CHEMICAL ENGINEERING TRANSACTIONS 
 

VOL. 61, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-51-8; ISSN 2283-9216 

Control Strategy for Dissolved Oxygen of Paper Mill Activated 

Sludge Wastewater Treatment Process 

Yi Mana, Wenhao Shena,*, Xiaoquan Chena, Marie-Noëlle Ponsb 

aState Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou, 510640, China  
bLaboratoire Réactions et Génie des Procédés (UMR CNRS 7274), Université de Lorraine, 1, rue Grandville BP 451, 

 F-54001 Nancy cedex, France 

 ppwhshen@scut.edu.cn 

A fuzzy logic system combined with PID (Fuzzy-PID controller) to control the dissolved oxygen concentration 

in the paper mill wastewater treatment process is proposed based on the developed sequential batch reactor 

simulation model of the wastewater treatment process in paper mills. A case study with the presence of noise 

has been studied and evaluated with the criteria considered in Benchmark Simulation Model No. 1. The 

simulation results with white noise on the dissolved oxygen reveal that the Fuzzy-PID controller possesses 

better control indices than that of conventional PID controller. The good anti-interference ability of the Fuzzy-

PID controller is meaningful and important for industrial application. 

1. Introduction 

An activated sludge wastewater treatment plant is regarded as a complex system due to its nonlinear 

dynamics, large uncertainty, multiple time scales in the internal process dynamics, and multivariable structure 

(Fajardo et al., 2016). The dissolved oxygen (DO) control method is the most widely spread in industrial 

process due to its significant influence on the behaviour and activity of the heterotrophic and autotrophic 

microorganisms living in the activated sludge (Olivieri et al., 2013). DO in the aerobic part of an activated 

sludge process needs sufficiently oxygen supply for the microorganisms, so that organic matter is degraded 

and ammonium is converted into nitrate. An excessively high level of DO, which requires high air flow rate, 

leads to a high-energy consumption and may cause the deterioration of sludge quality. The high DO in the 

internally recirculated water also makes the denitrification low efficient. For both economic and technical 

reasons, it is of important to control the DO level in the aerobic reactor. 

For the DO control in the activated sludge wastewater treatment, most of the control strategies were based on 

the conventional PID control method (Yang et al., 2014). The control effect of the DO was sometimes 

dissatisfactory due to the limitation of the PID controller (Bahita and Belarbi, 2015). In this paper, a fuzzy logic 

system combined with the PID controller for the DO in the sequential batch reactor (SBR) is studied based on 

the SBR simulation model of the wastewater treatment process for paper mill in the previous work (Fenu et al., 

2010). The new control strategy with on-line self-adjustment methods would adapt the changes of the 

activated sludge and optimize the wastewater treatment process. The criteria presented in the benchmark 

simulation model 1 (BSM1) is used for evaluating the accuracy of the control strategy. 

2. Methods and models 

As the basis of the control strategy for dissolved oxygen, simulation model should be set up firstly (Mohd and 

Aziz, 2016). Figure 1 shows the SBR wastewater treatment process of a paper mill. The influent is the mixture 

of paper mill wastewater and deinking wastewater. The developed model is based on a simplified version of 

Activated Sludge Model #1 (ASM1) of the International Water Association (IWA) (Henze et al., 2000). The 

ASM1 was chosen as the biological process model and the double-exponential settling velocity function was 

selected as a fair representation of the settling process. 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1761049

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Man Y., Shen W., Chen X., Pons M.-N., 2017, Control strategy for dissolved oxygen of paper mill activated sludge 
wastewater treatment process, Chemical Engineering Transactions, 61, 307-312  DOI:10.3303/CET1761049  

307



PendingInlet and aerobic

 reaction

Aerobic 

 reaction
Mix Settling, 

outlet

Air Air 

Influent from 

paper mill

Effluent

Waste

 

Figure 1: Schematic diagram of SBR wastewater treatment process for paper mill 

2.1 Bioprocess model 
ASM1 has become a reference for many scientific and practical projects and has been implemented in most of 

the available commercial software for modeling and simulating of activated wastewater treatment. Based on 

the ASM1, the SBR biological reactions part is first modeled, and the model is then modified and simplified 

according to the industrial SBR processes in a paper mill. 

