Multi-loop PI-based control strategies for the Activated Sludge

Process

R. Vilanova�, R. Katebi†, V. Alfaro��

�Departament de Telecomunicació i d’Enginyeria de Sistemes, ETSE

Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.

Ramon.Vilanova@uab.cat† Industrial Control Centre, University of Strathclyde, Glasgow, UK,

r.katebi@eee.strath.ac.uk��Departamento de Automática, Escuela de Ingeniería Eléctrica

Universidad de Costa Rica, San José, 11501-2060 Costa Rica.

Victor.Alfaro@ucr.ac.cr

Abstract

This paper proposes a multi loop decentralized con-trol strategy for the control of a wastewater treatmentplant based on an Activated Sludge (ASP) model. TheASP is a described by means of a nonlinear modeland results on a Two-Input Two-Output multivari-able system. Even though advanced control strategieshave been presented in the literature, the proposal ofthis paper is to show that by appropriate tuning ofdecentralized PI controllers, it is possible to get com-parable performance as with other approaches. Withthis purpose the paper proposes a way of addressingthe design of the decentralized controllers as well as aregulation based tuning for a PI controller. Simula-tions are carried out on the nonlinear model showingthe performance of the proposed approach.

1 Introduction

The Activated Sludge Process (ASP) is arguablythe most popular bioprocess utilized in the treatmentof polluted water, using microorganisms presentwithin the treatment plant in the biological ox-idation of the wastewater. With the provisionof adequate oxygen supply, this process can bemaintained to degrade the organic matter in thepollutant. Most modern wastewater treatment plantsis of this type and consists of a series of bioreactorsand settlers. In this report the configuration of asingle bioreactor connected to a single secondaryclarifier is considered. See fig. (1). More complexmodels such as ASM models can be used as proposedby the IWA working group, [3, 4, 5]. The simplifiedbut still realistic and highly non-linear four-statemultivariable model considered here is the Activated

Sludge Process (ASP) [9].

Figure 1. Activated Sludge Process layout

Wastewater treatment control has begun a grad-ual progress towards the use of more advancedtechnology, in the face of more stringent modernwater quality standards. Several approaches havebeen reported in the literature that attempt tocontrol the ASP process. These ranges from Fuzzy,Model Based Predictive control, and a number ofadvanced multivariable techniques. See for example[12, 6, 13, 2].

What is analyzed in this paper is the suitability ofapplying simple control strategies such as single-loopbased PI controllers. In principle, by using a fullmultivariable controller the expected performanceof the resulting controller is superior to that of justusing a single-loop based control strategy. However,there is a major advantage with the single-loopPI/PID based control strategy that is the simplicityof the control structure and tuning. The schemeprovides the plant operators with easy access to thecontroller tuning parameters in order to adjust theloop performance based on the output observation. Itis therefore important to know the tradeoff betweenthe level of performance lost in applying such simplestrategies in comparison with the complexity of

978-1-4244-2728-4/09/$25.00 ©2009 IEEE

more advanced full multivariable approaches. It isalso well known that despite the great advances ofmodern control approaches during the last decades,PI/PID controllers are still the most widely usedin the process industries, being difficult and costlyfor modern controllers to be introduced at plantlevel. The latter is the motivation for this work todevelop appropriate methods for designing PI/PIDcontrollers in such a way they provide reasonableperformance levels.

The implementation presented here therefore isthe regulation of the dissolved oxygen level to auser-specified set point in an activated sludge reactorwithin a wastewater treatment plant. The aim is tomaintain a satisfactory level of dissolved oxygen andsubstrate concentrations in the effluent. The paper isorganized as follows. Section 2 presents the processdescription as well as operating considerations. Adecentralized approach is pursued in section 3 jointlywith the tuning approach used to tune the two PIcontrollers to be used. In section 4 performanceis compared with a decentralized approach tunedby applying the IMC approach and also with amultivariable PI controller, and the final sectionconcludes with a summary, discussion and proposalof future work direction.

