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Movie Review Guidelines
I. Introduction
· Genre
· Movie Title
· Director
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· Mention your opinion –use a description
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ChE 460 Literature Review Due: Dec 03, 2019, 11 AM
Paper Review (50 pts.)
Read the paper: “Dissolved oxygen control of the activated
sludge wastewater treat-
ment process using model predictive control,” Computers and
Chemical Engineering, vol

32, 1270-1278, 2008, and write a note about that paper. Please
submit the printed hard
copy. Handwriting version is not accepted.
You need to show and discuss the following contents. Please do
not copy and paste
any sentences from that paper.
� Motivations (10 pts.): why is this work important from the
industrial or academic
perspective?
� Methodologies (10 pts.): including the modeling and
controller design methods.
� Your questions about the method in this paper (10 pts.):
Model predictive control
is the state-of-the-art technique for industrial automation. It is
very normal that
students cannot easily understand its concept. List all your
questions on this
method.
� Comments with critical thinking (10 pts.): List advantages &
drawbacks of the
proposed method. Provide your suggestions or possible
improvement.
Format Requirement (10 pts.): Print your review on A4 paper, at
least two full
pages (not including references), single space, Times New
Roman 12, margins 1 inch
on all sides, no figure. Please list references in the end of this
review (You can follow
the reference format of Computers and Chemical Engineering).
If your report does not

meet above requirements, then you can obtain at most 1 point in
this part.
1
Ashraf Al Shekaili
Chemical Engineering 460
Dr. Yu Yang
Literature Review
Dissolved Oxygen Control of The Activated Sludge Wastewater
Treatment Process Using Model Predictive Control
The process of waste water treatment is very complex and hard
to control due to non-linear behavior system. This happens
because of the variation in composition of the incoming
wastewater along with disturbances in flow and load. Many
control strategies were proposed to control the process;
however, their evaluation is difficult due to shortage in the
standard evaluation criteria.
The dissolved oxygen in the aerobic reactors play a role in
the activity of microorganisms that live in activated sludge.
High concentration of dissolved oxygen is required to feed
enough oxygen to microorganisms in the sludge so the organic
matters will be decomposed. However, excessive dissolved
oxygen may lead to increase the operational cost because of
high energy consumption.
Building a model to control a process is extremely important for
any industry because industries have to meet the effluent
requirements of the plant. The effluent requirements could be
determined by governmental institutions, such as European
Union, to protect the environment, or they could be determined
by the customers who buy the effluent product, such as
refineries products. The effluent standards lead to increase the
operational costs and economical paneities. Therefore,
designing a proper controller that represents the process

accurately to maximize the profit and avoid penalties is
essential.
However, not all controllers can be designed easily because
there are a lot of processes behave in a non-linear manner. Also,
the influent may experience a remarkable perturbation in flow,
load, and composition. Consequently, this work is important in
academic point of view because it teaches a new technique to
solve problems and design a controller for wastewater treatment
system. This work teaches process control engineers a way to
design a controller for abnormal conditions.
The controller used in wastewater treatment is Model Predictive
Control, or MPC, which is a computer control algorithm that
predicts the future response of a plant by employing an explicit
process model. It yields good results for both linear and non-
linear predictive control technologies. Therefore, model
predictive control is a good representation for the oxygen
control of wastewater treatment plants.
The modelling of the biological reactions used to simulate the
biological reactions in aerobic and anoxic reactor is Activated
Sludge Model 1, or ASM1, and double-exponential settling
velocity function is used in the second settler of waste water
treatment plant to model the clarification and thickening
processes. The modelling of the secondary clarifier is flux-
theory which is one-dimensional model. This model assumes
uniform horizontal velocities so the horizontal gradient in
concentration is negligible, and negligible biological reactions.
Therefore, only the vertical dimension processes are modelled.
The model of the aeration process has to be accurate
representation of the process because aeration process is very
critical for the entire activated sludge process. Microorganisms
need enough oxygen so that there is enough electron receptor
capacity for their metabolism process. The process of oxygen
transferring from air bubbles to microorganism cells is
complicated. Therefore, the slowest process, which is
convection of mass transfer within the air bubble to the gas
liquid border surface, was chosen as determining factor for the

whole process. A dissolved oxygen mass balance model was
used around a complete stirred tank reactor which uses oxygen
mass transfer coefficient as manipulated variable.
To control the dissolved oxygen concentration at a certain
level, the following process model is used. First, the
concentration of oxygen in the reactor is measured by an ideal
sensor. Then, the concentration value of oxygen is handled by
the control method to calculate the oxygen mass transfer
coefficient. Then, the oxygen mass transfer coefficient is
corrected to match the corresponding operational temperature.
Finally, the oxygen concentration level in the biological reactor
is changed by applying the oxygen mass transfer coefficient. As
a result, the volume of the air blown by the diffusors and the
operational cost for the aeration can be calculated.
Model Predictive Control is one of the classes of
algorithms that optimize the future behavior of a plant by
calculating a sequence of manipulated variable adjustments. The
controller design model linearizes the aeration process in ASM1
model at a steady state operation to build a state model of the
waste water treatment plant. The manipulated variable in the
controller is the oxygen mass transfer coefficient and the output
is the concentration of the dissolved oxygen. The sensor of the
oxygen is ideal without time delay and no consideration of
noise is taken. The aeration process has a second order model
which was proved to be sufficient representation of the real
aeration process. The performance assessment of the model is
performed using integral of absolute error, or IAE and integral
of square error, or ISE.
Model Predictive Control has difficult concepts that
beginners to process control may not be able to understand. The
following is a list of questions about MPC. How is the first
input in the optimal sequence of MPC is calculated? How does
the constants m and p are being optimized to minimize the
quadratic objective? What are the components of y and u that
could be penalize by the weighting matrices in this case? How
would the other tuning parameters, like control and prediction

