Revista Mexicana de Ingeniería Química Revista Mexicana de Ingenier´ ıa Qu´ ımica Vol. 10, No. 1 (2011) 137-146 ADAPTIVE SMOOTH OBSERVER DESIGN FOR STATE ESTIMATION IN Desulfovibrio alaskensis 6SR CULTURES DISE ˜ NO DE UN OBSERVADOR SUAVE ADAPTIVO PARA ESTIMACION DE ESTADOS EN CULTIVOS DE Desulfovibrio alaskensis 6SR M.I. Neria-Gonz´ alez 1 , J.C. Figueroa-Estrada 1 , M.R. Cruz-Diaz 1 and R. Aguilar-L´ opez 2* 1 Divisi´ondeIngenier´ ıa Qu´ ımica y Bioqu´ ımica, Tecnol´ ogico de Estudios Superiores de Ecatepec. Av. Tecnol´ogico S/N. CP 55120, Ecatepec, Edo. de M´ exico, M´ exico. 2 Departamento de Biotecnolog´ ıa y Bioingenier´ ıa, CINVESTAV-IPN Av. Instituto Polit´ ecnico Nacional, No. 2508, San Pedro Zacatenco, D.F. M´ exico. Received 9 of September 2010; Accepted 2 of January 2011 Abstract In this work the dynamics of a sulfate reducing bacteria is predicted by estimating the biomass concentration and sulfide production using only sulfate (substrate) concentration measurements. The estimation process is developed on batch, fed-batch and continuous cultures of Desulfovibrio alaskensis 6SR, where a mathematical dynamic model of the bioreactor is presented and tuned with experimental data. The design of the adaptive smooth state observer takes into account the model’s system structure and an adaptive gain of the output feedback which contain a hyperbolic tangent of the estimation error, an theoretical frame is provide in order to show the convergence characteristics of the proposed method. The results of the proposed estimation methodology are generated via numerical simulation in order to show its performance. Keywords: bounded error observer, hyperbolic tangent feedback, adaptive observer gain, bioreactor model, Desulfovibrio alaskensis 6SR. Resumen En este trabajo la din´ amica de una bacteria sulfato reductora es predicha v´ ıa estimaci´ on de la concentraci´ on de la biomasa y la producci´ on de sulfuro usando ´ unicamente mediciones de la concentraci´ on de sulfato (sustrato). El proceso de estimaci´on es aplicado en cultivos por lotes, lote alimentado y continuo de Desulfovibrio alaskensis 6SR, donde el modelo din´ amico del biorreactor es presentado y sintonizado con datos experimentales. El dise˜ no del observador de estados adaptable toma en consideraci´ on la estructura del modelo del sistema y una retroalimentaci´ on con una ganancia adaptable que contiene una tangente hiperb´ olica del error de estimaci´ on, un marco te´ orico es propuesto con el fin de mostrar algunas de las caracter´ ıstica de la convergencia del observador propuesto. Los resultados de la estrategia de estimaci´ on propuesta son generados por medio de simulaciones num´ ericas con el fin de mostrar su desempe˜ no. Palabras clave: observador con error acotado, retroalimentaci´ on con tangente hiperb´ olica, ganancia del observador adaptable, modelo del biorreactor, Desulfovibrio alaskensis 6SR. * Autor para la correspondencia. E-mail: [email protected]Publicado por la Academia Mexicana de Investigaci´ on y Docencia en Ingenier´ ıa Qu´ ımica A.C. 137
Transcript
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
Revista Mexicanade Ingenierıa Quımica
1
Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica, A.C.
Volumen 10, Numero 1, Abril 2011
ISSN 1665-2738
1
Vol. 10, No. 1 (2011) 137-146
ADAPTIVE SMOOTH OBSERVER DESIGN FOR STATE ESTIMATIONIN Desulfovibrio alaskensis 6SR CULTURES
DISENO DE UN OBSERVADOR SUAVE ADAPTIVO PARAESTIMACION DE ESTADOS EN CULTIVOS DE Desulfovibrio alaskensis 6SR
M.I. Neria-Gonzalez1, J.C. Figueroa-Estrada1, M.R. Cruz-Diaz1 and R. Aguilar-Lopez2∗
1Division de Ingenierıa Quımica y Bioquımica, Tecnologico de Estudios Superiores de Ecatepec. Av.Tecnologico S/N. CP 55120, Ecatepec, Edo. de Mexico, Mexico.