2 Activated Sludge Process (ASP)Description

The mathematical model considered in this paperis given in [9]. The ASP process comprises an aera-tor tank where microorganisms act on organic matterby biodegradation, and a settler where the solids areseparated from the wastewater and recycled to theaerator. The layout is shown in figure (1). The com-ponent balance for the substrate, biomass, recycledbiomass and dissolved oxygen provide the followingset of non-linear differential equations:

dX(t)

dt= μ(t)X(t) − D(t)(1 + r)X(t) − rD(t)Xr(t)(1)

dS(t)

dt= −

μ(t)

YX(t) − D(t)(1 + r)S(t) + D(t)Sin (2)

dDO(t)

dt= −

Koμ(t)

YX(t) − D(t)(1 + r)DO(t)

+ KLa(DOs − DO(t)) + DO(t)DOin (3)

dXr(t)

dt= D(t)(1 + r)X(t) − D(t)(β + r)Xr(t) (4)

μ(t) = μmax

S(t)

kS + S(t)

DO(t)

kDO + DO(t)(5)

where X(t) - biomass, S(t) - substrate, DO(t) -dissolved oxygen, DOs - maximum dissolved oxygen,Xr(t) - recycled biomass, D(t) - dilution rate, Sin

and DOin - substrate and dissolved oxygen concen-trations in the influent, Y - biomass yield factor,μ - biomass growth rate, μmax - maximum specificgrowth rate, kS and kDO - saturation constants,KLa = αW - oxygen mass transfer coefficient, α -oxygen transfer rate, W - aeration rate, Ko - modelconstant, r and β - ratio of recycled and wasteflow to the influent. The model parameterizationis according to tables (1) and (2). On the otherhand,the influent concentrations are set to Sin = 200mg/l and DOin = 0.5 mg/l.

Biomass X(0)=215 mg/lSubstrate S(0)=55 mg/lDissolved Oxygen DO(0)=6 mg/lRecycled Biomass Xr(0) = 400 mg/l

Table 1. Initial Contitions

β = 0.2 Kc=2 mg/lr = 0.6 Ks=100 mg/lα = 0.018 KDO=0.5Y = 0.65 DOs = 0.5 mg/lμmax = 0.15 h−1

Table 2. Kinetic parameters

With respect to the control problem definition, thewaste water treatment process is considered underthe assumption that the dissolved oxygen, DO(t),and substrate, X(t), are the controlled outputsof the plant, whereas the dilution rate, D(t), andaeration rate W (t) are the two manipulated variables.

2.1 Linearized model

For controller design purposes, the previous modelis linearized around the operating point defined bythe steady-state inputs of Dss = 0.0825 and Wss =90 . The resulting linear model will have a transferfunction matrix of the form:

G(s) =

(G11(s) G12(s)G21(s) G22(s)

)(6)

such that

(S(t)

DO(t)

)= G(s)

(D(t)W (t)

)(7)

The Gij(s) = nij(s)/d(s) transfer function compo-nents are given as:

G11(s) =134.0243s3 + 295.3529s2 + 53.5176s + .5855

s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008(8)

G12(s) =−0.0312s2 − 0.0062s − 0.0001

s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008(9)

G21(s) =−9.2834s3 − 15.0312s2 − 2.6325s − 0.0123

s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008(10)

2

G22(s) =0.0699s3 + 0.0340s2 + 0.0042s + 2.910−5

s4 + 2.4617s3 + 0.9859s2 + 0.1107s + 0.0008(11)

As it can be seen there is a clear interaction dueto the off-diagonal terms being different from zero.

3 Decentralized PI control approach

Here, the basic relationships to take into accountfor the decentralized control of a TITO system arepresented. As the application to the ASP need PItuning rules for good disturbance rejection and theapproximate models of ASP for design will be of firstorder with no delay, the tuning method presentedwill only consider the case of First Orders with nodelay plant models. However the approach extends(see [1]) to the case of First-Order-plus-Time-Delaymodels. Once the basic approach for tuning has beenpresented, it is applied to the ASP presented above.

3.1 Control of TITO Processes

Under a decentralized approach each loop has itsown noninteractive controller. Figure (2) show thebasic scheme of a Two-Input Two-Output (TITO)process, highlighting the additional loops that isbeing created to compensate the interaction. Theoff-diagonal terms G12(s) and G21(s) cause couplingbetween the two separate input-output pairs. Thisinteraction effect between loops causes to generateseveral undesirable effects for control design and itis necessary to take it into account at the design stage.

