP(z). Pre-
the problem of correlation between the two inputs is
pasteurisation temperature is denoted TPRE and
removed.
the pasteurisation temperature by TPAST.


4.3 Estimating the process models for GP(z), GD(z),
4.2 Improved System Identification Data
G
The following system identification experiments
W(z) and GS(z)
Relevant sections of data were chosen for the
were designed in order to obtain valid models for
estimation of the four transfer functions. The delays
GP(z), GD(z), GS(z) and GW(z). Referring to the
were obtained by visually inspecting the data. The
pasteurisation-loop data presented in Fig. 10, the
data was then inserted into MATLAB’s System
process was allowed to start up in the usual manner.
Identification Toolbox (Ljung, 2002) and Box-
After the process had settled (t ? 10Hrs), with the
Jenkins models were identified using the prediction
pasteurisation process tracking the set point of 75°C,
error algorithm. The identified models are presented
three set point changes were implemented. The first
in Table 1 along with their standard deviations and
set point change was from 75°C to 65°C, the second
loss functions. Assuming a Gaussian distribution,
from 65°C to 70°C and finally from 70°C to 75°C.
99.73% of the models will therefore lie within the
All other set-points were maintained constant and
b ? ? ? b ? b + ?
therefore, the pre-pasteurisation temperature is
range (
3 )
(
3 ) where
o
o
o
b is the
o
relatively constant throughout the duration of the
identified coefficient. The Loss Function is defined
three set point changes.
by Eq. (3).
To obtain an accurate model for G
N
D(z), it is
1
2
necessary to ensure that the process output is only
V (? ) =
?? (k) Eq. (3)
affected by changes in the pre-pasteurisation
N i=1
temperature. Thus it is required to switch controller
where N is the length of the data set and
PID_13 to manual (open-loop) to prevent it from
?(k) = y(k) ? ˆy(k) ; y(k) is the actual response and
correcting the pasteurisation temperature. The
ˆy(k) that of the model. The loss function and
temperature of the pre-pasteurised product is largely
determined by the amount of steam leaving the pre-
standard deviations were utilised to determine the
heater of the 3rd effect. Three steam pressure set
model order. In all cases it was found that a first-
point changes were made while the pasteurisation
order lag plus delay (FOLPD) model gave the best
unit was in open loop mode. The first change was
results. Higher-order models resulted in either larger
from 5.5 to 4.5 Bar. The second change was from 6.1
values of the loss function or standard deviations that
to 3.5 Bar and finally from 3.5 to 5.5 Bar.
were considered too large (the poles of either the

process or noise models could deviate outside the

unit circle for ± 3?). The sampling period is ten

seconds.

---

49
Table 1 Transfer functions, standard deviations of the
estimated parameters and loss functions for the
48.5
identified models

48
C)
? (x10-3)
o
Model
V(?)
(
b
p 47.5
0
a1
m
0 07828
.
16
Te
47
G (z)
?
=
z
±10.33 ±12.41 0.702
P
z ? 0 91
.
46.5
0 04495
.
Plant
1
G (z)
?
=
z
±12.57 ±19.95 0.105
Model
D
z ? 0.9328
460
200
400
600
800
?0 008819
.
1
G (z)
?
=
z
±0.2916 ±0.283 0.332
time (seconds)
W
z ? 0 9283
.

Fig. 14. Model and plant output using estimation
0.01998
1
G (z)
?
=
z
±2.734 ±14.18 0.017
data for GW(z).
S
z ? 0.9228


48.5
Due to space constraints, only validation results for
Plant
GP(z) and GW(z) will be presented. In the estimation
48
Model
of GP(z) the system is operating in closed loop, the
input to the system is the %opening of the steam
47.5
valve and output is the pasteurisation temperature.
C)o
(
The model was estimated from the 70°C to 75°C set-
p
47
m
point change with the means removed. The response
Te 46.5
of the pasteurisation process and model GP(z) are
compared in Fig. 12. The model was then validated
46
on a new data set where the set-point change was
from 75°C to 65°C. The response is shown in Fig.
45.5
13. Better results were obtained for G
0
100
200
300
400
500
600
D(z) (as
indicated by the loss function V(?) in table 1).
time (seconds)

Fig. 15. Model and plant output for the validation
76
data for GW(z).