2Departamento de Biotecnologıa y Bioingenierıa, CINVESTAV-IPN Av. Instituto Politecnico Nacional,No. 2508, San Pedro Zacatenco, D.F. Mexico.
Received 9 of September 2010; Accepted 2 of January 2011
Abstract
In this work the dynamics of a sulfate reducing bacteria is predicted by estimating the biomass concentration and
sulfide production using only sulfate (substrate) concentration measurements. The estimation process is developed
on batch, fed-batch and continuous cultures of Desulfovibrio alaskensis 6SR, where a mathematical dynamic model
of the bioreactor is presented and tuned with experimental data. The design of the adaptive smooth state observer
takes into account the model’s system structure and an adaptive gain of the output feedback which contain a
hyperbolic tangent of the estimation error, an theoretical frame is provide in order to show the convergence
characteristics of the proposed method. The results of the proposed estimation methodology are generated via
numerical simulation in order to show its performance.
Publicado por la Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica A.C. 137
M.I. Neria-Gonzalez et al./ Revista Mexicana de Ingenierıa Quımica Vol. 10, No. 1 (2011) 137-146
1 Introduction
In standard bioprocess operation, on-linemeasurements are often limited to basic variablessuch as temperature, pH, and dissolved oxygenO2. Measurements of component concentrations,i.e. essential substrates, biomass and productsof interest are obtained for off-line laboratoryanalysis at different discrete times. In recentyears, on-line probes for measuring componentconcentrations, e.g. biomass probes based oncapacitance measurements, have been developed,but their use is still very limited due to high costs.In particular, in sulfate-reducing bioreactors thebiomass growth and products are difficult ofmeasure on-line, given the anaerobic processconditions. Different methods for detection andenumeration of sulfate reducing bacteria (SRB)in natural and industrial environments havebeen developed, they have been grouped in: (i)direct detection methods and (ii) culture methods(APHA, 1989). The detection direct involved theusing antibodies raised against SRB (Daly et al.,2000), and the uses of molecular biology toolsas 16S rRNA, both techniques may be using insitu but required of a bigger knowledge and insome case is not possible by the nature of theconsidered sample (Vester and Ingvorsen, 1998).Culture methods for enumeration of SRB requiresof strict anaerobic conditions and special culturemedium, experience of handling of these bacterial,the incubation times are sometimes very large, etc(Neria-Gonzalez et al., 2006).
In this context, the design of “softwaresensors” based on state estimation techniquestakes on particular importance (Bastin andDochain, 1990). Software sensors allow the onlinereconstruction of non-measured variables (i.e.component concentrations) based on a processmodel and some available measurements (from“hardware sensors” or from on-line sampling).
From kinetic studies point of view, isimportant to determine the kinetic parametersand especially of kinetic rates inside bioreactor(Soroush, 1997). The estimates of these ratesare used for advanced control strategies (Aguilar-Lopez, 2003). The procedure to estimate thekinetic rates based on the adaptive systemstheory, consist of the estimation of unmeasuredstate with asymptotic observers (software sensor);later, the measurements (hardware sensor) andthe estimates of the state variables (software
estimator) are used for on-line estimation(Kazantzis and Kravaris, 1998; Aguilar-Lopezet al., 2010; Espinoza-Salgado et al., 2008).This method is useful, but in some cases, whenmany reactions are involved, the implementationrequires the calibration of too many parameters.A relative modern approach (Marin, 2002;Ohsumi et al., 2002) is the distribution based onidentification method. In this approach the setof nonlinear differential equations that describethe state evolution is mapped into a set oflinear algebraic equations respect to the modelparameters.