ASM1 has 13 components (state variables) and eight processes. However, for the limitation of the 

technological design of wastewater treatment, sensor technology and other factors, the whole ASM1 is rarely 

used directly for SBR modeling. The processes of the biological reactions are modified and simplified 

according to the industrial SBR process of the paper mill in this paper. The modification and simplification of 

ASM1 for bioprocess modeling is as follows. The SBR process of the paper mill does not contain anaerobic 

reaction, the anaerobic growth heterotrophic process and denitrification process could be neglected. In the 

SBR process, nutrient substances such as ceramide and phosphoric acid are added discontinuously to 

maintain the biological activity. The nitrogen and phosphorus in the wastewater treatment process are 

considered to be balanced as long as the nutrients nitrogen and phosphorus are added in the right amounts. 

To simplify the simulation model and make the model easier to be used in the industrial processes, nitrification 

and denitrification processes are neglected. This simplification has little impact on the aerobic growth 

heterotrophic process. Table 1 gives the matrix representation of the simplified ASM1 for the SBR process of 

the paper mill, which describes the components, process rate equations, and stoichiometry of the process. 

Nomenclatures in Table 1: SI: the soluble inert organic matter (mg /L), SS: the readily biodegradable substrate 

(mg /L), XI: the particulate inert organic matter (mg /L), XS: the slowly biodegradable substrate (mg /L), XB,H: 

the active heterotrophic biomass (mg /L), XP: the particulate products arising from biomass decay (mg /L), SO: 

the dissolved oxygen concentration (mg /L), YH: the heterotrophic yield (mg XBH COD formed/(mg COD 

utilized)), fP: the fraction of biomass to particulate products, KS: the half-saturation (heterotrophic growth) (mg 

/L), KOH: the half-saturation (heterotrophic oxygen) (mg /L), µH: the maximum heterotrophic growth rate (/day). 

Table 1: Matrix representation of the simplified ASM1 for paper mill SBR wastewater treatment process (Copp, 

2002) 

Component Xi 
1 2 3 4 5 6 7 Process rate rj 

SI SS XI XS XB,H XP SO [M/(L3 ×t)] 

Aerobic growth Heterotrophic - 
1

H
Y



 
- - 1 - 

1
H

H

Y

Y




 

( ) ( )S O
H BH

S S OH O

S S
X

K S K S


 

 

Decay Heterotrophic - - - 1- fP -1 fP - 

 

Hydrolysis organic compounds - 1  -1 - - - 

 

 

The general mass balance equations for the SBR bioprocess in a paper mill wastewater treatment process are 

as follows (Copp, 2002): 

H BH
b X

141

( / )

h S

X S BH

k X

K X X

308



in

dV
Q

dt


 
(1) 

3

, 0

1

j
i

i j j in

j

d X
p r V Q c

d t





   
 

(2) 

where V is the volume of activated sludge and wastewater (m3), Qin is the influent flow rate (m3/d), Xi is the 

weight of the i influent component (mg), pi,j is the j process of component Xi, rj is the process rate, c0 is the 

concentration of influent component (mg/L), and t is the time (h). 

2.2 Modeling the settling process 
The double-exponential settling velocity function of Takács et al. (1991) is selected to model the settling 

process: 

minmin
( )( )

0 0
( ) max{0, min[ , ( )]}pk

r X Xr X X

s
v X v v e e

  
 

 
(3) 

min ns f
X f X

 
(4) 

where X, Xmin and Xf are the total sludge concentration (mg/L), minimum attainable suspended solids 

concentration (mg/L) and mixed liquor suspended solids concentration (mg/L). The parameter fns is the non-

settleable fraction, and rp and rh are the flocculants zone settling parameter (mg/L) and hindered zone settling 

parameter (mg/L). The parameters v0, v0' and vs are the maximum settling velocity (m/d), maximum settling 

velocity (m/d) and settling velocity (m/d). 

The reactor is modeled as a 10-layer non-reactive unit during the settling process. According to the above 

notations, the mass balances for the sludge are written as: 

, , 1
min( , )

( 10)
s m m s m mm

m

v X v XdX
m

dt h




   (5) 

, , 1 , , -1
min( , )- min( , )

(1 10)
s m m s m m s m m s m mm

m

v X v X v X v XdX
m

dt h


    (6) 

, , 1
min( , )

( =1)
s m m s m mm

m

v X v XdX
m

dt h


  (7) 

where Xm is the suspended solids concentration in the layer m (mg/L), vs,m is the settling velocity of the layer 

m (m/d), and hm is the height of the layer m (m). 