horizon and weight matrices, affect the performance of MPC
controller? Why is the sampling time in control of the
simulation benchmark has as significant effect on the
performance of the controller?
Model Predictive Control of the dissolved oxygen concentration
shows successful results in an aerobic basin of a pre-
denitrification process with influent disturbances and in an
alternating activated sludge process. According to Copp, the
benchmark simulation results and Model Predictive Control
results for control strategy of activated sludge plant agree with
each other and give similar results (Copp, 2020). Predictive
model control has many advantages. For instance, it can follow
the rapidly changing dissolved oxygen, or control variable,
setpoint. Also, manipulating the parameters of the controller
can decrease the error between the output and the set point
which yield better results. Model Predictive Control can also
solve problems for linear and non-linear systems without
changing the controller design. Moreover, performing step test
in Model Predictive Control is sufficient to build a model and
obtain its parameters.
Even though Model Predictive Control has many advantages and
gives good results, it still has some drawbacks. For instance, a
lot of assumptions have been made to build the process models
which might yield inaccurate model to represent the real
process. For example, in the aeration process model, the mass
transfer of oxygen within the liquid phase to the microbial flocs
model was neglected because it is faster than the other
processes happening in the aeration process. What is more,
some of the input variables are separated to make the process
model simple, which might affect the final results of the
controller. For example, the only manipulated variable
considered is the oxygen mass transfer coefficient, and all other
inputs to the reactor are separated and considered as
unmeasured disturbances. Also, some of the parameters of the
controller are tuned by using trial-and-error method which
might be inaccurate and time-consuming way to obtain data.

Some possible improvement can be done to the controller
to make its performance better and more accurate, even though
it might be more difficult to obtain. One suggestion is to
consider the biological reaction in the model of secondary
clarifier since there will be sufficient oxygen concentration in
the fluid. Another suggestion is to consider more inputs to the
reactors of waste water treatment, not just the oxygen mass
transfer coefficient. For example, the microorganisms are
affected by temperature, PH, and many other factors that should
be considered in modeling the process.
In conclusion, Model Predictive Control is an accurate
strategy to control a dissolved oxygen concentration. It was
tested in two simulated case studies, one is to control the
dissolved oxygen concentration in aerobic basin of a pre-
denitrification process with influent disturbances, and another is
in alternating activated sludge process. Both studies show
successful results of the controller. This work is important for
industries to meet their effluent specifications; what is more, it
shows students and process control engineers a strategy to
control a non-linear process. The controller used is Model
Predictive Control and different models were built for different
units of the plant. The model has some drawbacks and
limitations, but it still gives reliable results.
References
Copp, J. B. (2002). The COST simulation benchmark:
Description and simulator manual(COST Action 624 & COST
Action 682). Luxembourg: Office for Official Publications of
the European Union.
Holenda, B., Domokos, E., Rédey, Á., & Fazakas, J. (2008).
Dissolved oxygen control of the activated sludge wastewater
treatment process using model predictive control. Computers &
Chemical Engineering, 32(6), 1270–1278. https://doi-

org.csulb.idm.oclc.org/10.1016/j.compchemeng.2007.06.008
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Available online at www.sciencedirect.com
Computers and Chemical Engineering 32 (2008) 1270–1278
treatment
process using model predictive control
B. Holenda a,∗, E. Domokos a, Á. Rédey a, J. Fazakas b
a Department of Environmental Engineering and Chemical
Technology, Faculty of Engineering, University of Pannonia,
P.O. Box 158, 8201 Veszprém, Hungary
b University Babes-Bolyai, College of Sfantu Gheorghe, RO-
3400 Cluj-Napoca, Romania
Received 1 August 2005; received in revised form 3 June 2007;
accepted 4 June 2007
Available online 19 June 2007
bstract
Activated sludge wastewater treatment processes are difficult to
be controlled because of their complex and nonlinear behavior,
however,
he control of the dissolved oxygen level in the reactors plays an
important role in the operation of the facility. For this reason a
new
pproach is studied in this paper using simulated case-study
approach: model predictive control (MPC) has been applied to
control the dis-
olved oxygen concentration in an aerobic reactor of a
wastewater treatment plant. The control strategy is investigated
and evaluated on
wo examples using systematic evaluation criteria: in a

simulation benchmark – developed for the evaluation of
different control strategies –
he oxygen concentration has to be maintained at a given level in
an aerobic basin; and a changing oxygen concentration in an
alternating
ctivated sludge process is controlled using MPC technique. The
effect of some MPC tuning parameters (prediction horizon,
input weight,
ampling time) are also investigated. The results show that MPC
can be effectively used for dissolved oxygen control in
wastewater treatment
lants.
2007 Elsevier Ltd. All rights reserved.
en co
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eywords: Activated sludge process; Model predictive control;
Dissolved oxyg
. Introduction