G11(s)K1(s)r1 u1

y1

G22(s)K2(s)u2 y2r2

G12(s)

G21(s)

Figure 2. Decentraliced control block dia-gram for a Two-Input Two-Output System

Assume a diagonal pairing 1-1/2-2 is selected anda controller K1(s) is applied to control y1 by usingu1, and a controller K2(s) to control y2 by using u2

as shown in figure (2). If we close the loops aroundG11(s) and G22(s) respectively, it would be naturalto state the design of each controller in terms of theseopen-loop diagonal terms and try to find K1(s) andK2(s) such that

T1(s) =K1(s)G11(s)

1 + K1(s)G11(s)≈ T d

1 (s) (12)

T2(s) =K2(s)G22(s)

1 + K2(s)G22(s)≈ T d

2 (s) (13)

where T d1 (s) and T d

2 (s) specify the desired closed-loopdynamics for the corresponding individual closed-loops. We will refer to these loops as the independentlocal-loops. Therefore the local controllers will acton the local-loops as if they were on a single-loop.

However, under such decentralized control strat-egy, the off-diagonal interaction terms G12 and G21

will introduce additional dynamics that will cause thetransfer functions seen by the controllers to be, re-spectively:

G1(s) = G11(s) −K2(s)G12(s)G21(s)

1 + K2(s)G22(s)(14)

G2(s) = G22(s) −K1(s)G12(s)G21(s)

1 + K1(s)G11(s)(15)

These relations clearly show the tuning of one ofthe controllers depends on the tuning of the otherone. This kind of interaction is the main problemthat arises in decentralized control. A better look atthe interaction terms can be obtained by introducingT1(s) and T2(s) from (12) and (13) into (14) and (15)obtaining:

G1(s) = G11(s)

(1 −

G12(s)G21(s)

G11(s)G22(s)T2(s)

)

= G11(s) (1 − I(s)T2(s)) (16)

G2(s) = G22(s)

(1 −

G12(s)G21(s)

G11(s)G22(s)T1(s)

)

= G22(s) (1 − I(s)T1(s)) (17)

where

I(s) =G12(s)G21(s)

G11(s)G22(s)(18)

is the Rijnsdrop interaction measure [14] that can,in turn, be related to other well known interactionmeasures such as the dynamic RGA

3

λ(s) =G11(s)G22(s)

G11(s)G22(s) − G12(s)G21(s)(19)

=1

1 − I(s)

I(s) = 1 −1

λ(s)(20)

In addition, the RGA term λ(s) can be related tothe Niederlinski index NI [10] as

λ(s)|s=0=

1

NI(21)

Among all these, otherwise classical, interactionmeasures, it is the I(s) index that enters the transferfunction seen by each local controller in a more directway. Therefore preferred in the developments thatfollow.

Expressions (16) and (17) reveal the total inter-action results from a combination of the inherent(open-loop) process interaction as measured by theRijnsdrop index and the control interaction expressedby the independent closed-loop transfer functions.Therefore, existing interaction can be either amplifiedor attenuated depending on the local control actions.It seems therefore not complete to take any decisionon the pairing of manipulated and control variablesas well as the design of the local controllers withouttaking control interaction into account.

3.2 Tuning relations for PI control

This section will present the controller structurewe will work with as well as the corresponding tuningrelations. The approach is taken from [1]. On thisrespect, consider the control system with a 2-DOFcontroller of Fig. 3 whose output to a change in anyof its inputs is given by

y(s) =Cr(s)P (s)

1 + Cy(s)P (s)r(s)+

P (s)

1 + Cy(s)P (s)d(s) (22)

The controller output is given to

u(s) = Cr(s)r(s) − Cy(s)y(s) (23)

where

Cr(s) = Kc

[β +

1

Tis

](24)

is the set-point controller transfer function and

Cy(s) = Kc

[1 +

1

Tis+ Tds

](25)

the feedback controller transfer function.Considering a First-Order (FO) controlled-process

given by

P (s) =Kp

Ts + 1(26)

Figure 3. 2-DOF Control System

the design equations for a PI controller are obtainedin ([1]) in terms of the nondimensional design param-eter (τc = Tc/T ). The normalized close-loop timeconstant τc is an indication of the relative speed of thecontrol system in relation with process model speedas:

κc = KcKp =2 − τc

τc

(27)

τi =Ti

T= τc(2 − τc) (28)

where κc and τi are the controller normalized param-eters.