The design of a stable and convergentstate estimator appropriates for a particularbioprocesses is a complex task, and an adequateresponse is only obtained studying each bioprocess(Aguilar et al., 2004). For example, sliding modecontrol can be used to design an observer thatbrings one estimated state’s error to zero in finitetime even in the presence of measurement error(Selisteanu, et al., 2007; Hong, et al., 2002); theother states have error that behaves similarly tothe error in a Luenberger observer after peakinghas subsided. Sliding mode observers also haveattractive noise resilience properties that aresimilar to a Kalman filter. As discussed forthe linear case above, the peaking phenomenonpresent in Luenberger observers justifies the useof a sliding mode observer. The sliding modeobserver uses non-linear high-gain feedback todrive estimated states to a hypersurface wherethere is no difference between the estimatedoutput and the measured output (Levant, 2001).The non-linear gain used in the observer istypically implemented with a scaled switchingfunction, like the signum (i.e., sign) of theestimated-measured output error. Hence, dueto this high-gain feedback, the vector fieldof the observer has a crease in it so thatobserver trajectories slide along a curve where theestimated output matches the measured outputexactly. So, if the system is observable from itsoutput, the observer states will all be driven to theactual system states. Additionally, by using thesign of the error to drive the sliding mode observer,the observer trajectories become insensitive tomany forms of noise (Boiko and Fridman,2005). Hence, some sliding mode observers haveattractive properties similar to the Kalman filterbut with simpler implementation. However, asit is well known, this switching happens at any
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instant the state trajectories cross the switchinghyper-plane, this leads to the named chatteringphenomenon caused by the discontinuity of theinput injection, undesirable in most applications(Davila, et al., 2006). In order to avoid the namedchattering phenomenon, several methodologieshave been proposed, as the high order sliding-mode observers, which provides some smoothnessto the estimation methodology diminishing thecorresponding chattering, however to avoid thepresence of the sign function (i.e., discontinuousfunction) a continuous one have been proposed(Bertoni and Punta, 2000).
From the above in this work it is proposed aclass of adaptive smooth bounded observer, wherethe feedback term is related with the hyperbolictangent of the estimation error, coupled with anadaptive gain which is close to high order sliding-mode observers but avoiding the discontinuousstructure of the sliding-modes, which allows asmooth convergence of the proposed observer,avoiding the chattering phenomena. Theconsidered observer allows infers biomass andproduct concentrations under the assumption thatthe substrate measurements are available. Theproposed observer is applied to kinetic modelfor cell growth for Desulfovibrio alaskensis 6SR.Desulfovibrio alaskensis was described in the firsttime by Feio (Feio et al., 2004) and subsequentlystudies of bacteria associated at biocorrosion, havereported that D. alaskensis is present in oil fieldsfrom Gulf of Mexico (Neria-Gonzalez et al., 2006,Hernandez-Gayoso et al., 2004; Padilla-Viveroset al., 2006). The strain 6SR was isolated ofbiofilm in oil pipeline, which have high resistanceto heavy metals (Cd+2 and Cr+6) in relation atother species, is tolerant at oxygen, grows at pH5.5-9 (7), 15-55 (45) ◦C and in 30% (w/v) NaCl,and produces extracellular polymeric substances.These bacterial characteristics are important inenvironmental process and other as corrosion.
2 Experimental
2.1 Organism, culture maintenance andpurity test
Desulfovibrio alaskensis 6SR was isolated of adeveloped biofilm inside face of oil pipeline(Neria-Gonzalez et al., 2006). The strain wasmaintained routinely in Hungate tubes with 5
mL of Postgate’s medium B (Hungate, 1969).To evaluate the organism purity decimal dilutionin plates of anaerobic agar supplemented with6 mL of lactate (60% w/w), 4.5 g of NaSO4,0.004 mg of FeSO4, and 27.5 g of NaCl werecarried-out. The plates were placed in anaerobicjar (BBLTM GasPakTM Anaerobic Systems) andincubated until to colonies appear. The presenceof black colonies indicated the growth of sulfatereducing bacteria. One black colony well definiteand isolated was picked and quickly transferred at45 mL sterile Postgate’s C medium in anaerobicconditions (Postgate, 1979), and subcultures waremade subsequently.