Wastewater treatment plants are large non-linear systems sub-
ect to significant perturbations in flow and load, together with
ariation in the composition of the incoming wastewater. Never-
heless, these plants have to be operated continuously, meeting
tricter and stricter regulations. The tight effluent requirements
efined by the European Union a decade ago (European Direc-
ive 91/271 “Urban wastewater”) become effective in 2005 and
re likely to increase both operational costs and economic penal-
ies to upgrade existing wastewater treatment plants in order to
omply with the future effluent standards. Many control strate-
ies have been proposed in the literature but their evaluation and
omparison, either practical or based on simulation is difficult.
his is partly due to the variability of the influent, to the com-
lexity of the biological and biochemical phenomena and to the
∗ Corresponding author.
E-mail address: [email protected] (B. Holenda).
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098-1354/$ – see front matter © 2007 Elsevier Ltd. All rights
reserved.
oi:10.1016/j.compchemeng.2007.06.008
ntrol; ASM1
arge range of time constants (from a few minutes to several
ays) but also to the lack of standard evaluation criteria (among

ther things, due to region specific effluent requirements and
ost levels). A benchmark has been proposed by the European
rogram COST 624 for the evaluation of control strategies in
he wastewater treatment plants (Copp, 2002; Vrecko, Hvala, &
ocijan, 2002). This study is strictly agreement with the bench-
ark methodology especially from the viewpoint of control
erformances.
In the literature several extensive surveys based on simula-
ion can be found on activated sludge process control (Coen,
anderhaegen, Boonen, Vanrolleghem, & Van Meenen, 1997;
evisscher et al., 2005). Dissolved oxygen concentration, inter-
al recycle flowrate, sludge recycle flowrate and external carbon
osing rate are the frequently investigated manipulated variables
n these systems (Barros & Carlsson, 1998; Cho, Sung, & Lee,
002; Marsi-Libelli & Giunti, 2002; Yuan & Keller, 2002; Yuan,
ehmen, & Ingildsen, 2002). Nevertheless, the dissolved oxy-
en (DO) control is the most widely-spread in real-life, since
he DO level in the aerobic reactors has significant influence on
mailto:[email protected]
dx.doi.org/10.1016/j.compchemeng.2007.06.008
emica
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B. Holenda et al. / Computers and Ch
he behavior and activity of the heterotrophic and autotrophic
icroorganisms living in the activated sludge. The dissolved
xygen concentration in the aerobic part of an activated sludge
rocess should be sufficiently high to supply enough oxygen to
he microorganisms in the sludge, so organic matter is degraded

nd ammonium is converted to nitrate. On the other hand, an
xcessively high DO, which requires a high airflow rate, leads
o a high energy consumption and may also deteriorate the
ludge quality. A high DO in the internally recirculated water
lso makes the denitrification less efficient. Hence, both for eco-
omical and process reasons, it is of interest to control the DO.
everal control strategies have been suggested in the literature.
s a basic strategy, a linear PI controller with feedforward from
he respiration rate and the flow rate was presented (Carlsson,
indberg, Hasselblad, & Xu, 1994; Carlsson & Rehnstrom,
002; Flanagan, Bracken, & Roesler, 1977). Bocken, Braae, and
old (1989) based their design on a recursively estimated model
ith a linear oxygen mass transfer coefficient, but the excita-
ion of the process was improved by invoking a relay which
ncreases the excitation. Carlsson et al. (1994) have applied
uto-tuning controller based on the on-line estimation of the
xygen transfer rate. A strategy for designing a nonlinear DO
ontroller was developed by Lindberg and Carlsson (1996).
adet, Beteau, and Carlos Hernandez (2004) have developed
multicriteria control strategy with Takagi–Sugeno fuzzysu-
ervisor system to decrease the total cost although keeping
ood performances. In this paper, a model predictive control is
epicted to maintain the dissolved oxygen concentration at a cer-
ain setpoint based on a linear state-space model of the aeration
rocess.
Model predictive control (MPC) refers to a class of com-
uter control algorithms that utilize an explicit process model
o predict the future response of a plant. Originally devel-
ped to meet the specialized control needs of power plants and
etroleum refineries, MPC technology can now be found in a
ide variety of application fields including chemicals, food pro-

essing, automotive, and aerospace applications (Bian, Henson,
elanger, & Megan, 2005; Garcia, Prett, & Morari, 1989). In
ecent years, the MPC utilization has changed drastically, with
large increase in the number of reported applications, signifi-
ant improvements in technical capability, and mergers between
everal of the vendor companies. Qin and Badgwell (2003)
ives a good overview of both linear and nonlinear commer-
ially available model predictive control technologies. Model
redictive control has also been implemented on several com-
lex nonlinear systems (Dowd, Kwok, & Piert, 2001; Sistu
Bequette, 1991; Weijers, Engelen, Preisig, & van Schagen,
997; Zhu, Zamamiri, Henson, & Hjortso, 2000), furthermore,
amaswamy, Cutright, and Qammar (2005) has recently applied
PC to control a non-linear continuous stirred tank bioreac-
or. Steffens and Lant (1999) already applied model predictive
ontrol on an activated sludge system, however, their work
as been based on the assumption of a multivariable control
roblem rather than focusing on the dissolved oxygen control.
onsequently, this control method seems to be a good can-
idate for the oxygen control of wastewater treatment plants,
oo.
2
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l Engineering 32 (2008) 1270–1278 1271
. Modelling aspects
.1. Modelling the biological reactions