Based on the simplified ASM1 and the general equations for mass balance in the settling process, the SBR 

simulation model of paper mill wastewater treatment process is developed by MATLAB/Simulink 6.0. The 

schedule of the SBR process in the paper mill is shown in Table 2, and its common time is used for the default 

time of simulation (Kriš and Hadi, 2010).  

Table 2: Schedule for the SBR process in the secondary fiber paper mill 

Reaction phase Common time (min) Time range (min) 

Inlet without aeration 60 30 - 90 

Inlet with aeration 60 30 - 120 

Aerobic reaction 120 60 - 180 

Settling 60 40 - 90 

Outlet 60 40 - 80 

Total 360 - 

3. Development of the adaptive controllers 

The PID controller is chosen to maintain DO at a given level in most of the activated sludge wastewater 

treatment processes. Since the wastewater treatment process has serious time-varying characteristics, the 

fixed parameters of the PID controller are not suitable for the constantly fluctuant situation. One online PID 

309



parameter adjusting module is added to the conventional PID controller in this work. The structure of the 

improved PID controller is illustrated in Figure 2. 

 

Online parameter 

adjusting module

PID
Plant

de/dt

errorrin +

-

u(k) yout

kp ki kd

 
kp: proportional coefficient; ki: integral coefficient; kd: differential coefficient 

Figure 2: Schematic of the improved PID control system 

As shown in Figure 2, rin is the set point of DO (2 mg/L), yout is the controlled DO variable, and u(k) is the flow 

rate of air (KLa) into the SBR process, which is the manipulated variable in the control system. The online 

parameter adjusting module was realized with fuzzy logic system combined with PID, which is used for 

controlling DO in the paper mill wastewater treatment process. 

Fuzzy logic control has good performance in the control of the non-linear complicated systems (Mendes et al., 

2014). In this study, a fuzzy logic system combined with the PID controller is used as an online PID parameter 

adjusting module to help the PID controller acquire appropriate parameters online.  

Referred to Figure 2, the main task of the fuzzy-PID is to find the fuzzy relationships between the PID 

parameters and the DO error (e) and the change of DO error (ec), and to make the corresponding adjustments 

of the PID parameters online. e and ec are selected as the input fuzzy linguistic variables, and △kp, △ki and 

△kd are the output fuzzy linguistic variables. The fuzzy control rules in the study are given in Table 3, and the 

PID parameters are on-line adjusted via the rule weighing based on Table 3. Abbreviations in Table 3: NB 

(Negative Big), NM (Negative Medium), NS (Negative Small), ZO (Zero), PS (Positive Small), PM (Positive 

Medium), PB (Positive Big).  

Table 3: Fuzzy control rules of △kp, △ki, △kd 

△ kp /△ ki /△ kd 
ec 

NB NM NS ZO PS PM PB 

e 

NB NS/NB/NS PB/PB/PB PB/PB/PB PB/PB/PB PB/PB/NB PS/NS/NB ZO/NM/NM 

NM NM/NB/PM PB/PB/PB PB/PB/PB PM/PM/PM PM/PM/NM ZO/NM/ZO NS/NB/PS 

NS NB/NB/PB PB/PB/PB PM/PM/PM PM/PS/PM PS/PS/NS NS/NB/PM NM/NB/PB 

ZO ZO/ZO/ZO ZO/ZO/ZO ZO/ZO/ZO ZO/ZO/ZO ZO/ZO/ZO ZO/ZO/ZO ZO/ZO/ZO 

PS PB/PB/PB NB/NB/PB NM/NB/PB NS/NB/PM PS/PS/NS PM/PS/PM PM/PM/PM 

PM PB/PB/PB NM/NB/PM NS/NB/ZO ZO/NM/ZO PM/PM/NM PB/PM/PM PB/PB/PB 

PB PB/PB/PB NS/NB/NS ZO/NM/NM PS/NS/NB PB/PB/NB PB/PB/PB PB/PB/PB 

4. Controlling results and discussion 

According to the proposed control strategies, the fuzzy-PID controller is applied to the simulated paper mill 

SBR wastewater treatment process. A case study with noise on DO sensors is conducted, and the 

performance of the controller is evaluated by Benchmark Simulation Model No. 1 (BSM1). 

The noise and disturbance are objective existence in the process of the activated sludge wastewater 

treatment process. To perform an actual simulation, a white noise signal was added on the DO sensor. Figure 

3 shows the controlling results of DO with white noise disturbance under the controlling actions of the different 

controllers. To observe the disturbing action, the variation of the measured DO with white noise is shown in 

Figure 3 (a). 

