regulación de aguas residuales petroquímicas en un sistema de

Revista Mexicana de Ingeniería Química

CONTENIDO

Volumen 8, número 3, 2009 / Volume 8, number 3, 2009

213 Derivation and application of the Stefan-Maxwell equations

(Desarrollo y aplicación de las ecuaciones de Stefan-Maxwell)

Stephen Whitaker

Biotecnología / Biotechnology

245 Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo

intemperizados en suelos y sedimentos

(Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil

and sediments)

S.A. Medina-Moreno, S. Huerta-Ochoa, C.A. Lucho-Constantino, L. Aguilera-Vázquez, A. Jiménez-

González y M. Gutiérrez-Rojas

259 Crecimiento, sobrevivencia y adaptación de Bifidobacterium infantis a condiciones ácidas

(Growth, survival and adaptation of Bifidobacterium infantis to acidic conditions)

L. Mayorga-Reyes, P. Bustamante-Camilo, A. Gutiérrez-Nava, E. Barranco-Florido y A. Azaola-

Espinosa

265 Statistical approach to optimization of ethanol fermentation by Saccharomyces cerevisiae in the

presence of Valfor® zeolite NaA

(Optimización estadística de la fermentación etanólica de Saccharomyces cerevisiae en presencia de

zeolita Valfor® zeolite NaA)

G. Inei-Shizukawa, H. A. Velasco-Bedrán, G. F. Gutiérrez-López and H. Hernández-Sánchez

Ingeniería de procesos / Process engineering

271 Localización de una planta industrial: Revisión crítica y adecuación de los criterios empleados en

esta decisión

(Plant site selection: Critical review and adequation criteria used in this decision)

J.R. Medina, R.L. Romero y G.A. Pérez

Vol. 13, No. 3 (2014) 919-931

REGULATION OF PETROCHEMICAL WASTEWATER AT AN ACTIVATEDSLUDGE SYSTEM VIA A SIMPLE ROBUST FEEDBACK CONTROL APPROACH

REGULACION DE AGUAS RESIDUALES PETROQUIMICAS EN UN SISTEMA DELODOS ACTIVADOS VIA UNA PROPUESTA SIMPLE DE CONTROL

RETROALIMENTADO ROBUSTOA. Velasco-Perez1∗, H. Puebla2, S. Martinez-Delgadillo3, M.A. Morales4 and R. Solar-Gonzalez5

1Facultad de Ciencias Quımicas, Universidad Veracruzana. Orizaba, Mexico2Departamento de Energıa, 3Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana,

Azcapotzalco, Mexico D.F.4Subgerencia de Calidad y Proteccion Ambiental, PEMEX Petroquımica, Coatzacoalcos, Veracruz.

5Universidad del Istmo. Tehuantepec, Oaxaca.

Received June 25, 2013; Accepted February 24, 2014

AbstractIn this paper the regulation of petrochemical wastewater from an activated sludge system is addressed via a simple robustfeedback control approach. The control approach is based on simple step response models and a favorable choice of thedischarge flow-rate from the settler as the manipulable variable. Based on simple first order model and first order modelplus input delay to account for dead-times induced by the measurement of COD two controllers are derived. The proposedcontrollers are composed by two parts: (i) an uncertainty observer to compensate uncertainties and neglected terms inthe input-output models, and (ii) an inverse dynamics feedback controller. Numerical simulations show good closed-loopperformance and robustness properties.

Keywords: petrochemical wastewater, wastewater treatment, activated sludge system, robust control, modeling errorcompensation.

ResumenEn este trabajo se aborda la regulacion de aguas residuales de la industria petroquımica en un sistema de lodos activadospor medio de un diseno simple de control robusto retroalimentado. La propuesta de control se basa en modelos de respuestaescalon simple y una eleccion favorable del flujo de descarga del sedimentador como la variable manipulable. Con base amodelos de primer orden y primer orden mas tiempo muerto, que considera el tiempo de retardo en la medicion de DQO,se derivan dos controladores robustos. Los controladores propuestos se componen por dos partes: (i) un estimador deincertidumbres para compensar incertidumbres y terminos despreciados en los modelos aproximados entrada-salida, y (ii)un control retroalimentado por inversion dinamica. Las simulaciones numericas, sobre un modelo validado de un sistemade lodos activados tratando aguas residuales de la industria petroquımica, muestran un buen desempeno a lazo cerrado ybuenas propiedades de robustez.