In addition, in order to obtain a non-oscillatoryresponse, an adequate selection of the set-pointweighting factor would be β = τcT/Ti.

3.3 Multi-loop PI Control of the ASP

In order to apply the proposed method to tune thePI controllers, a first order model approximation isneeded. Our starting point will be the linearized ver-sion of the ASP. On that basis and from the previousdiscussion, the design of the local PI controllers willbe done from a First Order model that approximatesthe dynamics of the effective transfer functions seenon each loop as expressed in (16) and (17). Note inorder to compute these approximations we need tostate a desired transfer function, T d

1 (s) and T d2 (s) for

each loop. From figure (4) we get a rough idea of theopen loop time constants of each loop (see the timeresponses of G11(s) and G22(s)) as, approximately,T1 ≈ 4 and T2 ≈ 0.5. As a first choice for the desiredclosed loop specifications we state the desired speedof response as half the open loop time constants.Therefore the desired input-output transfers willobey to:

T d1 (s) =

1

Tc1s + 1T d

2 (s) =1

Tc2s + 1(29)

with Tc1 = 2 and Tc2 = 0.25. The resulting G1(s)and G2(s) are plotted in figure (4) as well as theirfirst order approximation:

Gapp1

(s) =500

(4s + 1)Gapp

2(s) =

0.0355

(0.5s + 1)(30)

4

0 5 10 15 20 25 300

100

200

300

400

500

600

Step response of G11

(s)

Time (h)0 1 2 3 4 5

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Step response of G22

(s)

Time (h)

0 5 10 15 20 25 300

100

200

300

400

500

600

Step resp. of G1(s) (dash−dot) FO (solid) G

11(s) (dasehd)

Time (h)0 1 2 3 4 5

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Step resp. of G2(s) (dsah−dot) FO (solid) G

22(s) (dasehd)

Time (h)

Figure 4. First Order approximation of theeffective transfer functions seen by localcontrollers

Application of the above presented method for PIdesign involves the choice of the tuning parametersτc1 and τc2. According to the previously stated tar-get models for the individual closed loops, these non-dimensional tuning parameters should be chosen asτc1 = τc2 = 0.5. However as the PI controllers willfinally be applied to the non-linear model these tar-gets may result (and in fact this is the case) too fastresponse. At this moment an analytical check has notbeen performed as it will need some knowledge andmeasure of the uncertainty incurred when doing themodel approximation. The DO controller tuning pa-rameter has been increased till τc2=1.8 as for lowervalues the responses and control actions were to muchoscillating. Table (3) shows the PI controller settingsfor both loops.

τc Kc Ti β0.9 (loop 1) 0.0024 3.96 0.910.5 (loop 1) 0.0060 3.0 0.671.8 (loop 2) 3.13 0.18 1.0

Table 3. 2-DoF PI settings for Substrate(loop1) and DO (loop2)

Figure (5) shows the time responses when astep reference change is applied on both loops. Onthe other hand, the effect of changing the tuningparameter on the substrate loop is effectively seen.The applied step reference changes are step of 10units for the substrate at t = 10h followed by a stepchange of -2 units on the DO at t = 100h. As it canbe seen from the step responses the DO loop causesmore interaction disturbance on the substrate loopthan its counterpart.

As an additional test for performance, a change on

0 50 100 15040

42

44

46

48

50

52

54 Substrate:

Time (h)

0 50 100 1500.08

0.09

0.1

0.11

0.12

0.13 Dilution rate

Time (h)

0 50 100 1503.5

4

4.5

5

5.5

6

6.5

Time (h)

DO

0 50 100 15040

50

60

70

80

90

100

110 Aeration rate

Time (h)

τc1=0.9 & τ

c2=1.8

τc1=0.5 & τ

c2=1.8

Figure 5. Time responses for step changeson substrate and DO for two tunings ofthe Substrate controller: τc1=0.9 & τc1=0.5,whereas the DO controller is set to τc2=1.8

0 50 100 15040

40.5

41

41.5

42

42.5

43

43.5

44 Substrate:

Time (h)

0 50 100 150

0.075

0.08

0.085

0.09 Dilution rate

Time (h)

0 50 100 1506

6.05

6.1

6.15

6.2

Time (h)

DO

0 50 100 15089

89.5

90

90.5

91

91.5

92

92.5

93 Aeration rate

Time (h)