In Figures 3(b) and 3(c), the values between two red dotted lines represent the errors between the maximum 

and minimum DO values. A smaller error indicates that a controller has a better capacity for resisting 

disturbance. The errors of the PID controller the Fuzzy-PID controller between the maximum and minimum 

DO are 0.20 mg/L and 0.14 mg/L. That means the Fuzzy-PID controller performs better than the conventional 

PID controller in the aspect of anti-interference. The rising time for the PID controller and the Fuzzy-PID 

310



controller during the control are 9.8 min and 14.5 min, which demonstrates the response of the Fuzzy-PID 

controller is slower than the PID controller. For the case with white noise, the Fuzzy-PID controller shows the 

better performance in the DO control.  

0 50 100 150 200 250 300 350 400
-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

v
a
ri
a
ti
o
n
 o

f 
D

O
 

c
o
n
c
e
n
tr

a
ti
o
n
(m

g
.l

-1
)

Time(min)
0 50 100 150 200 250 300 350 400

1.4

1.6

1.8

2.0

2.2

D
O

 c
o

n
c
e

n
tr

a
ti
o

n
(m

g
.l

-1
)

Time(min)

0.2034

 
(a) (b) 

0 50 100 150 200 250 300 350 400

1.4

1.6

1.8

2.0

2.2

D
O

 c
o
n
c
e
n
tr

a
ti
o
n
(m

g
.l

-1
)

Time(min)

0.1378

 
(c)  

Figure 3: DO in the SBR reactor of the paper mill wastewater treatment process with different controllers (with 

white noise). (a) Variation of DO with white noise; (b) DO concentration of the paper mill wastewater with the 

conventional PID controllers; (c) DO concentration of the paper mill wastewater with the Fuzzy-PID controller. 

Table 4: Comparison of performance indices with the PID controller and the Fuzzy-PID controller for DO in the 

SBR reactor of the paper mill wastewater treatment process 

Item Performance index PID Fuzzy-PID 

Controlled variable 

(DO, mg/L) 

IAE 11.340 8.970 

ISE 1.280 1.377 

DEVmax 0.116 0.072 

VAR(e) 0.003 0.003 

Manipulated variable 

(KLa, h) 

DEVmv 2.588 2.397 

DEV
△u 0.555 0.297 

VAR(△u) 0.012 0.003 

 

According to BSM1, a group of performance assessment indices is suggested to evaluate the controller 

performance. It contains two parts: the controlled variable: IAE (integral of absolute error), ISE (integral of 

square error), DEVmax (maximal deviation from set point) and VAR(e) (error variance); and the manipulated 

variable: DEVmv (range), DEV△u (maximum deviation in the change in manipulated variable), VAR (△u) 
(variance of manipulated variable variations). These indices serve as a proof that the proposed control 

strategies are (or are not) applied properly. The above indices with the PID controller and the Fuzzy-PID 

controller for the DO control in the SBR reactor of the paper mill wastewater treatment process are 

summarized in Table 4. Compared with PID controller, with the presence of noise, almost all of the 

assessment indices of the controlled variable and the manipulated variable with the Fuzzy-PID controller are 

311



smaller, which means that it achieves better controlling performance than that of PID controller. Since the 

disturbance of noise are ubiquitous in the field, these improved indices of the Fuzzy-PID controller in Table 4 

manifest its good anti-interference ability, which is meaningful and important in the industrial application. 

5. Conclusions 

Based on the developed SBR simulation model of the wastewater treatment process for paper mill in our 

previous work, a Fuzzy-PID control strategy for the DO control in the SBR process have been studied and 

evaluated using the criteria considered in BSM1 by a case study. Simulation results with noise reveal that the 

Fuzzy-PID controller achieves the better controlled and manipulated indices than that of PID controller, where 

some of the controlling indices are improved, which demonstrates the Fuzzy-PID controller’s good ability for 

anti-interference. Although the Fuzzy-PID controller does not demonstrate good performance in the response 

rate, it could be applied to improve the control precision. 

Acknowledgments  

The research was supported by the Specialized Research Fund for the Doctoral Program of Higher Education 

of China (No. 20130172110014), Research Funds of State Key Laboratory of Pulp and Paper Engineering, 

South China University of Technology (No. 2017ZD03 and No. 2015C05), Science and Technology Planning 
Project of Guangdong, China (No. 2015A020215012), National Natural Science Foundation of Guangdong, 

China (No. 2016A030313478), and Science and Technology Program of Guangzhou, China (No. 

201607010050). 

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