# robust control of volatile fatty acids in anaerobic digestion processes

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PROCESS DESIGN AND CONTROL

Robust Control of Volatile Fatty Acids in Anaerobic Digestion Processes

Hugo O. Mendez-Acosta,*, Bernardo Palacios-Ruiz, Vctor Alcaraz-Gonzalez,

Jean-Philippe Steyer, Vctor Gonzalez-Alvarez, and Eric Latrille

Departamento de Ingeniera Qumica, CUCEI-UniVersidad de Guadalajara, BlVd. M. Garca Barragan 1451,C.P. 44430 Guadalajara, Jal, Mexico, and INRA, UR050, Laboratoire de Biotechnologie de lEnVironnement,AVenue des Etangs, Narbonne, F-11100, France

This paper is focused on the experimental implementation of a robust control scheme for the regulation ofvolatile fatty acids (VFA) in continuous anaerobic digestion processes. The robust scheme is made of anoutput feedback control, and an extended Luenberger observer is used to estimate the uncertain terms of theprocess (i.e., influent concentration and process kinetics). The control scheme is implemented in a pilot plantup-flow fixed-bed reactor that is treating industrial wine distillery wastewater. The performance of the robustscheme is tested over a period of 36 days, under different set-point values and several uncertain scenarios,including model mismatch, badly known parameters, and load disturbances. Experimental results show thatthe VFA concentration can be effectively regulated over a wide range of operating conditions. In addition, itis shown that the control scheme has a structure that improves its performance in the presence of noisymeasurements and control input saturations.

1. Introduction

Anaerobic digestion (AD) has regained the interest of thewastewater treatment scientific and industrial community toreduce and transform the organic matter from industrial andmunicipal effluents into a gaseous mixture called biogas,1 whichis composed mainly by methane and carbon dioxide. Neverthe-less, its widespread application has been limited, because ofthe difficulties involved in achieving the stable operation of theAD process, which cannot be guaranteed by regulating tem-perature and pH, because the microbial community within theAD process is quite complex2 (composed of more than 500species). In addition, the behavior of such a process may beaffected by the substrate composition, inhibition by substratesor products, and the type of bioreactor. Moreover, it is well-known that, to guarantee the so-called operational stability3 andto avoid the eventual breakdown of the anaerobic digester, theorganic matter in the liquid phase must be kept in a set ofpredetermined values, depending on factors such as the reactorconfiguration and the characteristics of the wastewater to betreated.4 However, the complex nonlinear and nonstationarynature of the AD process, the feed composition overloads, andthe presence of toxic and inhibitory compounds enhance thecontrol problems that are associated with the regulation of theorganic matter and the compliance of the stringent environmentalpolicies.

Over the past decade, the regulation of the organic matterhas been addressed by proposing many control techniques tokeep certain operating variables which are readily available (suchas the chemical oxygen demand (COD) and the biogas produc-tion) at a predetermined value.4-7 Classical proportional integral/proportional integral differential (PI/PID) control has beenrecognized as a good alternative for AD control when there is

little knowledge about the plant behavior and no mathematicalmodels are available.6,7 However, it is well-known that itsperformance is strongly dependent on the tuning parameters,which, in the application to nonlinear systems, are only validaround a given operating point. Moreover, the presence of inputconstraints (often called hard constraints) has been shown toseriously degrade the PI/PID performance limiting their practicalapplications. Nevertheless, the problem of the operationalinstability due to the accumulation of volatile fatty acids (VFA)remains open. The advent of reliable sensors8-10 for key ADvariables has brought about the possibility of implementing newcontrol alternatives to address the typical operating problemsin AD processes. In this context, the regulation of the VFAconcentration as a controlled variable seems to be very promis-ing, because the operational stability of the AD process is largelydependent on the accumulation of VFA.11,12 To our knowledge,only a few contributions among those that have addressed theregulation of VFA in AD processes13-16 have been experimen-tally implemented.13,15 Thus, the main motivation and contribu-tion of the present work is the experimental implementation ofa simple robust control scheme that is capable of regulatingthe VFA concentration in continuous AD processes in the faceof (i) uncertain load disturbances; (ii) model mismatch and badlyknown parameters due to the complex nonlinear nature of theprocess (i.e., uncertain kinetics), (iii) noisy measurements and(iv) control input constraints, because the dilution rate isbounded in practice to avoid undesired operating conditions,such as the washout condition.17 The paper is organized asfollows. First, a brief description of a mathematical model thatdescribes a typical continuous AD process is presented. Second,the control problem is stated in terms of the aforementionedmodel. Later, the robust control scheme is obtained and itsclosed-loop behavior is analyzed. The robust scheme then isexperimentally implemented in a pilot-plant up-flow fixed-bedreactor that is treating industrial wine distillery wastewater toevaluate the controller performance and robustness under the

* To whom correspondence should be addressed. Fax: 52 3339425924. E-mail address: hugo.mendez@cucei.udg.mx.

