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Multi Objective Cascade Controller for an Anaerobic Digester

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Multi Objective Cascade Controller for an Anaerobic Digester
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  Process Biochemistry 46 (2011) 900–909 Contents lists available at ScienceDirect Process Biochemistry  journal homepage: www.elsevier.com/locate/procbio Multi-objective cascade controller for an anaerobic digester Carlos García-Diéguez a , ∗ , Francisco Molina b , Enrique Roca a a USC - University of Santiago de Compostela, Department of Chemical Engineering/School of Engineering, Rua Lope Gomez de Marzoa s/n, 15782 Santiago de Compostela, Spain b Faculty of Engineering, University of Antioquia, A.A. 1226, Medellin, Colombia a r t i c l e i n f o  Article history: Received 3 September 2010Received in revised form 9 December 2010Accepted 25 December 2010 Keywords: Anaerobic digestionBiogasUSBF reactorCascade controlControl systemsOptimisationWastewater treatment a b s t r a c t In this work, a new multi-objective control strategy based on the concentration of volatile fatty acids(VFAs)intheeffluentandthemethaneflowrate(Qch 4 )hasbeenproposedforanupflowsludgebed-filter(USBF) reactor, which is used in the anaerobic treatment of winery wastewater. The approach presentedhere is novel due to the following reasons: (i) it considers two operational objectives, i.e., control of theeffluent quality and control of the maximum production rate of methane; (ii) it takes advantage of thedifference between the dynamics of the liquid and gas phases using variables from both phases. Thecontrol system is based on a cascade control strategy with a reference signal for the methane flow rate.Thecontrolsystemcomputesthefeedflowrateforadjustingtheorganicloadappliedtothereactor.Theperformanceoftheproposedcontrolschemeisillustratedthroughnumericalsimulationsandparameteroptimisation using the Anaerobic Digestion Model no. 1 (ADM1) with regards to influent disturbances.Moreover,thecontrollerhasbeenvalidatedintheclosed-loopcontrolofa1.15m 3 USBFreactortreatingwastewater containing ethanol, which emulates winery effluents under different operational scenarios:restart-up, long duration organic overload, long duration organic underload and successive organic dis-turbances.Thecontrolsystemsuppliedadequatecontrolactioninresponsetothedifferentdisturbancestested, and it demonstrated high reliability in achieving the desired set-point.© 2011 Elsevier Ltd. All rights reserved. 1. Introduction Biochemical processes are difficult to control because micro-organisms are highly sensitive to changes in environmentalvariables and are unable to fully influence the cells’ internal envi-ronment by manipulating the external environment in which theylive. In general, biological systems are known to be highly variableand difficult to measure, and no reliable biological law is availablefor their measurement [1]. Some of the factors that contribute to thedifficultyincontrollinganaerobicwastewatertreatment(AWT)systems are the following: (i) the nonlinear dynamic behaviour of the models; (ii) the different levels of complexity presented by theexistingmodelsandtheunpredictablevariationoftheparameters,that are partly influenced by biomass adaptation; (iii) the unpre-dictableloaddisturbancesintheinletstreamduetochangesintheinletflowrateandcomposition;and(iv)thelackofreliablesensorsto measure intracellular activities [2,3].In recent years, there have been significant advances in thedevelopmentofsensors,whichhaveledtotheavailabilityofon-linesensors for measurement/monitoring of key biological variablessuch as volatile fatty acids (VFAs), chemical oxygen demand (COD)and total organic carbon (TOC) [4–8]. However, COD and TOC ∗ Corresponding author. Tel.: +34 981 563100x16772. E-mail address:  carlos.garcia.dieguez@usc.es (C. García-Diéguez). analysers are expensive and are usually recognised as fragile mea-surement devices [9]. Furthermore, their maintenance is costly compared to VFA titrimetric sensors [7,8].The aim of an anaerobic reactor controller is to maintain condi-tionsofstabilityinabioreactoragainstpossiblechangesininfluentcharacteristics (flow rate or composition) and to attain adequateeffluent quality and maximise the methane productivity of theAWT plant [10]. Controllers can be designed for the management of the process under the following different operational scenar-ios: organic overload, hydraulic overload, toxic effects of inhibitorcompounds, thermal