MPC for Ozone Dosage in Water Treatment Process based on
Disturbance Observer
Dan Niu
1,2
, Xisong Chen
1,2
, Jun Yang
1,2
, Fuchun Jiang
3
and Xingpeng Zhou
1,2
1
Key Laboratory of Measurement and Control of CSE, Ministry of Education, China
2
School of Automation, Southeast University, No.2, Sipailou, Nanjing 210096, China
3
Xiangcheng Water Treatment Plant, Suzhou Running-water Company, Suzhou 215002, China
Keywords:
Ozone Dosage, Composite Control, Model Predictive Control, Disturbance Observer.
Abstract:
In the drinking water treatment, determining optimal ozone doses is vital for the treated water quality. An
effective control scheme is to control the dissolved ozone residual constant. However, it is not easy to be
achieved since some external disturbances always exist, such as large changes in water flow rate and raw water
quality. Moreover, the ozonation is a nonlinear process with long time delay and large time constant. The
conventional control strategies such as PID and traditional MPC reject disturbances merely through feedback
regulation, which will cause performance degradation in the presence of strong disturbances. In this paper, a
composite control scheme integrating MPC method as feedback controller and disturbance observer (DOB) as
feed-forward compensation is proposed to improve disturbance rejection of ozone dosage control system. The
test results demonstrate that the proposed method possesses a better disturbance rejection performance than
the MPC method in the ozonation process.
1 INTRODUCTION
In the water treatment, ozonation is considered as
an attractive alternative to chlorine for the disinfec-
tion, oxidation of micropollutants and organic mat-
ter, color and odor removal(Xie, 2016)(GAD et al.,
2015)(Hubner et al., 2015). In this process, deter-
mining the optimal ozone dosage is critical for its
effective application, since insufficient dosage is dif-
ficult for reliable disinfection and removel of wa-
ter matrix compounds(Lee et al., 2014). On the
other side, too high doses are uneconomical and also
lead to health problems related to high levels of dis-
infection byproducts (such as bromate)(Silva et al.,
2014)(Kaiser et al., 2013). A commonly used and ef-
fective control strategy for ozone dosage is to main-
tain a constant dissolved ozone residual(Kang et al.,
2008)(der Helm AWC et al., 2009). However, it is
known that apart from the ozone dosage, the raw wa-
ter quality (such as COD, turbidity and temperture)
and the water flow rate will also greatly affect the
dissolved ozone residual(Shin et al., 2015). In prac-
tice, the raw water quality and the water flow rate
always vary and these variations are hard to express
with an accurate mathematical model(der Helm AWC
et al., 2007). Moreover, the ozonation process con-
sists of many complicated chemical and physical re-
actions(Shin et al., 2015). In this case, undesirable
characteristics such as long time delay and nonlin-
ear exist when controlling the dissolved ozone resid-
ual(Oh et al., 2003). It is a challenge to control
the ozonation process with constant dissolved ozone
residual under the unpredictable raw water quality
change and water flow rate change.
To control the dissolved ozone residual, a widely
used method is to form a feedback control loop.
The classical PID control algorithm(der Helm AWC
et al., 2009) and some more advanced control al-
gorithms are proposed, including fuzzy logic algo-
rithm(Heo and Kim, 2004)(Chowdhury et al., 2007),
neural network(Wang et al., 2014)(Zahedi et al.,
2014), internal model control(Wang et al., 2013),
model-predictive control(Wang et al., 2014)(Taylor
and Akida, 2007)(Wang Dongshen, 2010) and so on.
Among these algorithms, traditional MPC algorithm
is very popular and widely adopted in the industrial
process control(Prakash et al., 2010)(Maciejowski,
2001), since MPC method has advantages for those
systems with long time delays due to its prediction
mechanism(Wang et al., 2013). However, the above-
mentioned advanced control principles can only re-
ject disturbances by the feedback regulation in a rel-
556
Niu, D., Chen, X., Yang, J., Jiang, F. and Zhou, X.
MPC for Ozone Dosage in Water Treatment Process based on Disturbance Observer.
DOI: 10.5220/0006410305560561
In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 556-561
ISBN: Not Available
Copyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
atively slow way and not directly by controller de-
sign. In the constant dissolved ozone residual control
system, various disturbances exist, including external
ones (raw water quality and flow rate changes) and in-
ternal ones (model mismatches). Considering the dis-
turbances are difficult to measure or forecast, distur-
bance observer (DOB) is introduced, which is an ef-
fective technique to estimate disturbances and widely
applied in various practical systems(Kobayashi et al.,
2007)(Chen et al., 2015)(Li et al., 2014).