The media was inoculated with 5 mL ofculture and incubated at 37 oC. Each medium wasprepared and dispended in anaerobic conditionsunder a N2 (99.998% purity) atmosphere, 120 and160 mL serum bottles were filled with 45 and 95mL of medium, respectively, and autoclaved at121oC.
2.2 Growth kinetics
The inoculum for kinetic study was cultured in45 mL of Postgate’s C medium for 25 h at 37◦C(logarithmic phase). A 5 mL aliquot was takenfrom Postgate’s C medium to inoculate 95 mLof fresh medium at 37 oC. The experiment wasdone using two series of triplicate independentcultures; each set of triplicate cultures wereinoculated with12 hours separated each other, theexperimental run time was 72 hours.
2.3 Analytic methods
The bacterial growing, consuming of sulfate andthe sulfide production were monitored each 3 or 4hours, the samples were taken carefully, avoidingcontact with oxygen. The bacterial growingwas followed through Optical Density (OD)methodology, the OD reading for cell growingwas transformed into dry mass (mg/L) through astandard growth curve. The consuming sulfate inthe medium was measured by the turbid metricmethod based on the precipitation of barium(Kolmert et al., 2000). Also, the production ofsulfide was measured by a colorimetric method(Cord-Ruwisch, 1985).
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2.4 Data analysis and mathematicalmodel
The experimental data of biomass, sulfate, andsulfide from two series of sulfate reducing culturewere analyzed using the average values of eachmeasurement point. As is well known, in sulfatereducing culture the accumulation of sulfide(product) in the medium has an inhibitory effecton bacterial growth. Therefore, to approximatethe average experimental data of bacterial growthin batch bioreactor, the Levenspiel’s inhibitionproduct model (Levenspiel, 1999) be used torepresent the specific growth rate (Eq. 1).Basically, this is an unstructured model thatdescribes the bacterial growth rate as a functionof substrate, product and biomass concentrationsas the unique biological state variable.
dx
dt= µ (S, P ) (x) = µmax
(1− P
P ∗
)n(S
KS + S
)(x)
(1)Where: µmax represents the maximum growingrate; KS represents the affinity substrate; P ∗
corresponds to inhibition concentration product,and n is the reaction order; meanwhile S,P , and x are substrate, product, and biomassconcentrations, respectively.
2.5 Estimation of the kinetic parameters
Levenspiel growth kinetic parameters wareestimated by the rate of change of biomassproduction, using central finite differencesaccording to the following equation:(
dt
dt
)ti
∼=(
∆X
∆t
)=
(Xi+1 −Xi
ti+1 − ti
)(2)
and a nonlinear multivariable regression forthe rates of change of biomass production andexperimental data (X, S, and P ) was done.POLYMATH 6.0 Professional software was used,the program allow applying effective numericalanalysis techniques, and Levenberg-Marquardtalgorithm was using for this case (see Table 1).
The mathematical model was simulated usingthe same software. Besides, a linear regressionbetween the experimental and the predicted datawere obtained, and overall correlation coefficientwas calculated, see figs. 1-2 (Tejeda, 2007).
Table 1. Growth kinetic parameters andyields for Desulfovibrio alaskensis.
Parameter Value
µmax, h−1 0.188KS , mg L−1 5699.86µd, h−1 0.0038P ∗, mg L−1 735.0n 0.89Y(S/X), mg S mg−1 X 14.13Y(P/X), mg P mg−1 X 2.14
2
0 10 20 30 40 50 60 700
100
200
300
400
500
600
700
0
1000
2000
3000
4000
5000
6000
7000
Su
lfate
Co
nce
ntr
atio
n [m
g/L
]
Bio
ma
ss, S
ulfi
de
Co
nce
ntr
atio
n [m
g/L
]
Time [hours]
1 2
Figure 1. 3 Fig. 1: Comparison of the experimental andpredicted kinetics of growth of Desulfovibrioalaskensis on Postgate’s C medium. The solidline represents predicted data for each responsevariables.