shock and restart-ups [11].Robust control of anaerobic processes is crucial for avoidingpossible instability due to disturbances. Consequently, importantresearcheffortshavebeenfocusedonthedevelopmentofdifferentfeedbackcontrolstrategiesforAWTprocesses.Inthelastfewyears,several control feedback structures have been developed to over-comethedifficultyincontrollingAWTprocesses.Researchershavereported a simple on/off control algorithm that uses the alkalinityconsumption and the feed flow rate as the process state variableand the manipulated variable, respectively [12]. A combination of  the on/off and neural networks algorithm to control bicarbonatewas proposed by Guwy et al. [13]. Other researchers have used PID (proportional–integral–derivative) controllers for regulatingAWT processes [14–17] because this type of controller can be eas- ily implemented in wide variety of plants. However the tuning of these controllers is based on heuristic rules. Anaerobic digestion is 1359-5113/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.procbio.2010.12.015  C. García-Diéguez et al. / Process Biochemistry 46 (2011) 900–909  901 a complex and nonlinear process. Therefore, traditional and linearcontrollers (e.g., on/off, PID, etc.) may fail in certain ranges unlessthey have been properly adapted and their parameters have beenprecisely calibrated to handle specific situations.Rule-based expert systems have also been reported for thesupervision and control of AWT systems [18–22]. Most of the recently published work about expert systems for AWT controlis based on fuzzy logic [23–27]. Moreover, fuzzy structures have been used to develop control systems from expertise of operatorsand phenomenological information [23,28–30] to derive gain-scheduling schemes for tuning on-line control parameters and tomanage process uncertainties [10]. With this aim and due to the initial difficulty in modelling AWT systems, neural networks havebeen applied to develop controllers using data from AWT plants[13,31,32].Adaptive controllers for AWT plants [28,33–39] have beendeveloped to account for the nonlinearities and transient featuresof the anaerobic digestion process. The drawback of such strate-gies is that complete knowledge of the parameter structure of thesystem is required, which can be difficult to obtain when dealingwith bioprocesses such as AWT. In addition, adaptive controllersusually respond more aggressively against disturbances than lin-ear controllers, and therefore, strong variations may occur in themanipulated variable, which is usually the feed flow rate [16].Interval controllers have been successfully applied to the AWTof distillery vinasses to solve the problem of COD and VFA regula-tion[40].Theuseofthistypeofcontrollerpermitsmanagementof  therelativelylargeuncertaintyinsomekeyprocessvariables.Nev-ertheless, its performance is strongly dependent on the definitionof the uncertainty intervals. Another interesting approach of theinterval-based control application, which has not yet been experi-mentally validated, is the regulation of the influent COD acting onthe dilution rate [41].A variant in the feedback control topology is cascade control,whichconsistsoftwoormorefeedbackcontrolloops.Afewcascadeapplications can be found in the literature. Alvarez-Ramirez et al.[15] have shown a direct feedback control system using only PIDcontrollersinacascadeconfiguration.Thissystemallowstheregu-lationofananaerobicdigesterworkingatalowCODconcentration.Liuetal.[10,42,43]developedacascadecontrollerembeddedintoa fuzzy rule-based supervisory system. This approach demonstratedthe ability to achieve high productivity conditions for the produc-tion of methane by the AWT reactor.Control strategies have often been tested for different reactorconfigurations, different scales and under different operating con-ditions, which makes it difficult to compare their performance.However, it has been recognised that a suitable combination of directandindirectfeedbackcontrolprovidesthebestcontrolstrat-egy [15]. Direct feedback control acts at a regulatory level whereas indirect feedback control acts at a supervisory level (e.g., fuzzylogic). An ideal control system must fulfil different characteristicsat the regulatory level for simultaneously ensuring the followingcriteria: (a) high effluent quality; (b) maximum methane produc-tion; (c) general system stability; and (d) applicability to differenttypes of wastewater [23].In this work, a new robust multi-objective controller has beendeveloped and used for the control of an upflow sludge