Palabras clave: aguas residuales petroquımicas, tratamiento biologico de aguas residuales, sistema de lodos activados,control robusto, compensacion de error de modelado.

∗Corresponding author. E-mail: [email protected]

Publicado por la Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica A.C. 919

Velasco-Perez et al. / Revista Mexicana de Ingenierıa Quımica Vol. 13, No. 3 (2014) 919-931

1 Introduction

High strength wastewaters are currently producedfrom various industrial plants such as petrochemicalindustries, coke-processing plants, metal finishingunits, etc. Wastewaters generated from theseprocesses contain a large number of pollutants athigh concentrations and have adverse environmentalimpacts. The activated sludge system (ASS) iswidely used treatment process for both domesticand industrial wastewater, which is based on thedevelopment of appropriate bacterial aggregates andother associated organisms in an aeration tank (Olssonand Newell, 2001; Greenberg et al. 1989; Dochainand Vanrolleghem, 2001). These organisms areeasily separated from the aqueous phase during thesubsequent sedimentation. In general, the mainobjective of a biological wastewater treatment is todecompose the organic compounds contained intothe wastewater. That is, the reduction of thepollutant concentration in the outlet stream below aspecified value, which is fixed by environmental andsafety regulations (Dochain and Vanrolleghem, 2001;Velasco-Perez et al. 2011; Velasco-Perez and Alvarez-Ramirez, 2007; Hamilton et al. 2006; Sment et al.2004).

Operating a wastewater treatment plant is not asimple task, as raw wastewater varies continuouslyin quantity and composition and the heart of theprocess, the biomass, also changes under the influenceof internal and external factors. Then, it is necessaryto design control strategies to keep the process ingood working condition (Dochain and Vanrolleghem,2001; Velasco-Perez et al. 2011; Velasco-Perez andAlvarez-Ramirez, 2007; Hamilton et al. 2006; Smentet al. 2004). It is well known that the control ofbiological systems is a very delicate problem since onehas to deal with highly nonlinear systems describedby poor quality models (Dochain and Vanrolleghem,2001; Velasco-Perez et al. 2011; Velasco-Perez andAlvarez-Ramirez, 2007; Hamilton et al. 2006; Smentet al. 2004; Weiland and Rozzi, 1991; Puteh etal. 1999). To solve this problem, many authorshave proposed controllers that were able to regulatewastewater concentration using the dilution rate of thebioreactor as input (Koumboulis et al. 2008; Ma etal. 2005; Charef et al. 2000, Georgieva and Feyo deAzevedo, 1999; Holenda et al. 2008; Polihnorakiset al. 1983; Neria-Gonzalez et al. 2008). Thesecontrol laws are however difficult to apply in practicedue that most of them assumes perfect knowledge ofthe mathematical model of the process. Moreover, by

essence they act on the influent flow-rate, and theymay therefore not accept all the incoming wastewater.It means that this type of controllers implies storageof the wastewater to be treated. In real wastewatertreatment plants, the influent flow rates are very highand storage tanks are very small, then this solutionis impractical. As a consequence, the controllersare often disconnected at the industrial scale and theplant manager manually operates the process tryingboth to avoid process destabilization and wastewaterstorage. In this work a simple robust control approachfor the regulation of the pollutant concentration (exitsubstrate concentration) in petrochemical wastewaterat an (ASS) is presented. To this end, a robust controlapproach based on modeling error compensation ideaswas followed (Alvarez-Ramirez, 1999). The controldesign is composed by an uncertainty estimatorcoupled with an inverse dynamics feedback functionto provide robustness against uncertain and neglectednonlinear terms. The control approach is based onsimple step response models. The discharge flow-rate from the settler is proposed as the manipulablevariable to regulate the substrate concentration.Based on results shown in numerical simulationsthe main contributions of this paper are two: (i)The introduction of the discharge flow-rate from thesettler as a suitable control input for the regulationof substrate concentration in ASS and (ii) the designof simple robust controllers based on modelingerror compensation ideas for the control of substrateconcentration in ASS using the minimum systeminformation obtained from simple input-output modelsincluding the case of time-delay measurements. Thus,the results in this work should be seen as a reliablecontrol to regulate the pollutant concentration atindustrial-scale ASS. The case study is the treatmentof wastewater of the Mexican petrochemical industry,Morelos S.A. de C.V., which has an ASS to treat itswastewater flow, which is about 7000 m3/d (Moraleset al. 2006; Martinez et al. 2005).