74
Of the two models that describe the dynamics of the
Plant
evaporator, the loss function of Table 1 would
C)
Model
o
suggest that the model G
(
W(z) is least accurate (Gw
p 72
characterises the effect of water temperature on
m
evaporation temperature). The performance of this
Te
model is illustrated in Fig. 14 and Fig. 15. In the
70
estimation of GW(z), the data was chosen from the
first water valve change (76.1% to 60%). The plant
68
and model responses are shown in Fig. 14 and a very
0
1000
2000
3000
good fit is obtained. A new data set was used to
time (seconds)

validate the model; in this case the change was from
Fig. 12. Response of pasteurisation process and
60% to 75% and the comparison between
model G
evaporation temperature and model response is
p(z). This data was used for
identification.
presented in Fig. 15. Similar, but slightly better,

results were obtained for model GS(z).

75
5. CONCLUSIONS AND FUTURE WORK
Plant

Model
This paper has presented a detailed description of an
70
industrial evaporation process that is widely used in
C)o
the dairy industry in the production of products such
(
p
as milk, skim-milk and whey. While the process
m
Te
consists of a number of basic units, the falling-film
65
effects and DSI pasteurisation unit are important
from a quality and economic perspective. Hence, the
work completed by the authors to date has
60
concentrated on understanding the behaviour of, and
0
1000
2000
3000
4000
modelling, these two units. As a unit the evaporation
time (seconds)

process is a little unusual in that the variable of
Fig. 13. Validation of model accuracy using new data
primary interest, the temperature of the final product
set over 75°C to 65°C set-point change.
concentrate, is not used as the CV. Instead, a highly
correlated signal, the evaporation temperature is

---

used. This temperature is regulated by the steam
Písecký, J. (1997). Handbook of Milk Powder
pressure and water temperature entering the
Manufacture. Niro, A/S, Denmark.
condenser, Fig. 1. The two MV’s are the valves for
Press, W.H., S.A. Teukolsky, W.T. Vetterling and
steam and cold water.
B.P. Flannery (1992). Numerical Recipes in C:

The Art of Scientific Computing, 2nd Edition, pp.
In this work we have shown that the falling film
545-546, Cambridge University Press, New
evaporator can be modelled as a two-input single-
York.
output system while the DSI pasteurisation unit can
Quaak, P., M. P. C. M. van Wijck, and J. J. Van
be represented by a SISO process model and a SISO
Haren, (1994). Comparison of process
disturbance model. Relatively simple system
identification and physical modelling for falling-
identification experiments were designed and four
film evaporators. Food Control, 5, (2), 73–82.
first-order lags with delay were estimated. The

standard deviations of the coefficients, the loss
ACKNOWLEDGEMENTS
functions and the validation experiments all suggest

that these models are sufficiently accurate for control
Funding for this research was provided by the Walsh
purposes. Furthermore, the validation tests, which
Fellowship (Teagasc Postgraduate Research Grants)
were performed about a different set-point range,
and The Environmental Protection Agency, under the
indicate the identified models are reasonably
Cleaner Greener Production Programme. The authors
accurate over the typical (steady-state) operating
wish to gratefully acknowledge this support.
ranges of the evaporation process.


The linearity of these models is an obvious limitation
and over large operating ranges (e.g. during start-up,
shut-down, etc) poor performance can be anticipated.
Future work will explore the potential for estimating
or deriving simple non-linear models to overcome
this limitation. Furthermore, it is likely that the
accuracy of the models could be improved by using
better input test sequences e.g. pseudo-random type
sequences or optimal test sequences. Since the
process response times are all relatively short (less
than 300sec) this option is certainly a possibility,
however, as experimentation time is quite limited it
was initially decided to extract the maximum amount
of useful data as quickly as possible and therefore
simple step inputs were utilised.

Future work will focus on identifying linear models
for the remainder of the loops and then examine the
potential performance improvement that can result
from optimising the existing PID controllers. In
parallel the development of non-linear models will
be pursued and a model predictive controller based
on the linear, or non-linear models, will be designed.

REFERENCES
Alfa-Laval (1986), Dairy Handbook, Alfa-Laval,
Lund, Sweden.
Bakker H.H.C., C. Marsh, S. Paramalingam and H.
Chen. (2006). Cascade controller design for
concentration control in a falling-film evaporator
Food Control, 17, (5), 325-330.
Crosland, A. 2003. Evaporator and Dryer
Optimisation Delivers Significant Benefits for
Abbott Laboratories in Ireland. APV Food and
Drink, March.

http://www.apv.com/us/eng/newsandevents/food
anddrink/march2003/Evaporator+and+dryer+opt
imisation+for+Abbott+Laboratories.htm
Kessler, H.G. (1981). Food Engineering and Dairy
Technology, Verlag A. Kessler, Germany.
Ljung, L. (2002). System Identification Toolbox for
use with MATLAB, The MathWorks, Inc.
www.mathworks.com/products/sysid

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