Departamento de Ingeniera Qumica, CUCEI-Universidad deGuadalajara.

INRA, UR050, Laboratoire de Biotechnologie de lEnvironnement.

Ind. Eng. Chem. Res. 2008, 47, 77157720 7715

10.1021/ie800256e CCC: $40.75 2008 American Chemical SocietyPublished on Web 09/13/2008

influence of the aforementioned factors (i-iv). Finally, someconcluding remarks are given.

2. Model Description

The success of designing and applying most of the controltechniques to biological processes is dependent strongly on theaccuracy of the underlying dynamics and representation of theprocess, in terms of control relevant properties. In this regard,

extensive research efforts are still being conducted on themodeling of AD processes18-25 for several purposes, includingprocess control. Nevertheless, many of the AD models availablein the current literature only describe particular aspects of theprocess resulting in complex highly dimensional models difficultto use for control purposes.26 Moreover, the identification andvalidation of several of these models have been restricted tostable operating conditions that are also called normal operatingconditions3 (NOC). Fortunately, simpler models have been alsodeveloped and they are still being used to synthesize efficientcontrollers for certain bioprocess variables, such as chemicaloxygen demand (COD) regulation and methane production.18-20

Recently, a generic AD model was developed in 2001 byBernard et al.,23 which has been widely used for monitoringand control purposes, because of its simplicity and its capabilityto represent the dynamics of a various continuous AD biore-actors (e.g., continuous stirred tank, fixed-bed, expanded-bed,or fluidized-bed reactors).

In this paper, a reduced version of the AD model proposedby Bernard et al.23 is used in the design of the control schemeand it is given by the following set of ordinary differentialequations (ODEs):

X1 ) (1(S2)-RD)X1X2 ) (2(S2)-RD)X2S1 ) (S1,in - S1)D- k11(S1)X1S2 ) (S2,in - S2)D+ k21(S1)X1 - k32(S1)X2 (1)

where X1, X2, S1, and S2 denote, respectively, the concentrationsof acidogenic bacteria (g/L), methanogenic bacteria (g/L),primary organic substrate (expressed as chemical oxygendemand (COD, g/L)), and volatile fatty acids (VFA, mmol/L).The subscript in denotes the influent concentration of eachcomponent. The dilution rate, D (h-1), is defined by the ratioD ) Q/V, where Q (L/h) is the feeding flow and V (L) thedigester volume, while k1, k2 (mmol/g), and k3 (mmol/g) areconstant yield coefficients. The introduction of R in Model (1)has made possible to describe the dynamic behavior of variouscontinuous bioreactor configurations. It is evident that by settingR ) 1, Model (1) describes the dynamics of the classicalcontinuous stirred tank reactor (CSTR) where the biomass iscompletely suspended in the liquid phase. Model (1) has beenalso used to describe the dynamics of fluidized-bed reactors orfixed-bed reactors (FBRs). Although it is well-known that FBRsare usually modeled by partial differential equations (PDEs), ithas been demonstrated that, under good mixing and recyclingconditions, together with generous biogas production, it ispossible to neglect the axial dispersion.27 Moreover, as aconsequence, one may use Model (1), with 0 < R < 1, todescribe the dynamics of the aforementioned bioreactors withbiomass suspended in the liquid phase. Finally, the biomassgrowth rates (1 and 2) are assumed to be described by theMonod and Haldane expressions, i.e.,

1(S1)) 1,max( S1S1 +KS1)

Table 1. Admissible Equilibrium Points of Model 1

X1* X2* S1* S2*

P1 0 0 S1,in S2,inP2 (S1,in - S1*)/(Rk1) 0 RD*KS1/(1,max - RD*) S2,in + {[k2(S1,in - S1*)]/k1}P3 0 (S2, - S2*)/(Rk3) S1,in see eq 2P4 (S1,in - S1*)/(Rk1) [(S2,in - S2*) + Rk2X1*]/(Rk3) RD*KS1/(1,max - RD*) see eq 2

Figure 1. Block diagram of the robust control scheme described by eq 4.

Figure 2. Diagram of a fully instrumented anaerobic up-flow fixed-beddigester.

Figure 3. Response of the VFA concentration when the robust controlscheme that is described by eq 4 is implemented.

Table 2. Set-Point Changes at Various Times during the ADExperimental Run

0 h 127 h 192 h

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