This work is organized as follows. In Section 2the ASS for petrochemical wastewater treatment ispresented and its mathematical model is recalled. InSection 3, both the input-output model identificationant the robust feedback control approach arepresented. In Section 4 numerical simulations ofthe closed-loop performance of the proposed controlapproach are shown. Finally, conclusions are given inSection 5.

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2 Activated sludge system

2.1 Process description

The Mexican petrochemical company Morelos SAde CV produces wastewater generated in variouschemical processes. The wastewater flow producesis about 7000 m3 per day and it contains volatileorganic carbon substances classified as toxic materialssuch as 1,2-dichloroethane, chloroform and benzene,among others volatile compounds (VOCs) (Moraleset al. 2006; Martinez et al. 2005). To comply withthe effluent quality required by Mexican environmentlegislation (SEMARNAP-1996, 1997), the wastewateris processed in the treatment plant before beingdischarged to the river. The treatment process consistsof oil removal, using a corrugated plate interceptor(CPI), equalization basin and an ASS implemented bythree independent bioreactors each with a volume of5000 m3.

The residence time in each bioreactor is about2 days. The biological sludge produced isconcentrated by centrifugation and the treated effluentis subsequently chlorinated. Some drawbacks arepresented because Morelos’ petrochemical wastewatertreatment plant is localized in the Mexican coast,where the mean temperature is 33 °C in the hottestmonths and in extreme conditions, it goes up to 40 °C.These high temperatures affect the air temperature atthe compressor exit that produces, in the spring andsummer, an increase in the bioreactor temperature atmore than 40 °C, affecting the bacterial growth. Fig. 1shows a simplified scheme of the ASS.

2.2 Mathematical model

A simple mathematical model of the ASS of theMexican petrochemical company Morelos SA deCV was derived and experimentally corroborated byMorales et al. (2006) and Martinez et al. (2005). Themodel was developed and validated with laboratoryreactors with 14 L of capacity, which were operatedat the same conditions as actual bioreactors of thepetrochemical plant. The model is derived from amacroscopic mass balance of the key variables of theprocess. For completeness we briefly discuss mainmodel features.

The dynamical model to describe the behavior ofthe chemical oxygen demand (COD), (S) biomass orvolatile suspended solids (X), and dissolved oxygen(CO2 ) in the reactor are expressed as,

Figure 1

Aerated Reactor

V, S, CO2, X

Settler

VS

Qf Qo S0

Qo Qe

Qu Xr

Qw = u Qr

Fig. 1 Schematic diagram of the activated sludgesystem.

dSdt

=Q f

VS in −

Q f

VS −

µmax

Yx/s

(S

Ks + S

)(

CO2

KOH + CO2

)X + kd(1− fn)X − kevS (1)

dXdt

=Qr

VXr −

Q0

VX + µmax

(S

Ks + S

)(CO2

KOH + CO2

)X

− kdX (2)dCO2

dt=

Qr

VCO2in −

Q0

VCO2 −

µmax

YO2

(S

Ks + S

)(

CO2

KOH + CO2

)X + kla

(CO2,sat −CO2

)(3)

and the biomass concentration (Xr) in the settler,

dXr

dt=

Q0

VSX −

QU

VSXr (4)

andQ0 = Q f + QrQU = QW + Qr

where Q f is the influent flow-rate, Qr is the recycleflow-rate, Qw is the discharge flow-rate, S in is theconcentration in the influent, CO2,in is the dissolvedoxygen concentration in the influent, CO2,sat is thedissolved oxygen saturation concentration, µmax is themaximum specific growth rate, Ks is the substratesaturation coefficient, KOH is the substrate saturationcoefficient, kd is the death coefficient, Yx/s is the yieldcoefficient, YO2 is the yield oxygen coefficient, kla isthe mass transfer coefficient, kev is the stripping ratecoefficient of volatile agents, fn is the fraction of inertson decay and Vs is the settler volume (Morales et al.,2006; Martinez et al., 2005).