3 Bioreactor mathematicalmodel
The unstructured models are using nowadaysas the main tool for the bioprocess modeling,but also for being applied in overall computercontrol. Considering the above kinetic model,it is proposed by following the mathematicalmodel for a class of continuous stirred bioreactor,which is based on classical mass balances forbiomass, sulfate (substrate) and sulfide (product)concentrations:Sulfate (S).-
dS
dt= D (Sin − S)− µ(S)
X
YS/X(3)
Biomass (X).-
dX
dt= −DX + µ(S)X (4)
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Fig. 2: Linear regressions for experimental andpredicted data in a batch anaerobic growth withinitial substrate concentrations of 5379 mg/L.a) experimental Biomass (�), predicted biomass,R2 = 0.982; b) experimental Sulfide (•), predictedSulfide, R2 = 0.985; c) experimental Sulfate (N),predicted Sulfate, R2 = 0.976. Overall coefficientwas 0.979.
Sulfide (P).-
dP
dt= −DP + µ(S)
X
YP/X(5)
Here D is the dilution rate, µ is the specific growthrate, YS/X is the sulfate coefficient yield and YP/Xis the sulfide coefficient yield. In accordancewith the specific experimental setup the followinginitial conditions are considered for the batchculture and model validation purposes Xo = 100mg/L, So = 5200 mg/L, Po = 10 mg/L. Figure1 shows the performance of the kinetic modelconsidering a comparison with the experimentaldata which looks satisfactory. The above modelpredicts batch operation when D = 0, the fed-batch operation is considered when D = f(t) andthe output flow terms are null and finally the
continuous operation which considers inputs andoutputs flow terms.
4 Methodology for theobserver design
Consider a canonical control representation formof the bioreactor model:
•x = f (x)
y = Cx(6)
Now, the following state observer is proposed:
•x = f (x) + l tanh (y − y)•l = −α abs(y − y)
1/m(7)
where the observer’s gain l is given by anupdate adaptation algorithm and α is a parameterdesign. To prove the convergence of the proposedobserver, let us to consider the dynamic equationof the estimation error (ε = x− x), as follows:
•ε =
•x−
•x = f (x)− (f (x) + l tanh (ε))
•l = −α abs(ε)1/m
(8)
under the following assumptions:A1. f (x) − f (x)− 6 L (x− x) Taking normsto both sides of Eq. (8) and applying A1 it isobtained: ∣∣∣•ε∣∣∣ 6 L |ε| − l |tanh (ε)| (9)
Now, suppose that the function abs(ε)1/m
is apositive continuous function on the integrationinterval [a, b]; then H is the maximum ofthe function on the domain [δ, γ], then abs (ε)is bounded, i.e. abs (ε) 6 H ∀ t ∈[δ, γ], such that: abs(ε)
1/n 6 H1/n n >
0 ⇒γ∫δ
abs(ε)1/n 6 H1/n (γ − δ), considering
n an odd number i.e. n = 2p + 1, p ∈
Z+, therefore; lim supγ∫δ
abs(ε)1/(2p+1) 6
lim sup H1/(2p+1) (γ − δ) 6 (γ − δ) for p largeenough.