In the simulation studies two internationally accepted models
ere chosen to simulate the processes in the wastewater treat-
ent plant: the Activated Sludge Model No. 1 (Henze, Grady,
ujer, Marais, & Matsuo, 1987) was chosen to simulate the
he biological reactions in the aerobic and anoxic reactors and
ouble-exponential settling velocity function of Takacs, Patry,
nd Nolasco (1991) has been applied to model the clarifica-
ion and thickening processes in the secondary settler of the
astewater treatment plant.
Since the first introduction of ASM1 several modifications
ave been suggested (ASM2, ASM2d, ASM3) and there are
everal limitations with ASM1, however, its universal appeal and
ractical verification overshadow these limitations. The values
sed for simulation can be found in Appendix A. The values
pproximate those that are expected at 15 ◦C.
.2. Modelling the secondary clarifier
The model of the secondary clarifier is based on a traditional
ne-dimensional model applying flux-theory. It is assumed that
he horizontal velocities profiles are uniform and that horizontal
radients in concentrations are negligible. Consequently, only
rocesses in vertical dimensions are modelled. Biological
eactions are also neglected. The transport of solids takes
lace via the bulk movement of the water and the settling of
he sludge relative to the water. The differential conservation
quation describing this process is:
∂X
∂t
= V ∂X

∂y
+ ∂vsX
∂y
(1)
ith t as time, y as vertical coordinate with origin to the surface,
as solids concentration and V as the vertical bulk velocity. The
wo terms of the right-hand side refer to the bulk flux and the
ettling flux. Assuming constant horizontal cross-section A over
he entire depth, the bulk velocity V depends only on whether
he observed cross-section is in the underflow region or in the
verflow region above the inlet position. The settling velocity
unction is related only to the suspended solids concentration
ccording to the double-exponential settling velocity function
f Takács et al. (1991):
s(X) = max[0, min{
′
v
0
, v0(exp
−rh(X−Xmin ) − exprp(X−Xmin ))}]
(2)
here v′0 is the maximum settling velocity, Xmin the minimum
ttainable suspended solids concentration and rh and rp are
he hindered and flocculant zone settling parameters. The exact
arameters used for the simulation can be found in Appendix A.
.3. Modelling the aeration process
Aeration is a crucial part of the whole activated sludge pro-
ess, because microorganisms have to be supplied with enough

1 emical Engineering 32 (2008) 1270–1278
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272 B. Holenda et al. / Computers and Ch
xygen so that they have enough electron acceptor capacity for
heir metabolism process. The equipment used to deliver oxygen
o the aeration system is typically provided by surface mechani-
al type aerators or diffused aeration systems. Diffused aeration
ystems include a low pressure, high volume air compressor
blower), air piping system, and diffusers that break the air into
ubbles as they are dispersed through the aeration tank.
The whole process while oxygen transports from the air bub-
les to the cells of the microorganisms is complex, which can
e divided into several subprocesses: convective mass transfer
ithin the air bubble to the gas–liquid border surface; getting
hrough the phase border; mass transfer within the liquid phase
o the microbial flocs. Within the flocs, after getting to the cell
all the oxygen has to diffuse through the cell wall. Neverthe-
ess, the slowest of these processes is the second one (transfer
hrough the phase border), so it soon becomes the determining
actor for the whole transfer process. This complex process can
e described with the oxygen mass transfer coefficient (KLa)
hich is used as a manipulated variable during the simulations.
The aeration details of the model are introduced as a dissolved
xygen mass balance around a complete stirred tank reactor. This
s shown by the following equation:
dSO
dt
= Q × SO,in − Q × SO

V
+ KLa(Ssat − SO) + rSO (3)
here V is the rector volume, SO the concentration of dissolved
xygen in the reactor, Q the flow rate, SO,in the DO
concentration
ntering the reactor, KLa the overall mass transfer coefficient,
sat the DO saturation concentration and rSO is the rate of use
f DO by biomass.
.3.1. Control of the dissolved oxygen concentration
In order to maintain the dissolved oxygen concentration at a
iven level, the following process model is used. The dissolved
xygen concentration is measured by an ideal sensor in the reac-
or; the concentration value is processed by the control method
o calculate KLa; the KLa is corrected according to the tem-
erature if needed; finally KLa is applied to change the oxygen
oncentration level in the biological reactor. Using this value,
he cost for the aeration and the volume of air blown by the
iffusors can also be calculated (Fig. 1).
. Model predictive control
Model predictive control refers to a class of algorithms that
ompute a sequence of manipulated variable adjustments in
rder to optimize the future behavior of a plant. At each control
nterval the MPC algorithm attempts to optimize future plant
Fig. 1. Schematic view of the dissolved oxygen control process.
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Fig. 2. Model predictive control.
ehavior by computing a sequence of future manipulated vari-
ble adjustments. The first input in the optimal sequence is
hen sent into the plant, and the entire calculation is repeated
t subsequent control intervals (Fig. 2).
For any assumed set of present and future control moves
u(k), �u(k + 1), . . . , �u(k + m − 1) the future behavior of
he process outputs y(k + 1|k), y(k + 2|k), . . . , y(k + p|k) can
e predicted over a horizon p. The m present and future control
oves (m < p) are computed to minimize a quadratic objective
f the form:
min
�u(k),�u(k+1),...,�u(k+m−1)
p∑
l=1
||�y
l
[y(k + l|k) − r(k + l)]||2
+
m∑