Temperature effects on the performance of theASS were incorporated on O2,sat, kev , µmax, kla andkd as follows (Morales et al., 2006; Martinez et al.,

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2005),

O2,sat =(0.0035Tw2 − 0.3355Tw + 14.465)(0.985)(1.4185)

kev =0.016Tw − 0.165

µmax =0.7594exp

(−Tw − 26.4233.27

)2 (5)

kla =kla1.02(Tw−20)

kd =kd1.05(Tw−20)

where Tw is the reactor temperature.The following comments are in order:

• ASS is a complex biological degradationprocess resulting from the action of numerousmicroorganism species (Olsson and Newell,2001; Greenberg et al., 1989; Dochain andVanrolleghem, 2001). Although the modelgiven by Eqs. (1) - (5) represents in a simpleway the behavior of the ASS, it retains mostimportant dynamical features of the process,making it suitable for control study purposes.

• The underlying structure of the ASS modelconsists of two parts: (i) a linear part based onmass-balance considerations; and (ii) a numberof nonlinear terms that describes the biologicalreaction rates (kinetics). These kinetic terms areoften poorly known in practice.

3 Simple robust feedback controldesign

In this section, it is presented a robust feedbackcontrol approach to regulate the pollutant (substrate)concentration of petrochemical wastewater at an ASS.From control theory viewpoint, it is required toidentify both the measurable (system output) and themanipulated variables (control input) (Ogunnaike andRay, 1994).

The amount of decomposable organic matterin a wastewater can be measured in terms ofthe COD, since the COD determines the quantityof oxygen required to oxidize the decomposableorganic matter into CO2 and H2O. Then, thechosen measurable output is the regulated substrateconcentration COD. Total substrate concentrations Scan be made available for measurements via standardCOD methods (Greenberg et al. 1989; Weiland andRozzi, 1991).

Main parameters affecting the regulation of CODare the influent flow-rate Q f , and the recycle flow-rateQr. However, as discuss above, the manipulation ofQ f is impractical for industries with large wastewaterflows, as is commonly found in petrochemicalindustries and the manipulation of Qr can lead toinstabilities of the ASS. In this work, we introduceas the manipulated variable the discharge flow-rateQw. The manipulation of Qw exert a strong influenceon the exit substrate concentration of the ASS, asthe discharge flow-rate is used to manipulate solidsretention time, which in turn controls the net growthrate of microorganism in the process. The solidsretention time thus has a large impact on the overallplant dynamics.

3.1 Input-output models

It can be seen from model given by Eqs. (1) - (5)that the control input u = Qw, does not affect directlythe regulated output COD, such that it is hard tocompute a required control policy. An alternativeis to use simple input/output models, which retainthe main characteristics of the process dynamics forcontrol design (Ogunnaike and Ray, 1994). In thiswork, the feedback control design is based on input-output response models. Fig. 2 shows the numericalsimulation of positive and negative step response onthe non-lineal model of the ASS. Parameters for thesimulation are reported in Table 1 (Morales et al.,2006; Martinez et al., 2005). Input-output modelswere determined from the reaction curve process(Ogunnaike and Ray, 1994). It can be seen that thestep responses are smooth, almost monotonous, andconvergent, such that, it is reasonable to model theinput-output response with a simple stable first-ordermodel,

G(s) =Y(s)U(s)

=kp

τ0s + 1(6)

where kp is the steady-state gain and τ0 is a processtime-constant. Based on the input-output responseshown in Fig. 2, the first-order model parameters arekp ≈ 0.14 (mg/L)/(m3d) and τ0 ≈ 6 d. To account forthe delay in the measurement of COD, the model givenby Eq. (6) is completed as follows,

G(s) =Y(s)U(s)

=kp

τ0s + 1exp(−τd s) (7)

where τd ≥ 0 is the measurement time-delay, which isconsidered as τd = 0.02 d (≈ 120 minutes).

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80 90 100 110 120 130 140 150580

600

620

640

660

680

700

720

Time (d)

Qw

(m3 /d

)

80 90 100 110 120 130 140 150100

110

120

130

140

150

Time (d)

CO

D (m

g/L

)

Figure 2

Fig. 2 Step response of the substrate of the activated sludge system to changes in the waste flowrate.

Table 1 Parameter values for numerical simulations of the ASS model (1)-(5).

Parameter Value Parameter Value

Qw 650 m3/d Yx/s 0.69 mg biomass produced/mg COD consumed.Q f 7300 m3/d YO2 2.1 mg biomass produced/mg O2 consumed.Qr 1600 m3/d Ks 150 mg/LV 15000 L KOH 0.45 mg/LVs 750 L kd0 0.09 d−1

S in 1000 mg/L kla0 30 d−1

CO2,in 0.3 mg/L Tw 30ºCfn 0.9

3.2 Control problem

The control problem consists of regulating theoutput COD concentration at a prescribed effluentconcentration despite the fluctuation of the inputpollution and environment conditions, by acting onQw, under the following assumptions:

A1. The control input u = Qw, is subjected to asaturation nonlinearity, i.e. umin ≤ u ≤ umax.