This work is based on a pilot-scale ozonation fa-
cility of Xiangcheng water treatment plant in Suzhou,
China. A DOB-MPC scheme is proposed to improve
the disturbance rejection performance of the ozona-
tion process. The proposed scheme consists of a feed-
forward compensation based on DOB and a feedback
regulation using MPC. It can take advantages of both
MPC and DOB.
2 CONTROL SCHEME BASED ON
MPC AND DISTURBANCE
OBSERVER
In the ozonation control system, the dissolved ozone
residual y(mg/L) is the most important controlled
variable, which needs to be kept at a desired setpoint.
Larger or smaller dissolved ozone residual than the
setpoint will influence the treated water quality or de-
grade the production efficiency. The ozone dosage
x(mg/L), controlled by the PLC controller, is the ma-
nipulated variable. Note that, the changes of raw wa-
ter quality (mainly the COD value d
c
) and water flow
rate d
f
will cause the continuous fluctuations of the
dissolved ozone residual. They are deemed as exter-
nal disturbances in the control system.
The ozonation is a typical and commonly used in-
dustry process. In this process, the dissolved ozone
residual can be regulated by controlling the ozone
dosage. As shown in(Wang Dongshen, 2010)(Wang
et al., 2013), this dynamic can be modeled as a first-
order plus dead-time (FOPDT) form, which is most
commonly used model to describe the dynamic of
industrial process. Here the nonlinear parts can be
deemed as the unmodeled dynamics (internal distur-
bances)(Chen et al., 2015)(Li et al., 2014). The trans-
fer function can be represented as
G
1
(s) =
K
1
T
1
s+ 1
e
−θs
, (1)
where K
1
is the static amplification coefficient, T
1
is
the time constant, θ is the time delay.
Moreover, the bandwidth of the dissolved ozone
concentration analyzer can satisfy the system require-
ments, so the transfer function of the dissolved ozone
concentration analyzer can be approximated by a pro-
portional cycle K
2
.
In summary, the total transfer function of the dis-
solved ozone residual control can be represented as
G
P
(s) = K
2
G
1
(s) =
K
1
K
2
T
1
s+ 1
e
−θs
. (2)
The control system can be considered using the
following model
Y(s) = G
P
(s)X(s) + D
ex
(s), (3)
where
G
P
(s) = g(s)e
−θs
, (4)
D
ex
(s) =
M
∑
i=1
G
di
(s)D
i
(s). (5)
In Eqs. (3)-(5), X(s) the manipulated variable;
Y(s) the controlled variable; D
ex
(s) the effects of ex-
ternal disturbances on Y(s); D
i
(s) (i=1,2,· · · ,M) the
ith external disturbances. G
P
(s) is the model of the
process channel. g(s) is the minimum-phase part of
G
P
(s). G
di
(s) (i=1,2,· · · ,M) is the model of ith dis-
turbance channel. The nominal model G
n
(s) can also
be represented as a product of a minimum-phase part
g
n
(s) and a dead-time part e
−θ
n
s
.
G
n
(s) = g
n
(s)e
−θ
n
s
. (6)
2.1 Model Predictive Control
The process dynamic of system (Eq. (6)) can be
shown as
y(t) =
∞
∑
k=1
T(k)∆x(t − k), (7)
∆x(t) = x(t) − x(t − 1), (8)
where x(t) the manipulated variable; T(k) the dy-
namic matrix got from the coefficients of unit step
response; y(t) the output under the ∆x(t − k)(k =
1, · · · , ∞). From the Eq. (7), the qth step ahead predic-
tion of the output with the prediction correction term
ey(t + q) can be shown as
ey(t + q) =
q
∑
k=1
T(k)∆x(t + q− k)
+
∞
∑
k=1
T(k+ q)∆x(t − k) + ξ(t), (9)
ξ(t) = ey(t) − y(t), (10)
MPC for Ozone Dosage in Water Treatment Process based on Disturbance Observer
557
where ξ(t) the prediction correction term. In Eq. (9),
∆x(t + q − k)(k = 1, · · · , q) represents the future ma-
nipulated variable moves, which can be obtained by
computing the below optimization problem
min
∆x(t)···∆x(t+C−1)
J =
P
∑
m=1
[e
T
(t + m)M
e
e(t + m)]
+
C−1
∑
m=0
[x
T
(t + m)M
i
x(t + m)], (11)
e(t + m) = ey(t + m) − r(t + m), (12)
where r(t + m) the desired reference trajectory; e(t +
m) the prediction error. P denotes the prediction hori-
zon. C denotes the control horizon. M
e
is the error
weighting matrix and M
i
is the input weighting ma-
trix. Only the first move is employed. For the next
sampling instance, this step is repeated.
The parameters, such as control horizon (C), pre-
diction horizon (P) and sampling time T
s
, are very im-
portant for the robustness and stability performance.