From the above, Eq. (9) can be rewritten as:∣∣∣•ε∣∣∣ 6 L |ε| − α (γ − δ) (10)
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Solving Eq. (9) and considering t → ∞, canbe concluded that the estimation error belongs toball:
|ε| 6 α (γ − δ)L
(11)
5 Numerical experimentsand discussion
Besides to show the performance of the proposedestimation methodology, an important additionalissue concerns with the evaluation of thecapacities Desulfovibrio alaskensis 6SR forbiotechnological applications. Both two of thesepossible applications are related with wastewatertreatment for degradation of sulfate compoundsand heavy metal mobility. From the kinetic modelpresented in Section 3, the proposed observeris applied to batch, continuous and fed-batchoperating modes; each one of the above mentionedoperating modes is related with a specific processtask, on the batch operation an optimal trajectorymust to be reached in order to provide an adequateperformance, besides a finite time operationpolitics must be considered; related with thecontinuous operation process the main tasks isto lead the bioreactor trajectories to an optimaland stable steady state, where the convergence ofobservers and controllers can be designed withasymptotic convergence and finally the feed-batch operation can be considered as a batchoperation with input disturbances, therefore arobust monitoring and controlling methodologiesare needed. The initial concentration conditionsfor the batch culture was above mentioned andthe corresponding for the continuous and fed-batch operating modes are Xo = 980 mg/L,So = 6850 mg/L and Po = 15 mg/L. The initialconditions imposed to the proposed observer are5000 mg/L, 96 mg/L and 8 mg/L, respectively,for the batch operation and 950 mg/L, 6250mg/L and 20 mg/L for biomass, sulfate andsulfide concentrations, respectively, for continuousand fed-batch operation modes. The estimationprocedure considers the sulfate concentration(substrate) as measured output in order to inferthe biomass and sulfide concentrations.
Batch operation is considered from figs. 3-5,where the performance of the proposed observeris satisfactory, a fast convergence to the namedreal concentrations is achieved, without large
Fig. 11: Sulfide concentration estimation with theproposed observer (fed-batch operation).
the observer’s performance when a fed-batchoperation is considered; for this case a dilutionrate of D = 0.01 1/h is considered from the start-
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up of the bioreactor operation to 75 hours, laterthe input flow is null (D = 0). Despite of thissudden disturbance the proposed observer keeps asatisfactory performance following the named realconcentrations.
Conclusions
In this work is modeled the biomass growth andsulfide production of a sulfate reducing bacteriaDesulfovibrio alaskensis, which has been recentlydescribed, and its biotechnological properties arenot studied yet enough. For the above mentioned,a nonlinear state observer to infer biomass andsulfide concentration from sulfate concentrationmeasurements is implemented for a batch, fed-batch and continuous operating bioreactor modes,where can be observed a satisfactory performance.A mathematical analysis to show the convergencecharacteristics of the proposed methodology isdone. Future work will be oriented to analyzethe effect of model uncertainties and noisymeasurements in order to try to design robustestimation methodologies.
Acknowledgment
JCFE is grateful with CONACyT for thecorresponding support via a postgraduatescholarship.
sulfide/mg-biomass)Greek symbolsα observer gain (1/h)ε estimation error (mg/L)ι adaptive observer gain (1/h)µ, µd, µmax specific growth rate, specific death
rate, maximum rate growth (1/h)
Referencias
Aguilar-Lopez, R. (2003). Integral observersfor uncertainty estimation in continuouschemical reactors: differential-algebraicapproach. Chemical Engineering Journal 9,113-120.
Aguilar, R., Soto, G., Martınez, S., Maya-Yescas,R. (2004). Substrate regulation in fixed bedbioreactors via feedback control. RevistaMexicana de Ingenierıa Quımica 3, 1-11.
Aguilar-Lopez, R., Lopez-Perez, P. A., Neria-Gonzalez, M.I., Domınguez-Bocanegra,A.R. (2010). Observer based adaptivemodel for a class of aerobic batch bioreactor.Revista Mexicana de Ingenierıa Quımica 9,1, 29-35.
APHA. (1989). Estimation of bacterial density.In standard methods for the examinationof water and waste-water. AmericanPublic Health, Pp. 977-980. AssociationWashington D.C.
Bastin, G., Dochain, D. (1990). On-line estimation and adaptive controlof bioreactors. Elsevier Science Ltd.Amsterdam.
Bertoni, G., Punta, E. (2000). Chatteringelimination with second order sliding-modesrobust to Coulomb friction. Journal ofDynamics, Measurement and Control 122,679-684.