A2. The exit COD, concentration of the activatedsludge system, i.e.,y = COD, is available witha measurement delay.

A3. Input-output models representation given byEqs. (6) and (7) are affected by unmodelled

nonlinearities ξ(y) and external disturbancesπ(t).

The following comments are in order:

• From a practical implementation viewpoint, thecontrol input u, which is the discharge flow-rate,is limited by maximum and minimum values.On the one hand, physical constraints limitsthe minimum value to zero, i.e., u = 0 m3/d,corresponding to a zero discharge of waste inthe settler. On the other hand, a maximum valueof u = 750 m3/d was set, which can be estimatedfrom the mass balance in the settler in order toprevent a depletion of the biomass in the settler.Moreover, for high Qw turbulence causes the

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sludge blanket to become “fluffy” diluting theunderflow stream and reducing the settling tankefficiency.

• The COD is measured routinely in industrialoperation. Traditional COD measurementmethods can take around 120 minutes(Greenberg et al., 1989; Weiland and Rozzi,1991). In general, the measurement time-delay can lead to both instabilities andpoor performance of the closed-loop system.In order, to reduce the time delay of theCOD measurement, a state estimator can bedesigned to estimate the COD measurementfrom the other measurements since it isobservable through the other state (Dochainand Vanrolleghem, 2001; Neria-Gonzalez et al.2008; Hadj-Sadok and Gouze, 2001).

• Assumption A3 is realistic since we have toassume that the input-output dynamics can beapproximated as an invariant linear first-orderplant, it is clear that the plant is affectedby unmodelled nonlinearities and externaldisturbances.

3.3 Control design

In this section, the control design for regulation ofthe COD based on a first order model and a firstorder model with measurement time-delay will beaddressed. The proposed controllers are based onmodeling error compensation techniques that leads tocontrol laws with simple structure and good closed-loop performance (Alvarez-Ramirez, 1999).

3.3.1 Control design without time-delay

Let us consider first the case where the CODconcentration is available without time-delay. Then,under Assumptions A3, the first-order input-model (6)can represented as,

e(t) = −τ−10 e(t) + kpτ

−10 u(t) + η(t) (8)

where e(t) = y−yre f is the regulation error, and η(t) is amodeling error function that contains uncertain termsand external disturbances, i.e.

η(t,y) = ξ(y) + π(t) + τ−10 yre f (9)

The modeling error function can be estimated with areduced order observer, which after simple algebraic

manipulations and introducing the variable w(t) =

τeη(t)− e(t) can be written as,•w(t) = τ−1

0 e(t)−kpτ−10 u(t)−η(t) η(t) = τ−1

e (w(t)+e(t))(10)

Where τe is an estimation time constant. Then giventhe regulation error e(t) and the input u(t) signals, thefirst-order filter given by Eq. (10), provides an estimateη(t) of the modeling error η(t).

An inverse-dynamics feedback control law, basedon model given by Eq. (8) with the estimatedmodeling error instead the real modeling error, is givenas,

u(t) = k−1p τ0[(τ−1

0 − τ−1c )e(t)− η(t)] (11)

Where τc is a prescribed closed-loop time constant. Inthis way, the proposed controller comprises the linearuncertainty estimator (10) and the linear feedbackcontroller (11).

The tuning of parameters τc and τe, can be setin two steps (Alvarez-Ramirez, 1999): (i) determinea value of τc up to a point where a satisfactorynominal response is attained, and (ii) the estimationtime constant τe, which determines the smoothnessof the modeling error and the velocity of the time-derivative estimation respectively, can be chosen asτe < 0.5τc.