bed-filter(USBF) reactor. Methane flow rate has been used as the inner con-trol loop variable and VFA has been chosen as the external controlloop variable. The final control variable is the variation (increaseor decrease) in the feed flow rate. The proposed scheme has beendesigned to deal with modelling errors, and its structure allowsthe attenuation of disturbances in the COD concentration in theinlet stream. Validation of the control system has been performedusing simulations with ADM1 (Anaerobic Digestion Model no. 1)andclosed-loopcontrolofapilot-scaleUSBFreactor.Theapproachis novel as it considers the main operational criteria in the samecontrol structure. Moreover, this controller takes advantage of thedifferent dynamics of the liquid phase and gas phase through acascade structure with a reference signal. 2. Reactor, model description and problem statement  2.1. Anaerobic reactor  Experiments for the closed-loop validation of the cascade con-troller were conducted in a USBF, pilot-scale reactor (UpflowAnaerobicSludgeBlanket—UASBzone+AnaerobicFilter—AFzone)[26] with an approximate liquid volume of 1.15m 3 (Fig. 1). The reactor temperature was controlled at 37 ± 2 ◦ C using a singleon/off loop. The on-line measurement devices that were availableincluded feed and recycling electromagnetic flow-meters (ABB,COPA-XE and Siemens, 7ME2531), input and output reactor pHmeters (Cole Parmer) and thermometers (Pt-100), a biogas flow-meter (Brooks, 3240), an infrared gas analyser (Siemens, Ultramat22P) for the measurement of CH 4  and CO concentrations in the gasphase and an electrochemical hydrogen gas analyser (Sensotrans,Sensotox 420). On-line TOC and total inorganic carbon (TIC) weredetermined by catalyst combustion oxidation and non-dispersiveinfrared (NDIR) CO 2  detection (Shimadzu, 4100). All data weremonitored on-line with the sensors and recorded at 15-min inter-vals. Detailed descriptions of the equipment and data acquisitionsystem have been reported elsewhere [23,44].Duringtheexperiments,thebiomassinsidethereactorshowedspecific methanogenic activity of 0.66 ± 0.18kg CODkgVSS − 1 d − 1 .Theaveragetotalbiomassobservedinthereactorwas18.6 ± 1.5kgVSS,correspondingtoanaverageVSSconcentrationof16.9 ± 1.4kgVSS/m 3 [45]. These values corresponded to a maximum organicloading rate of 12kg COD/m 3 d.Synthetic wastewater, containing ethanol which emulateswinery effluents, was used in the experiments. The influent com-position consisted of dilute white wine, nutrients and sodiumbicarbonate. The wine was diluted  in situ  using a static mixer justbeforeitenteredthereactortoavoidpre-acidificationinthefeedingtank. Nutrients and sodium bicarbonate were added to maintain aCOD/bicarbonate/N/P ratio of 1000/400/7/1, which is required forbiomass growth, and to maintain an adequate buffering capacityinside the reactor [46].A titrimetric AnaSense analyser [7,8] was used to determinethe following operational reactor parameters: VFA (volatile fattyacids), bicarbonate, and partial and total alkalinity. After thedetermination of these parameters, the IA/TA ratio (intermediatealkalinity/total alkalinity ratio) was calculated (IA corresponds tothe difference between total and partial alkalinity).  2.2. Anaerobic Digestion Model no. 1 (ADM1) ADM1 [48] is a complex model of the multi-step anaerobic process transformations. This tool is adequate for predictions of anaerobic wastewater treatment processes with sufficient accu-racy for use in process development, optimisation, and control.It is a standard benchmark for developing operational strategiesandevaluatingcontrollers[16].ADM1incorporatesprocessessuch as the hydrolysis of particulates, acidogenesis, acetogenesis andmethanogenesis, and it includes 26 dynamic state concentrationvariables, 19 biochemical kinetic processes, 3 gas–liquid transferkinetic processes, and 8 implicit algebraic variables per liquid ves-sel. A modified version of the ADM1 toolkit was used in this study.The modified version incorporates an extension to ethanol degra-dationpathwaysthroughanadditionalgroupofethanoldegradersand a new state variable for ethanol concentration, which is cali-  902  C. García-Diéguez et al. / Process Biochemistry 46 (2011) 900–909 Fig. 1.  USBF reactor and cascade control scheme. USBF—upflow sludge bed filter reactor; GFC—gas phase controller; LFC—liquid phase controller; GM—gas measurements;LM—liquid measurements. brated for a USBF reactor [49]. The extension for ethanol considers thehydrogenandacetatepathwaysandaccountsfortheVFAspath-ways(propionateandbutyrate)throughstoichiometry.Thus,VFAsare suitably predicted by the model, including any possible over-load or transitions between steady states. 