τc1=0.9 & τ

c2=1.8

τc1=0.5 & τ

c2=1.8

Figure 6. Regulation performance for a peri-odical discharge on Sin of about 10% duringone hour every 24h. Tunings are τc1=0.9 &τc1=0.5, whereas the DO controller is set toτc2=1.8

5

the influent conditions is applied. When forcing themodel it was assumed that the influent concentrationwas Sin = 200mg/l. However this concentrationwill not remain constant but change periodically.Regulation performance of the controllers is tobe able to keep the substrate and DO values attheir set-point despite variations in the influentcharacteristics. In this case a periodical dischargehas been simulated. It is considered that every 24h, adischarge of 1h takes place that increases the value ofSin by a 10%. Figure (6) show the two PI controllersperform on such sittuation. As the distrubancemainly enters on the substrate loop, the DO loop willreceive the substrate control actions as disturbancesbecuase of the existing process interaction. For thecontrollers at hand it is seen that the DO variable isset at its set-point with a variation no larger than 1%.

4 Comparison with other techniques

In this section a comparison of the proposeddecentralized approach is carried out. First theproposed Pi tuning is tested against the well knownInternal Model Control (IMC) approach. Bothtunings will be based on the same process models,therefore adopting the framework for decentralizeddesign just presented in the previous section. Ona second step, the approach is also compared witha full multivariable controller. The Maciejowskimethod [7] as it is applied in [11] that produces amultivariable PI controller.

4.1 Internal Model Control PI tuning

For comparison purposes, the PI tuning relationsthat arise by application of the Internal Model Con-trol (IMC) approach are also introduced [8]. As theprocess model is just of first order the IMC parameterresults as

Q(s) =1

Kp

Ts + 1

λs + 1(31)

therefore the resulting feedback controller reads

K(s) =Q(s)

1 − Q(s)P (s)=

1

Kp

Ts + 1

λs(32)

that can be identified to a PI controller with tuning

κc = KcKp =T

λ(33)

τi =Ti

T= 1 (34)

where κc and τi are the controller normalized parame-ters. In this case, the IMC parameter λ directly deter-mines the desired closed-loop time constant. There-fore, for a fair comparison, similar tunings will be

used. The values of λ for each loop are thereforetaken as λ1 = τc1T1 and λ2 = τc2T2, where we takeτc1 = 0.5 (λ1 = 2) and τc2 = 1.98 (λ2 = 0.98). How-ever, with this specification the DO loop becomesunstable when applied to the nonlinear system. It istherefore needed to specify a larger time constant forthat loop. λ2 has to be increased by a 50% to getreasonable responses ((λ2 = 1.5τc2T2). The step re-sponses and load disturbance performance, comparedwith the proposed method are shown in figures (7)and (8).

0 50 100 15040

42

44

46

48

50

52

54 Substrate:

Time (h)

0 50 100 1500.08

0.085

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13 Dilution rate

Time (h)

0 50 100 150

3.5

4

4.5

5

5.5

6

6.5

Time (h)

DO

0 50 100 15040

50

60

70

80

90

100

110 Aeration rate

Time (h)

PI−IMC (λ1=2 & λ

2=1.38)

τc1=0.5 & τ

c2=1.8

Figure 7. Time responses for step changeson substrate and DO for the proposed andPI IMC tuings

0 50 100 15040

40.5

41

41.5

42

42.5

43 Substrate:

Time (h)

0 50 100 1500.06

0.065

0.07

0.075

0.08

0.085

0.09 Dilution rate

Time (h)

0 50 100 1506

6.02

6.04

6.06

6.08

6.1

6.12

6.14

6.16

6.18

6.2

Time (h)

DO

0 50 100 15089

89.5

90

90.5

91

91.5

92

92.5

93 Aeration rate

Time (h)

PI−IMC (λ1=2 & λ

2=1.38)

τc1=0.5 & τ

c2=1.8

Figure 8. Regulation performance for a peri-odical discharge on Sin of about 10% duringone hour every 24h. Comaprison of the pro-posed tuning and the PI IMC approach

6

4.2 Multivariable PI tuning

There are different ways of approaching the designof a multivariable controller. Among them there aresome attempts to produce multivariable versions ofthe PI and PID structures. See for example [11]and [12]. Just for comparison purposes, one of thosemethods, the Maciejowski method, is considered herefor comparison purposes. Also due to a lack of spaceother methods are avoided but it has been testedthat the results are similar to the ones reported here.