l=1
||�ul [�u(k + l − 1)]||2 (4)
ubject to inequality constraints:
y ≤ y(k + j) ≤ ȳ, j = 1, . . . , p
u ≤ u(k + j) ≤ ū, j = 0, . . . , m − 1
∗u ≤ ∗u(k + j) ≤ ∗ū, j = 0, . . . , m − 1
ere �
y
l
and �u
l
are weighting matrices to penalize partic-
lar components of y or u at certain future time intervals.
(k + l) is the (possibly time-varying) vector of future reference
alues (setpoints). Though m control moves �u(k), �u(k +
), . . . , �u(k + m − 1) are calculated, however, only the first
ne (�u(k)) is implemented. At the next sampling interval, new
alues of the measured output are obtained, the control horizon
s shifted forward by one step, and the same computations are
epeated. The predicted process outputs y(k + 1|k), . . . , y(k +
|k) depend on the current measurement (y(k)) and assumptions
e make about the unmeasured disturbances and measurement
oise affecting the outputs.
.1. Controller design
The state-space model for the controller design model is
enerated by the linearization of the aeration process in the
SM1 model at a steady-state operating point of the wastewater
reatment plant. The steady-state is reached by applying con-

tant concentration parameters for the influent for 100 days,
hich can be also used as a starting point for later simu-
ations. The exact parameters can be found in the simulator
emical Engineering 32 (2008) 1270–1278 1273
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anual (Copp, 2002), however, they are beyond the scope of this
aper.
From the point of view of process modeling for model pre-
ictive control, the following input variables can be separated:
anipulated variables, unmeasured disturbances and measured

isturbances. Moreover, measurement noise can also be added
o the plant output. In the investigated example, the concentra-
ion of the dissolved oxygen is considered as the plant output,
he manipulated variable is the oxygen mass transfer coefficient
KLa, [day
−1]), all the other inputs to the reactor are considered
s unmeasured disturbances. No noise on the value of the mea-
ured dissolved oxygen concentration is supposed which is also
alls in with the recommendations of the benchmark: the oxy-
en sensor is ideal, neither sampling, nor delay time, the low
etection limit is zero and no measurement noise is taken into
onsideration.
Using sampling time low enough to capture the dynamic
roperties of the system, the dissolved oxygen concentration
as been determined around the steady-state at different aer-
tion intensity. This resulted in the following continuous-time
tate-space model:
dx
dt
= Ax + Bu, y = Cx + Du (5)
here x is the state vector, u and y are the input and output
vectors
nd A, B, C and D are the state-space matrices. A second-order
odel proved to be a good representation of the aeration process.
State-space models of the aeration process have been set up
round different steady states of the wastewater treatment plant
sing prediction error method based on iterative minimization.
tate-space models can be characterized by their step response:
tep response at high dissolved oxygen level is depicted by the
ashed line (Step response 2) in Fig. 3. Responses at lower

issolved oxygen level gave results of lower amplitude (Step
esponse 1 at 1.5 mg/l, response 2 at < 1 mg/l). Since in the
issolved oxygen concentration generally has to be maintained
bout 2 mg/l, the following continuous spate-space matrices
ig. 3. Step response of the identified model at different steady-
states of the
ystem.
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ig. 4. Controller response to input disturbance and setpoint

change at different
uning parameters.
ere selected for the simulation:
=
[
−100.03 115
167.77 −211.47
]
, B =
[
0.87
−1.55
]
,
=
[
7.55 0.32
]
, D = 0 (6)
number of tuning parameters such as control and prediction
orizons, weight matrices, influence the performance of the con-
roller. Trial-and-error method was used for the identification of
hese parameters.
For the tuning process a setpoint-change at t = 0.03 day
nd an input disturbance (reducing the input dissolved oxy-

en concentration with 1 mg/l) at t = 0.07 day were used. In
ig. 4 the responses of the contolled and manipulated vari-
bles to the setpoint change and the input disturbance can be
een at different tuning parameters. The setpoint can be seen
n the upper figure marked with dashed line. The continu-
us line represents the response of a controller with sampling
ime �t = 2.5 × 10−4 day and controller tuning parameters:
y = 1, �u = 0.01, m = 1 and p = 10. Reducing the predic-
ion horizon gave the response marked with dotted line if Fig. 4
nd increasing the input weight resulted in the line marked with
ashed-dotted line. The simulation studies show the lower pre-
iction horizon gave faster responses but significantly increasing
he overshot amplitude, while larger input weight increased both
esponse time and overshoot.
. Performance assessment
The process assessment is performed at two different lev-
ls: IAE (integral of absolute error) and ISE (integral of square
rror), maximal deviation from setpoint and error variance serve
s a proof that the proposed control strategy has been applied
roperly. In this paper emphasis is placed on the first level of
ssessment, however, assessment of a activated sludge treatment
rocess (effluent quality, costfactor for operation) in the bench-
1 emical Engineering 32 (2008) 1270–1278
m
L
a