3.3.2 Control design including time-delay

To design a feedback controller based on the first-ordermodel with time-delay (7) the Pade approximation forthe time-delay term is introduced (Ogunnaike and Ray,1994),

exp(−τd s) ≈1− (0.5τd)s1 + (0.5τd)s

(12)

such that the model (7) can be written as,Y(s)U(s)

=β

s2 +α1s +α0(1− τzs) (13)

Where τz = 0.5τd is the zero time constant, α1 =

(τ0 + τz)/(τ0τz), α0 = (τ0τz)−1 and β = kp/(τ0τz).By introducing a first-order filter in model (13) thefollowing causal approximation is obtained,

Y(s)U(s)

=β

s2 +α1s +α0

(1− τzs1 + τ f s

)(14)

where τ f is the filter time constant. In the timedomain, model (14) with assumption A1 to A3 isrepresented as follows,

••e (t) +α1

•e(t) +α0e(t) = −βu(t) + η(t) (15)

where η(t) includes unmodelled nonlinearities,external disturbances and the time-delay operator.

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Introduce the variable φ =•e(t) to rewrite (15) as

follows,

•e(t) =ϕ(t)•ϕ(t)=−α1φ(t)−α0e(t)− βu(t) + η(t) (16)

The modeling error function can be estimated with areduced order observer, which after some algebraicmanipulations and using ω = τeη − ϕ can be writtenas,

•ω = α1ϕ(t) +α0e(t) + βu(t)− η(t) (17)

It can be seen that the estimator (17) is driven by theregulation error e(t), and the input ϕ(t), i.e. the time-derivative of e(t), which can be approximated with asimple first-order filter,

ϕ(t) = −τ−1f (yre f − y(t)) (18)

The advantage of using the filter form (18) is thatthe uncertainty estimators are driven by the actualmeasurement y(t) and not by the time-derivative ofe(t).

An inverse-dynamics feedback control law, basedon model (16) with the estimated modeling errorinstead the real modeling error, and considering asecond order model as reference, is given as,

u(t) = β−1 [(k1 −α1)ϕ(t) + (k0 −α0)e(t) + η(t)

](19)

where k1 = 2ε/τc, k0 = τ−2c , and ε is a damping factor

of a general second-order model.The tuning of parameters k1, k0, and τe can be set

in three steps: (i) choose the close loop time-constantτc > 0 and the damping factor ε > 0 to obtain a desiredclosed-loop performance, (ii) following classical filterdesigns choose τ f smaller than the closed-loop timeconstant τc, (iii) the estimation time constant τe canbe chosen as τe > 0.5τc. From classical dampingcriteria, choose ε around 1.25 to avoid excessive signalovershooting (Ogunnaike and Ray, 1994).

4 Numerical simulationsIn this section, numerical experiments are presentedfor the regulation of the COD concentration inpetrochemical wastewater at the ASS (1-5) with thefeedback controllers based on a first-order model (10-11) and a first-order model plus time-delay (17-19).

To test the robustness of the proposed controllerunder uncertainties in the nominal parametersof the transfer functions (these uncertainties are

associated with the modeling error induces by externaldisturbances and neglected nonlinearities), numericalexperiments shown below were computed withestimated values of the parameters kp and τ0 above20 % of the nominal parameter values obtained fromsimulations shown in Fig. 2, i.e., proposed controllerare designed on input-output models with significantmodel uncertainties and implemented on the nonlinearmodel of the ASS. The control parameters were setaccording to the tuning guidelines described above. Inorder to obtain a fair comparison, both controllerswere assigned with the same control parameters.Namely, τc = 3, and τe = 1. The control action wasconnected at t = 50 days.

4.1 Regulation and set point change of theeffluent COD concentration

Figures 3 and 4 shows the control performance for theregulation of the COD concentration to the referencevalue of 100 mg/L, as well as a set point change in thedesired COD effluent concentration, from 100 to 125mg/L, at t = 150 days. The regulation value of 125mg/L is chosen in order to assure the operation belowof the maximum concentration of COD permittedby the environmental Mexican regulations despiteexternal perturbations.

Fig. 3 shows that the closed-loop system withouttime-delay provides an acceptable smooth transition toachieve the desired reference values. The control effortis also acceptable with final values about 450 m3/dand 650 m3/d for the desired set points, respectively.Despite the fast response of the control input, changingfrom the nominal value of 650 m3/d to 420 m3/d in1-2 days, this can be achieved with standard flowactuators.

Fig. 4 shows the closed-loop behavior for thesystem with time-delay. It can be seen from thisfigure that the controller including time-delay is alsoable to provide an acceptable closed-loop behavior,although the control performance is affected by themeasurement time-delay, as some oscillatory behaviorand a slight overshoot are displayed.