The Maciejowski [7] technique proposed to diago-nalize the system near the bandwidth, ωb. In orderto do this, a multivariable PID controller is proposedwhere the proportional, integral and derivative termsof:

K(s) = Kp + Ki

1

s+ Kds (35)

are computed as:

Kp = ρG(jωb)−1 Ki = εG(jωb)

−1 Kd = δG(jωb)−1

(36)

where ρ, ε and δ are the scalar tuning parameters.The G(jωb)

−1 term will produce a complex gain.Therefore in order to realize such a controller, a realapproximation of G(jωb)

−1 is needed. In order to doso, the Align algorithm can be applied [7]. This al-gorithm attempts to get a constant real matrix K sothat the following index is minimized:

J(K,Θ) = (KG(jωb)−1−e−jΘ)T (KG(jωb)

−1−e−jΘ)(37)

where Θ =diag(θ1, ..., θn). The application of thismethod follows [11], where the initial selection ofbandwidth is 0.02 rad/s. This value is chosen fromthe lowest settling time in order to get the faster speedof transient response. K as a real approximation ofthe system’s gain at that frequency is given as:

K ≈ G(j0.02)−1 =

[0.0021 0.00331.2955 28.67

](38)

When ρ = 1, the integral action scaling may takevalues of 0 < ε < 3.12 to produce acceptable closedloop response. Thus, ε is set to 0.312 to achieved themaximum speed of a closed-loop response. As it canbe seen in figures (9) and (10) performance of bothschemes is highly comparable, specially on the regu-lation aspects that are of utmost importance if oneconsiders that for a waste water plant, uncertaintyon the influent concentration is a common situation.

0 50 100 15040

42

44

46

48

50

52

54 Substrate

Time (h)

0 50 100 1500.08

0.085

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125 Dilution rate

Time (h)

0 50 100 1503.5

4

4.5

5

5.5

6

6.5 DO

Time (h)

0 50 100 15030

40

50

60

70

80

90

100

110 Aeration rate

Time (h)

Decentraliced PI

Maciejowski Multivariable PI

Figure 9. Regulation performance for a peri-odical discharge on Sin of about 10% dur-ing one hour every 24h. Comaprison ofthe proposed tuning and the MultivariablePI method of Maciejowski

0 50 100 15040.5

41

41.5

42

42.5

43

43.5 Substrate

Time (h)

0 50 100 1500.072

0.074

0.076

0.078

0.08

0.082

0.084 Dilution rate

Time (h)

0 50 100 1506.04

6.05

6.06

6.07

6.08

6.09

6.1

6.11

6.12

6.13

6.14 DO

Time (h)

0 50 100 15089.4

89.6

89.8

90

90.2

90.4

90.6

90.8

91

91.2 Aeration rate

Time (h)

Decentraliced PI

Maciejowski Multivariable PI

Figure 10. Regulation performance for a pe-riodical discharge on Sin of about 10% dur-ing one hour every 24h. Comaprison of theproposed tuning and the the MultivariablePI method of Maciejowski

7

5 Conclusions

This paper has presented a suitable approachfor decentralized control of the activated sludgeprocess. Even other advanced control methods arepossible, the practical advantage of a multiloopPI based control scheme is clear. On one handeach loop can be readjusted independently (becauseit is decentralized) and on the other hand, it issuitable to the plant operator as the controllers aresimple PI controllers tuned by means of one singleparameter. This single parameter approach is basedon a regulation specification and, when applied tothe nonlinear system, exhibits superior performancethan the well known IMC based PI controller.

The proposed approach (approach for decentral-ized design as well as PI tuning) has also been com-pared with a full multivariable PI controller, showingcomparable performance for tracking step referencesignals and even superior performance for regulationpurposes against variable influent concentration.

6 Acknowledgments

This work has received financial support fromthe AECI-PCI program A/018462/08, the MICINNProExt mobility program grant PR2008-0102 andfrom the Spanish CICYT program under grantDPI2007-63356.

References

[1] V. M. Alfaro, R. Vilanova, and O. Arrieta. An-alytical Robust Tuning of PI controllers for First-Order-Plus-Dead-Time Processes. In 13th IEEE

International Conference on Emerging Technologies

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