q
E
d
e
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c
E
w
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a
t
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i
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A
w
c
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a
e
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w
r
m
5
b
b
a

l
i
w
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c
A
a
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m
m
v
i
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t
a
t
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r
o
d
a
s
d
p
m
c
is emphasized that sampling time has a significant effect on the

effectiveness of the controller. Sampling time was selected at
�t = 10−3 day ≈1 min 25 s, later simulations were carried out
ark example is also carried out for the sake of comparison.
ength of the observation period is 7 days in the first example
s defined in the benchmark and 12 h in the second example.
At the second level of the controller assessment, effluent
uality operating cost is defined in the simulation benchmark.
ffluent quality index represents the levies or fines to be paid
ue to the discharge of pollution in the receiving bodies. The
ffluent quality is averaged in the first example over a 7-day
bservation period based on a weighting of the effluent loads of
ompounds:
Q = 1
1000T
∫ t2
t1
BSS × SSe(t) + BCOD × CODe(t) + BNKj
×SNKj ,e(t) + BNO × SNO,e(t) + BBOD5 × BOD5,e(t) dt
(7)
here EQ is the effluent quality index (kg poll. unit/day), Bi are
eighting factors, SS the suspended solids concentration, COD
nd BOD the chemical and biological oxygen demands, SNO is
he nitrite- and nitrate-concentration and STKN is the total N
(all
oncentrations are in g/m3). The energy needed for the aeration
s of special interest in this study, which is determined by the
ollowing formula:

E = 24
T
∫ t2
t1
n∑
i=1
[0.4032(KLa(t))
2
i + 7.8408KLai]dt (8)
here KLa is the mass transfer coefficient in h
−1 of the i-th
ompartment. The sludge production to be disposed (Psludge) is
alculated from the total solid flow from wastage and the solids
ccumulated in the system over the 7-day period. The pumping
nergy is calculated as:
E = 0.04
T
∫ t2
t1
(Qa(t) + Qr(t) + Qw(t))dt (9)
here Qa is the internal recirculation flow rate, Qr the sludge
ecirculation and Qw is the wasteage flow rate, all expressed in
3/day.
. Application example I: control of the simulation

enchmark
The COST 682 Working Group No. 2 has developed a
enchmark for evaluating by simulation, control strategies for
ctivated sludge plants (Copp, 2002). The benchmark is a simu-
ation environment defining a plant layout, a simulation model,
nfluent loads, test procedures and evaluation criteria.
The layout is relatively simple: it combines nitrification
ith pre-denitrification, which is most commonly used for
itrogen removal. The benchmark plant is composed of a five-
ompartment reactor with an anoxic zone and a secondary settler.
basic control strategy is proposed to test the benchmark: its
im is to control the dissolved oxygen level in the final com-
artment of the reactor by manipulation of the oxygen transfer
oefficient and to control the nitrate level in the last anoxic com-
artment by manipulation of the internal recycle flow rate. In this
Fig. 5. Simulation benchmark plant layout.
aper, only the control of the dissolved oxygen level is selected
or the demonstration of the efficiency of the MPC controller.
The plant layout can be seen in Fig. 5. The first two compart-
ents makes up the anoxic zone with individual volume of 1000
3, and 3 compartments create the aerobic zone with individual
olume of 1333 m3. The oxygen mass transfer coefficient rate
s set to 240 day−1, while the KLa at the last compartment is
ontrolled in order to maintain the dissolved oxygen concentra-
ion at 2 mg/l. The flowrate of the internal recirculation is kept
t 55338 m3/day. The secondary settler has a conical shape with
he surface of 1500 m2and the depth of 4 m. The flowrate of the
ludge recirculation is 18446 m3/day and the excess sludge is

emoved from the settler at 385 m3/day.
Since disturbances play an important role in the evaluation
f controller performances, influent disturbances are defined for
ifferent weather conditions. In this paper, dry-weather data
re considered containing 2 weeks of influent data at 15 min
ampling interval. Parameters for the second week influent are
epicted in Fig. 6. Diurnal variations and weekly trends (lower
eaks in weekend data) are also depicted by these data. The pri-
ary goal of the control is to maintain the dissolved oxygen
oncentration at the 2 mg/l level in the last compartment.
The controller tuning process in described in Section 4, but it
Fig. 6. Influent characteristics.
B. Holenda et al. / Computers and Chemical Engineering 32
(2008) 1270–1278 1275
F
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o
a
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T
T
P
I
E
S
A
P
ig. 7. The dissolved oxygen concentration and the oxygen mass
transfer coef-
cient in the third aerobic basin (solid line �t = 2.5 × 10−4;
dashed line
t = 10−3).
t �t = 2.5 × 10−4 day ≈ 20 s what resulted in considerable
ffect on the performance of the controller. Parameters of the
ontroller were tuned by trial-and-error method. On one hand,
he main goal was to maintain the dissolved oxygen concentra-
ion at the desired level, on the other hand, high energy
consump-
ion and rapid changes in the air flow rate should be avoided.
Data of the second week of a 2-week dry weather dynamic
imulation are of interest, preceding days are used for stabiliza-
ion of the system. The assessment – as described in Section 4–
an be seen in Figs. 7 and 9 and in Tables 1 and 2 compared to
he PI controller described originally in the benchmark for pro-