The readers can refer to (Maciejowski, 2001) for de-
tailed tuning guidelines of MPC parameters.
2.2 Disturbance Observer-enhanced
MPC Algorithm
In this paper, a composite control scheme is pro-
posed to enhance the performance of the MPC feed-
back controller by adding a disturbance observer. The
block diagram is presented in Fig. 1.
MPC
r(s)
M(s)
X(s)
g(s)e
-θs
+
Y(s)
G (s)
dc
G (s)
df
D (s)
c
D (s)
f
+
+
+
R(s)e
-θ s
R(s)g
-1
n
n
(s)
+
-
D (s)
ex
D (s)
de
+
-
DOB
Figure 1: Block diagram of the disturbance observer-
enhanced MPC control.
In this figure, r(s) denotes the reference trajectory
of controlled variable. M(s) represents the output of
the MPC controller.
e
D
de
(s) is the disturbance estima-
tion. The output can be represent as
Y(s) = G
m
(s)M(s) + G
d
(s)D
ex
(s), (13)
with
G
m
(s) =
g(s)e
−θs
1+ R(s)g
−1
n
(s)[g(s)e
−θs
− g
n
(s)e
−θ
n
s
]
,
(14)
G
d
(s) =
1− R(s)e
−θ
n
s
1+ R(s)g
−1
n
(s)[g(s)e
−θs
− g
n
(s)e
−θ
n
s
]
.
(15)
From the Eqs. (13)-(15), it can be obtained that
the performance of disturbance rejection mainly de-
pends on the design of filter R(s). It can be found
that lim
w→0
G
d
( jw) = 0 when R(s) is selected as
a low-pass filter with a steady-state gain of 1, i.e.,
lim
w→0
R( jw) = 1. It means that low-frequency dis-
turbances can be attenuated asymptotically. In this
work, R(s) is selected as a first-order low-pass fil-
ter with a steady-state gain of 1, which can be rep-
resented as
R(s) =
1
ηs+ 1
, η > 0. (16)
2.3 Control Implementation
In this work, the proposed control scheme focuses on
disturbance rejection against external disturbances as
well as model mismatches. The detailed control struc-
ture is shown in Fig. 2. The variations of water COD
value d
c
and water flow rate d
f
are the main external
disturbance variables.
MPC
Dissolved
ozone residual
+
-
Ozone generator
DOB
Ozonation process
Ozone concentration analyzer
Dosage
Disturbance
estimation
Disturbances
d
c
d
f
Raw water COD
Water flow rate
r
x
y
Figure 2: Control structure of constant dissolved ozone
residual.
From Fig. 2, the ozone dosage directly affects the
primary output (the dissolved ozone residual). For
control study, step response of ozone dosage in pilot-
scale facilities has been tested to develop the transfer
function as follows:
G
n
(s) =
0.42
148s+ 1
e
−86s
. (17)
The nominal value of the dissolved ozone residual
is 0.3 mg/L. The external disturbances are imposed on
the process through disturbance channels. It is known
that the water COD and water flow rate have great
influences on the dissolved ozone residual. These dy-
namics can be also modeled as a first-order plus dead-
time (FOPDT) form (Wang Dongshen, 2010). Note
that DOB does not reply on precise disturbance mod-
els(Li et al., 2014). The transfer functions of distur-
bance channels G
dc
(s) and G
d f
(s) are also obtained
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
558
by step response tests in pilot-scale facilities and ex-
pressed as follows
G
d f
(s) =
0.19
108s+ 1
e
−60s
, (18)
G
dc
(s) =
−0.23
165s+ 1
e
−108s
. (19)
The time constants are expressed in seconds here.
G
dc
(s) and G
d f
(s) donote the transfer functions of
disturbance channels water COD value variation and
water flow rate variation, respectively. Here the dis-
turbances are expressed in a relative change form
rather than a real physical unit form. For example,
d
f
=10% means that the water flow rate has an in-
crease of 10% compared with its nominal value.
Moreover, based on the above discussions, the fil-
ter of DOB is employed as
R(s) =
1
0.2s+ 1
. (20)
The MPC controller parameters are designed as
P = 20,C = 1, T
s
= 1min, M
e
= 1, M
i
= 1. (21)
3 PERFORMANCE ANALYSIS
AND COMPARISONS
In this part, some results are shown to demonstrate the
benefits of the proposed method. For comparison, the
MPC controller is employed. Meanwhile, the distur-
bance rejection performance is studied not only in the
nominal case but also in the model mismatch case.
3.1 Disturbance Rejection in Nominal
Case
Firstly, the nominal case is considered, which means
that G
n
(s) = G
P
(s) holds.