3. Controller design  3.1. Controller objectives Previously, many authors have used the Haldane kinetic model(Fig. 2) to describe the behaviour of anaerobic digesters [50–52]. Haldanekineticmodelalsoprovidesasimplemethodofexplainingcontroller objectives.Haldane kinetics have an obvious equilibrium point (biomasswashout)andtwooperationalregions,i.e.,astableoperatingregionand an unstable operating region (see Fig. 2), which have different dynamic properties in terms of stability [50]. In practice, the risk of destabilisation of an AWT process can be avoided by operatingin the stable region or far below the maximum reactor capacity Fig. 2.  Haldane kinetic model for an anaerobic digester. (- · - · - · ) Methane flow ratesetpoint. ( ··· ) Operational point with the objective of fulfilling environmental regu-lations. (optimum methane flow rate production), i.e.,   K  I   · K  S  ( K  I   is theinhibition kinetic constant and  K  S  is half saturation constant) forthe Haldane kinetic model [10].Normally, AWT plants attempt to fulfil environmental regula-tions. Therefore, the process requires a controller, which keeps thesystemstableatafixedset-point.However,whenAWTplantsseektomaximisemethaneproduction,anoptimalorsuboptimalcontrolstrategy must be proposed. In practice, the risk of system overloadcan be reduced by operating with a security margin that is belowthe maximum reactor capacity. In any case, the main objective of any controller for AWT plants is to keep the system in the stableregion [53].As a consequence, the development of a controller that is ableto integrate both objectives, i.e., the emission level set-point andthe maximum methane flow rate, and is able to robustly regulatethe process in the same single structure is of great interest to suchwastewater treatment systems. Different control structures couldbe considered for developing the controller. However, a cascadeframework has been used in our study.  3.2. Selection of control variables The first step during the development of a control system isthe selection of a group of process variables, which can provideinformation about the metabolic state of the process. Differentcombinationsofvariableswerestudiedtoestablishthemostappro-priatecombinationformaximumcontrolofregulationinacascadestructure. In this sense, when two of the variables for state iden-tification in the anaerobic process are considered with winerywastewater,severalcombinationsofvariablepairsareabletopro-vide accomplish a complete classification of states [54]. A similar study [55] with other types of wastewaters has showed that anappropriate combination of variables in the gas and the liquidphases can be used to develop a monitoring, diagnosis and control(MD&C)system.Furthermore,variablesintheliquidphasepresenthigher response times than gas phase variables. Therefore, accord-ingtothiscriterionaninnercontrolloopwithasecondaryvariableintheliquidphasedoesnotseemappropriate.Besides,theuseofacascadecontrolstructurehasbeenproposedtoreducetheadverse  C. García-Diéguez et al. / Process Biochemistry 46 (2011) 900–909  903  Table 1 Evaluation criteria for inner-loop variables suitability. (Y—yes; N—no or notappreciable; N/A—not applicable; A—advanced instrumentation; O—in occasions;S—similar).Criterion Qch 4  %CH 4  Q  gas  %CO 2  CO H 2 Secondary variable is available A A Y O A AIndicates a key disturbance Y O Y N N Y Causal relationship with thecontrolled variableY N Y N N NSecondary dynamic faster thanprimaryY Y Y Y Y Y  effectsofmeasurementdelaysandexploitthefasterresponsetimesof gas phase variables (e.g., biogas flow rate or methane flow rate)compared to liquid phase variables.Methaneflowrate(Qch 4 )waschosenastheinner-loopvariableafteraccountingforthetechnical,economicalanddynamicprocessresponse criteria. A combination of this variable with the VFA con-centration allows the detection of any potential imbalance in theAWT process.The selected inner-loop variable determines the performanceof cascade structures because the cancellation of the error in theinner-loop affects the cascade efficiency. A suitable internal vari-able must fulfil a series of criteria or requirements such as thoselisted above for the considered variables. These criteria establisha ranking amongst the variables under consideration in terms of their adequacy for the development of a cascade controller for anAWT plant. The methane flow rate (Qch 4 ) and the biogas flow rateare considered the best inner-loop variables, as shown in Table 1.A feature of the cascade control structure is that it can beswitched to operate as a single loop that seeks a suboptimal valueof Qch 4 . This is easily achieved by turning off the external controlloop and by providing an external reference trajectory to the slaveloop.  