ess control. It has to be noted, that internal recycle flow control
as also applied in the benchmark besides the DO control, how-
ver, for the sake of direct evaluation only DO control has been
pplied in this simulation, recycle flow rate is kept at constant
owrate. Using this setting, better effluent quality index was
chieved, nevertheless, pumping energy is almost double of that
chieved with control. The energy consumptions for the aeration
re approximately the same using either control strategy.
The performance of the model predictive controller – largely
etermined by the parameters of the controller, like sampling
ime, prediction horizon and input weight – is compared to the
enchmark results. PI controller performance is also influenced
y the parameters, the values presented here are the average
esults taken from the simulator manual. In this simulation, two
ampling times were used for evaluation. It can be seen from
m
w
m
t
able 1
erformance of the activated sludge process
PI control benchmark
nfluent quality (kg poll. unit/day) 42,042
ffluent quality (kg poll. unit/day) 7,605
ludge production (kg SS) 17,100
eration energy (kWh/day) 7,248
umping energy (kWh/day) 1,458
Fig. 8. The alternating activated sludge process.

able 2 that that reducing the sampling time to its one-fourth,
from 10−3 to 2.5 × 10−4 day) reduced the integral of absolute
rror with more than 50% and reduced the integral of square
rror with more than 80%. Maximum deviation from setpoint
nd variance also descreased as the absolute error is significantly
ess during the whole observation period.
. Application example II: control of an alternating
ludge process
Most municipal wastewater treatment plants use an activated
ludge process. More specifically, for small-size treatment facil-
ties the process generally consists of a single aeration basin
onfiguration in which oxygen is either supplied by surface
urbines or diffusers, and is known as the alternating activated
ludge (AAS) process. Nitrogen removal is realized by simply
witching the aeration system on and off to create continuous
lternating aerobic and anoxic conditions, respectively. During
witched-on periods, ammonium is converted into nitrate which
s subsequently used to remove organic carbon in switched-off
eriods. An important feature of the AAS process is its flexi-
le control ability which makes it suitable for optimization of
perating costs. Since the process consists of alternating aer-
ted and nonaerated periods and the aeration induces 60–80%
f the global energy consumption (and subsequently operating
osts) of a treatment plant, oxygen control is therefore of great
mportance.
In this study, an industrial-scale AAS treatment plant is
onsidered described by Chachuat, Roche, and Latifi (2005).
he process consists of a unique aeration tank (V = 2050
3
) equipped with three mechanical surface aerators (turbines)
hich provide oxygen (P = 3 × 30 kW,KLa = 4.5 h−1) and
ix the incoming wastewater with biomass (Fig. 8). The set-

ler is a cylindrical tank where the solids are either recycled
DO MPC, �t = 10−3 day DO MPC, �t = 2.5 × 10−4 day
42,042 42,042
7,560 7,560
17,117 17,116
7,277 7,277
2,966 2,966
Ashraf Al shekaili
1276 B. Holenda et al. / Computers and Chemical Engineering
32 (2008) 1270–1278
Table 2
Performance of the oxygen controller
PI control benchmark DO MPC, �t = 10−3 day DO MPC, �t =
2.5 × 10−4 day
Controlled variables (SO,5)
Setpoint (gCOD/m3) 2 2 2
Integral of absolute error (gCOD/(m3 day)) 0.15 0.1950 0.0892
Integral of square error ((gCOD/(m3 day))2) 0.02 0.0128 0.0026
Max deviation from setpoint (gCOD/m3) 0.21 0.1648 0.0781
Variance of error (gCOD/m3) 0.04 0.0427 0.0196
Manipulated variable (KLa5)
Max deviation of MV (day−1) 204.5 187.39 187.19
Max deviation of � MV (day−1) 28.71 33.12 18.89

Variance of MV 59.85 59.79 59.76
Table 3
Performance of the oxygen controller in the alternating
activated sludge process
Prediction horizon p = 3 p = 5 p = 10
Controlled variables (SO)
Setpoint (gCOD/m3) 0/2 0/2 0/2
Integral of absolute error(gCOD/(m3 day)) 2.08 ×10−2 2.18
×10−2 3.48 ×10−2
Integral of square error ((gCOD/(m3 day))2) 9.46 ×10−3 5.99
×10−2 1.33 ×10−2
Max deviation from setpoint (gCOD/m3) 2.32 ×10−2 2.73
×10−2 4.55 ×10−2
M
8
t
t
i
e
c
c
i
a
2
c
o
m
c
p