Despite +20% uncertainty in the input-outputmodel parameters used for the control design, it canbe concluded form results shown in Figures 3 and 4,that controllers takes the exit COD concentration tothe reference values with an acceptable control effort.In order to achieve the substrate set-point of 100 mg/La major solids retention time is required that the setpoint of 125 mg/L.

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4.2 Robustness against external disturbances

Although a rigorous robustness analysis is beyond thescope of this study, numerical experiments will showthat the feedback controller is able of regulate theeffluent COD concentration at the activated sludgesystem despite significant external disturbances. Inparticular, numerical experiments were carried outconsidering typical disturbance to the wastewatertreatment system, namely: (i) COD concentrationdisturbances at the inlet conditions from a nominalvalue of 1000 mg/L to 1150 mg/L, (ii) reactortemperature operation Tw from a nominal value of 30°C to 35 °C, (iii) input flow-rate Q f from a nominalvalue of 730 m3/d to 840 m3/d, and (iv) the recycleflow-rate Qr from a nominal value of 1600 m3/d to1760 m3/d.

Fig. 5, for the controller design free of time-delay and Fig. 6 for the controller design includingtime-delay, shows the closed-loop performance fora 15 % positive perturbation of the nominal inputCOD concentration and an increase of 5 °C, at t =

100 days and t = 150 days, respectively. Fig. 5and 6 shows that the closed-loop system is able toreject both applied disturbances in acceptable times.It can be seen from Fig. 5 that perturbation leadsto a slight departure of about 10-15 mg/L of thenominal regulation value. The rejection times forthe above applied perturbations are 20 days and 15days, respectively. As expected, it is noted that betterperformance is obtained with the controller free ofdelay. However, acceptable closed-loop performanceis also obtained with the controller based on the first-order model with time-delay. It can be observed fromthe closed-loop response shown in Figures 5 and 6 thatin order to reject the positive 15 % perturbation of thenominal input COD concentration the control inputdecreases leading to an increase of the sludge retentiontime. On the other hand, for the positive increaseof 5 °C in the reactor temperature, the control inputsreach lower values with respect to the regulation caseas the reactor´s temperature perturbation is applied.In this case, the control input diminishes in order tocompensate the increase of temperature. The increaseof temperature slows the COD degradation, such thatin order to maintain the COD set point, a moreconcentration of microorganism acting on the blanketsludge is necessary.

Figures 7, for the controller design free of time-delay and Fig. 8, for the controller design includingtime-delay, shows the closed-loop performance forperturbations in Q f and Qr at t = 100 days and t = 200

days, respectively. It can be seen in both cases thatcontrollers are able to reject flow-rate perturbationswith an acceptable closed-loop performance. For theperturbation in Q f the control input decreases untilvalues of Qw = 120 m3/d. On the other hand, tohandle the perturbation in Qr the controller increasesslightly Qw in order to compensate the increase ofthe microorganisms in the reactor of the ASS due theincrease of Qr.

Based on the above observed results, it is notedthat both controllers can successfully regulate theoutput even in the presence of significant disturbanceswith an acceptable closed-loop performance. Sucha robustness property is introduced by the observer-based estimator that provides an estimate of alluncertain terms that are compensated with the inverse-dynamics feedback function.

4.3 Comparison of the proposed controllerwith conventional PI controllers

As was stated in the introduction, Q f and Qr, arethe commonly control inputs used for the control ofCOD in AS S . In order to compare the closed-loopperformance of the proposed controller using Qw asthe control input, Figure 9, shows the closed-loopperformance for conventional PI controller and ourproposed controller for the case of control design freeof delay. PI controllers were tuned following IMCtuning rules with parameters obtained from input-output responses. Input-output parameters are thefollowing: (i) Q f − COD, kp ≈ 0.016 (mg/L)/(m3d)and τ0 ≈ 6 d, (ii) Qr−COD, kp ≈ −0.036 (mg/L)/(m3d)and τ0 = 3.6 d.