3.3. Methane productivity – inner control loop The scheme for the inner control loop corresponding to theset-point of methane productivity is illustrated in Fig. 3. In this case, the controller works as an auto-setting control system with amethane reference signal (Qch 4ref  ). Note that Qch 4ref   provides theset-point of the inner controller, and it is changed to achieve opti-mum methane productivity. In other words, the inner controllerwas designed to maintain the process near the operational pointcorresponding to maximum methane production (Qch 4max ) whenthe output loop was disconnected, and thereby push the systemto higher organic loading rate (OLR), which avoided working in adangerous and unstable operational zone (see Fig. 2).TheinnercontrollerwasimplementedasaPIDcontroller.There-fore, the equation of this controller can be expressed as follows: Q  in ( t  )  =  Q  in ( t  − 1) + K  Ps · eQch 4 ( t  ) + K  Is    eQch 4 ( t  ) dt  + K  Ds d (eQch 4 ( t  )) dt   (1) Fig. 3.  Block diagram of the methane productivity controller (inner-loop). where Q  ( t  )representsthecurrentreactorfeedflowrateorthecon-trolleroutput, Q  in ( t  − 1)istheinitialvalueofthefeedflowrate, K  Ps is the proportional gain,  K  Is  is the integral gain,  K  Ds  is the deriva-tive gain, and eQch 4  is the error between the actual value of Qch 4 and the reference signal (i.e., eQch 4 ( t  )=Qch 4ref  ( t  ) − Qch 4 ( t  )). Theproblem of controlling the output of a system to track a prescribedreference in the presence of model uncertainties and input distur-bances is of great interest in the control of bioreactors.Themethaneflowratewasmeasuredatintervalsof5sandwasfiltered using a moving window of 15min. Identical time intervalswere considered for modifying the action of the controller. Thesetime intervals are considered appropriate when the scale of indus-trial anaerobic bioreactors and the slow dynamics of this processare taken into account.  3.4. Tracking methane reference In anaerobic digestion, if one is primarily interested in theamount of methane generated, the total methane production dur-ing the transition period between two steady states can be used asanappropriatemeasureofthesystem’sperformance,whichinturncan be maximised (see Eq. (2) – optimal control approach).  J  ( Q  in ( t  )) =    tf  0 Qch 4 ( t  ) · dt   (2)However, optimal control is a very sensitive technique for theproposed model. It requires complete knowledge of the processmodel, including an analytical expression for each specific rate inthe system. In biotechnology, particularly in the field of anaerobicdigestion, this assumption is never fulfilled in practice; an opti-mal profile is generally calculated using a model that describes theprocess correctly from a qualitative viewpoint. Therefore, it is veryuseful to construct suboptimal strategies that do not suffer fromthe above difficulties.Based on a two-step anaerobic model structure provided byBernard et al. [51], it is possible to express the methane produc- tionrate( q M  )asafunctionofVFAconcentrationandmethanogenicbiomass concentration. q M   = k M   ·  max VFAVFA + K  s + (VFA 2 /K  I  )  X  met   (3)where  k M   represents the yield coefficient for methane productiondetermined from previous experimental data calibration,   max  isthemaximumspecificgrowthrateformethanogenicbacteria,  X  met  is the methanogenic biomass concentration, and  K  s  and  K  I   are thekineticparametersforHaldane’skineticexpression(halfsaturationconstant and inhibition constant, respectively).Consider that the nonlinear adaptive parameter    1  is definedaccording to Eq. (4):   1  = q M  VFA  K  s + VFA +  VFA 2 K  I    (4)where  q M   is expressed in kgmol/m 3 d and therefore needs to beconverted into units of m 3 /d through the ideal gas law Eq. (5),assumingaconstanttemperature( T  )of37 ◦ Candapressureequiv-alent to 1atm. The same temperature and pressure conditions areused in the remaining equations in this manuscript.Qch 4  = q M   · RT P   (5)where VFA* is the concentration of the volatile fatty acids at theoptimum methane flow rate production (see Eq. (6) and Fig. 2): VFA ∗ =   K  I   · K  S  (6)
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