F
(
e
o
s
v
fi
100. The results showed that lower prediction horizon reduced
significantly the integral of absolute and square error, how-
ever, input weight had insignificant effect on the error
according
anipulated variable (KLa)
Max deviation of MV (day−1) 240
Max deviation of � MV (day−1) 157.2
o the aeration tank (Qrec = 7600 m3/day) or extracted from
he system (Qw = 75 m3/day). During the simulation constant
nfluent flow rate and composition were supposed in order to
valuate the efficiency of the controller subject to rapid setpoint
hanges.
In this simulation the alternating sludge process is realized by
hanging the dissolved oxygen setpoint between 0 and 2 mg/l
n the bioreactor at 72 min (0.05 day). The manipulated vari-
ble (oxygen mass transfer coefficient) is varied between 0 and
40 day−1 to reach the desired DO-level using model predictive
ontrol. The controller is based on a linear state-space model
f the aeration process assuming ideal controller and measure-
ent described in Section 4. The changing dissolved oxygen
oncentration can be seen in Fig. 9 and in Table 3 with different
rediction horizons of the controller.
ig. 9. Dissolved oxygen control in the alternating activated
sludge process

solid line: p = 3; dashed line: p = 10; dotted line: p = 20).
240 240
126.05 45.38
Simulations were carried out at several parameter settings to
valuate the performance of the controller during the 0.5 day
bservation period. Sampling time was 2.5 × 10−4 day (≈ 20
). The output weight was fixed to 1, while the input weight was
aried between 0.001 and 0.01. The control horizon was also
xed to 1, the prediction horizon was changed between 3 and
Fig. 10. Integral of absolute error over the 12-h simulation
period.
emica
t
z
o
c
i
t
s
K
K
(
7
g
s
h
p

a
a
t
t
S
t
t
t
o
t
s
i
e
o
F
c
t
r
a
t
l
r
i
t
o
w
v
Appendix A
See Tables A.1–A.3 .

Table A.1
Double-exponential settling velocity parameters
Parameter Unit Value
v′0 m day
−1 250
v0 m day
−1 474
rh m
3 (g SS)−1 5.76 ×10−4
rp m
3 (g SS)−1 2.86 ×10−3
fns – 2.28 ×10−3
Table A.2
Weighting factors for the different types of pollution
he prediction horizon (Fig. 10). Reducing the prediction hori-
on from 10 to 3 moves (�u = 0.005), decreased the integral
f absolute error with more than 40%, nevertheless, maximal
hange in the manipulated variable between two sampling times
ncreased from 45 to 157 day−1. It can be observed in Fig. 11
hat both lower prediction horizon and lower input weight can
ignificantly increase the maximum deviation in the change of
La, at �u = 0.001 and p = 3 the change in the value of the
La reaches 240 day
−1, which is near to its maximal value
270 day−1).

. Conclusion
Model predictive control strategy of the dissolved oxy-
en concentration has been quantitatively investigated on two
imulated case-studies: the dissolved oxygen concentration
as to be maintained at 2 mg/l in the an aerobic basin of a
re-denitrification process with influent disturbances and an
lternating dissolved oxygen level has to be kept up in an
lternating activated sludge process. To evaluate the results sys-
ematic performance criteria were set up and calculated during
he simulations concerning the performance of the controller.
everal tuning parameters of the controller (input weight, predic-
ion horizon, sampling time) were also investigated. According
o the results of the paper, model predictive control can be effec-
ively applied in the control of dissolved oxygen concentration
f wastewater treatment plants.
Results from the first case-study show that the performance of
he controller can be considerably enhanced by decreasing the
ampling time, however, this improvement has no significant
mpact either on the the whole activated sludge process, or the
nergy consumption used for the aeration process. The integral
f absolute error decreased with 40% by reducing the sampling
ig. 11. Maximum deviation in the change in the oxygen mass
transfer coeffi-
ient over the 12-h simulation period.
F
B

B
B
B
B
T
S
P
Y
Y
f
i
i
μ
K
K
K
b
η
η

K
μ
K
b
K
k
l Engineering 32 (2008) 1270–1278 1277
ime from 1 min 25 s to 20 s, however, the effluent quality index
emained at 7560 kg (pollution unit)/day and the energy for the
eration remained at 7277 kWh/day.
The goal of the alternating sludge process simulation was
o investigate how efficiently model predictive control can fol-
ow the rapidly changing dissolved oxygen setpoint. From the
esults it can be concluded that lower prediction horizon and
nput weight can decrease the error between the setpoint and
he dissolved oxygen concentration, however, this will increase
vershot and cause rapid moves of the manipulated variable
hat can be avoided imposing constraints on the manipulated
ariable.
actor Value
SS 2
COD 1
NKj 20
NO 20

BOD5 2
able A.3
toichiometric and kinetic parameters of the activated sludge
model
arameter Unit Value
A g cell COD formed (g N oxidized)
−1 0.24
H g cell COD formed (g COD oxidized)
−1 0.67
p dimensionless 0.08
XB g N (g COD)
−1in biomass 0.08
XP g N (g COD)
−1 in endogenous mass 0.06
H day
−1 4
S g COD m
−3 10.0
O,H g O2 m
−3 0.2
NO g NO3-N m
−3 0.5
H day

−1 0.3
g dimensionless 0.8
h dimensionless 0.8
X (g cell COD)
−1 0.1
A day
−1 0.5
NH g NH3-N m
−3 1.0
A g day
−1 0.05
O,A g O2m
−3 0.4
a m
3COD (g day)−1 0.05
1 emica
R
B
B
B

C
C
C
C
C
C
C
D
D
F
G
H
L
M
Q
R
S
S

T
V
W
Y
Y
eferences
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treatment process using model predictive
controlIntroductionModelling aspectsModelling the biological
reactionsModelling the secondary clarifierModelling the
aeration processControl of the dissolved oxygen
concentrationModel predictive controlController
designPerformance assessmentApplication example I: control of
the simulation benchmarkApplication example II: control of an
alternating sludge processConclusionAppendix AReferences

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