The closed-loop performance was evaluated forthe regulation task to a desired set point of COD =

100 mg/L and same external perturbations applied inFigures 5 and 6, i.e. the input COD concentrationand the reactor temperature, at t = 200 days and t= 300 days, respectively. Figure 9 shows that theproposed controller has better regulation capabilitiesthan conventional PI controller using Qw, Q f and Qras control inputs. Indeed, the control input effortwith the proposed controller is less than the obtainedwith PI controllers, which reaches saturation valuesfor the corresponding control inputs. The closed-loopperformance for the applied external perturbations iscomparable for the proposed controller and the PIcontroller using Qw as control input. This result isexpected due the well know robustness capabilitiesof PI controllers, which are also displayed with theproposed controller with the advantage of a control

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design endowed with a transparent incorporation ofmodel uncertainties. The worst performance of theclosed-loop performance for external perturbations is

observed for the PI controller using Qr as control inputdue the saturation of the control input to the uppercontrol input value.

0 50 100 150 200 250 300400

450

500

550

600

650

700

Time (d)

Qw

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)

0 50 100 150 200 250 30050

100

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CO

D (m

g/L)

Figure 3

Fig. 3. Regulation and set point change closed loop performance for the controller design without time delay.

0 50 100 150 200 250 300300

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700

800

Time (d)

Qw

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)

0 50 100 150 200 250 30050

100

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g/L)

Figure 4

Fig. 4. Regulation and set point change closed loop performance for controller design with time delay.

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0 50 100 150 200 250100

200

300

400

500

600

700

Time (d)

Qw

(m3 /d

)

0 50 100 150 200 25050

100

150

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Time (d)

CO

D (m

g/L)

Figure 5

Fig. 5. Closed loop performance for perturbations in inlet COD concentration and reactor temperature for controllerdesign free of time delay.

0 50 100 150 200 250100

200

300

400

500

600

700

Time (d)

Qw

(m3 /d

)

0 50 100 150 200 25050

100

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Time (d)

CO

D (m

g/L)

Figure 6

Fig. 6. Closed loop performance for perturbations in inlet COD concentration and reactor temperature for controllerdesign with time delay.

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0 50 100 150 200 250 300100

200

300

400

500

600

700

Time (d)

Qw

(m3 /d

)

0 50 100 150 200 250 30050

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Time (d)

CO

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g/L)

Figure 7

Fig. 7. Closed loop performance for perturbations in the input flow rate Q f and the recycle flow-rate Qr for controllerdesign free of time delay.

0 50 100 150 200 250 300100

200

300

400

500

600

700

Time (d)

Qw

(m3 /d

)

0 50 100 150 200 250 30050

100

150

200

Time (d)

CO

D (m

g/L)

Figure 8

Fig. 8. Closed loop performance for perturbations in the input flow rate Q f and the recycle flow-rate Qr for controllerdesign with time delay.

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0 50 100 150 200 250 300 350 4000

2000

4000

6000

Time (d)

Qr (m

3 /d)

0 50 100 150 200 250 300 350 4000

50

100

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CO

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g/L)

0 50 100 150 200 250 300 350 4000

5000

10000

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3 /d)

0 50 100 150 200 250 300 350 4000

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1000

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)

PI control, contol input Qr

PI control, control input Qf

PI control, control input Qw

Proposed controller, control input Qw

+ PI control* Proposed controller

(b)

(c)

(d)

(a)

Figure 9

Fig. 9. Comparison of the closed loop performance of the proposed control scheme versus PI controllers tuned withIMC-PI tuning rules.

Conclusions

In this work we have introduced the discharge-flowrate as control input to regulate the COD concentrationin activated sludge systems. Two simple robustcontrollers based on a simple step response to identifyinput-output models, including the case where thecomposition is measured with time-delay, were alsoderived to regulate the effluent COD concentrationof petrochemical wastewater at an activated sludgesystem are designed using the waste-flow rate. Theresulting controllers have a simple structure with easytuning rules. The control approach includes a linearuncertainty observer used as dynamic estimator ofthe uncertain terms, and a linear feedback function,which allows achieving the COD regulation in spite ofmodeling errors (associated with external disturbanceand process nonlinearities). Numerical simulations ona nonlinear model of a petrochemical activated sludgesystem show that the resulting control performancewith the proposed design is satisfactory for regulationtasks and reject typical perturbations in these systems.According to numerical results, the COD removalcan be achieved by the controlled manipulation ofthe discharge flow from the settler. Thus, the use ofthe discharge flow-rate can be used in combinationwith the conventional manipulation of flow-rate andthe recycle flow-rate in multivariable control schemes

in order to balance the control effort and lead tobetter closed-loop performance than the use of a singlecontrol input.

AcknowledgementThis work was partially supported from projectPROMEP-Redes Tematicas, Tratamiento Biologico deAguas Residuales, 2012.

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