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Computers and Chemical Engineering 32 (2008) 1270–1278

Dissolved oxygen control of the activated sludge wastewater 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

l d o c p t K m p

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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).

n d i 2 O g t

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

emica

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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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. 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.

p

w n

3

g A t s w l

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.

g F a s i o t �

t a d d t r

4

e e a p a p

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 o c

E

w w a t c i f

A

w c c a e

P

w r m

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b a l i

w n c A a p c p

p f

m m v i c t a t s 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

274 B. Holenda et al. / Computers and Ch

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 fi �

a e c t t t

s t c t c w e a fl a a a

d t b b r s

T ( e e a l

6 s

s i c t s s a s i p b o a o c i

c 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

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

B. Holenda et al. / Computers and Ch

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

278 B. Holenda et al. / Computers and Ch

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