Step external disturbances in the nominal case: the
water flow rate has an increase of 20% at t = 20min,
while the water COD value has an increase of 20% at
t = 50min.
Figure 3(a) shows the response curves of the dis-
solved ozone residual under the control of both DOB-
MPC and MPC in this case. Fig. 3(b) gives the ef-
fects of external disturbances and the estimations on
the controlled variables. From Fig. 3(a), the dynamic
performance of the dissolved ozone residual under
the proposed method is much better than those under
the MPC method. Compared with the MPC method,
the proposed method can obtain a faster convergence
speed, smaller overshoot amplitudes. From Fig. 3(b),
it can be observed that the errors between the esti-
mated and real external disturbances are very small,
which means that the disturbance observer can effec-
tively estimate the effects caused by disturbances.
(a)
0 10 20 30 40 50 60 70 80
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (min)
The dissolved ozone residual(mg/L)
MPC−DOB(nominal case)
MPC(nominal case)
(b)
20 30 40 50 60 70 80
−0.01
−0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Time (min)
Effects of disturbances on the ozone residual
Real time value
Estimation in nominal case
Figure 3: Response curves of variables in the presence
of step external disturbances under DOB-MPC and MPC
schemes in the nominal case: (a) controlled variable, (b)
disturbances and their estimations.
In order to quantitatively analyze the disturbance
rejection performance, two performance indexes in-
cluding peak overshoot and integral of absolute er-
ror (IAE) are employed, which are shown in Table 1.
From Table 1, it is clear that both the overshoot and
the IAE value under the proposed method are much
smaller than those under the MPC method.
3.2 Disturbance Rejection in Model
Mismatch Case
In real practice, besides external disturbances, inter-
nal disturbances caused by model mismatches are an-
other important factors for the control performance of
MPC for Ozone Dosage in Water Treatment Process based on Disturbance Observer
559
Table 1: Performance indexes under step external distur-
bances in the nominal case.
Performance the dissolved the dissolved
index ozone residual ozone residual
(MPC) (MPC-DOB)
Overshoot(%) 9.63% 5.65%
IAE 0.402 0.132
the closed-loop system. As illustrated in section 2,
the proposed method can reject not only external dis-
turbances, but also the internal disturbances caused by
model mismatches. In this part, some simulation stud-
ies are done to demonstrate the lumped disturbance
rejection performance of the proposed method.
Suppose that the transfer function model of pro-
cess channel is expressed as
G
P
(s) =
0.47
168s+ 1
e
−72s
. (22)
Comparing (22) with (17), it is clear that severe
model mismatch exists.
Step external disturbances in the model mismatch
case: the the water flow rate has an increase of 20% at
t = 20min, while the water COD value has an increase
of 20% at t = 50min.
The response curves of the dissolved ozone resid-
ual under the two methods in this mismatch case are
shown in Fig. 4(a). The effects of lumped distur-
bances and the estimations in this mismatch case are
presented in Fig. 4(b). It can be observed from Fig.
4(a) that the proposed method possesses a smaller
peak overshoot and a faster convergence speed. This
means that the proposed method has achieved a much
better step disturbance rejection performance than
that of the MPC method even in the case of severe
model mismatches. Moreover, the errors between the
estimated and the real lumped disturbances are also
very small.
Those results demonstrate that the proposed
method has remarkable superiorities in rejecting such
lumped disturbances consisting of external distur-
bances and internal disturbances caused by model
mismatches.
4 CONCLUSIONS
In the ozonation process, various disturbances have
undesirable influences on the control of the dis-
solved ozone residual. Many existing methods includ-
ing MPC have limitations in handling strong distur-
bances. For improving the disturbance rejection per-
formance, a compoundcontrol structure combining of
a feedforwad compensation part using DOB with a
(a)
0 10 20 30 40 50 60 70 80
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (min)
The dissolved ozone residual(mg/L)
MPC−DOB(mismatch case)
MPC(mismatch case)
(b)
Figure 4: Response curves of variables in the presence
of step external disturbances under DOB-MPC and MPC
schemes in the mismatch case: (a) controlled variable, (b)
disturbances and their estimations.
feedback regulation part based on MPC is proposed.
Both external disturbances and internal disturbances
caused by model mismatches are taken into consider-
ation. The results have demonstrated that, compared
with the MPC method, the proposed method has ex-
hibited excellent disturbance rejection performance,
such as a smaller overshootand a shorter settling time.
ACKNOWLEDGEMENTS
This work was supported by the National Natural Sci-
ence Foundation of China (No. 61504027), the NSF
of Jiangsu Province (No. BK20140647), the Priority
Academic Program Development of Jiangsu Higher
Education Institutions.
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
560
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MPC for Ozone Dosage in Water Treatment Process based on Disturbance Observer
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