Boiko, I., Fridman, L. (2005). Analysisof chattering in continuous sliding-mode
144 www.amidiq.com
M.I. Neria-Gonzalez et al./ Revista Mexicana de Ingenierıa Quımica Vol. 10, No. 1 (2011) 137-146
controllers. IEEE Transactions onAutomatic Control 50, 1442-1446.
Cord-Ruwisch, R. (1985). A quick method fordetermination of dissolved and precipitatedsulfides in cultures of sulfate-reducingbacteria. Journalof Microbiololy Methods 4,33-36.
Daly, K., Sharp, R.J., McCarthy A.J. (2000).Development of oligonucleotide probes andPCR primers for detecting phylogeneticsubgroups of sulfate-reducing bacteria.Microbiology 146, 1693-705.
Davila, J., Fridman, L., Levant, A. (2005).Second order sliding-mode observer formechanical systems. IEEE Transactions onAutomatic Control 50, 1785-1789.
Espinoza-Salgado, S., Reyes-Reyes, J. Alvarez-Castillo, A., Astorga-Zaragoza, C. M.,Mendizabal-Mijares, E., Cadenas-Pliego, G.(2008). High gain adaptive nonlinearobserver for emulsion copolymerizationprocess. Revista Mexicana de IngenierıaQuımica 7, 1, 89-98
Feio, M.J., Zinkevich, V., Beech, I.B., Llobet-Brossa, E., Eaton, P., Schmitt, J.,Guezennec, J. (2004). Desulfovibrioalaskensis sp. nov., a sulphate-reducingbacterium from a soured oil reservoir.International Journal of Systems, Evolutionand Microbiology 54,1747-1752.
Hernandez-Gayoso, M. J., Zavala-Olivares, G.,Ruiz-Ordaz, N., Juarez-Ramırez C., Garcıa-Esquivel, R., Padilla-Viveros, A. (2004).Microbial consortium influence upon steelcorrosion rate, using polarization resistanceand electrochemical noise techniques.Electrochemistry Acta 49, 4295-4302.
Hong, Y., Xu, Y., Huang, J. (2002). Finite-timecontrol for robot manipulators. Systems &Control Letters 46, 243-253.
Hungate, R.E. (1969). A roll tube methodfor cultivation of strict anaerobes. In:Methods in Microbiology (J.R. Norris andD.W. Ribbons eds.), Pp. 117-32. London:Academic Press.
Kazantzis, N. y Kravaris, C. (1998). Nonlinearobserver design using Liapunov´s auxiliarytheorem. Systems & Control Letters 34,241-247.
Kolmert, A., Wikstrom, P., Hallberg, K.(2000). A fast and simple turbidimetricmethod for the determination of sulfate insulfate-reducing bacterial cultures. JournalMicrobiology Methods 41, 179-184.
Levant, A. (2001). Universal single-input-single-output (SISO) sliding-mode controllers withfinite-time convergence. IEEE Transactionon Automatic Control 46, 1447-1451.
Levenspiel, O. (1999). Chemical ReactorEngineering. John Wiley & Sons, New York.
Marin, C. (2002). System IdentificationBased on Distribution Theory. June25-28, Crete, Greece. Proceedings ofIASTED International Conference onApplied Simulation and Modelling. (ASM2002), 1125-1131.
Neria-Gonzalez, I., Wang, E.T., Ramırez,F., Romero, J.M., Hernandez-Rodrıguez,C. (2006). Characterization of bacterialcommunity associated to biofilms ofcorroded oil pipelines from the southeastof Mexico. Anaerobe 12, 122-133.
Ohsumi, A., Kameyama, K. y Yamaguchi,K. (2002). Subspace identification forcontinuous-time systems via distribution-based approach. Automatica 38, 63-79.
Padilla-Viveros, A., Garcia-Ochoa, E., Alazard,D. (2006). Comparative electrochemicalnoise study of the corrosion processof carbon steel by the sulfate-reducingbacterium Desulfovibrio alaskensis undernutritionally rich and oligotrophic cultureconditions. Electrochimica Acta 51, 3841-3847.
Postgate. J.R. (1979). The sulphate-reducingbacteria. Cambridge University Press, NewYork.
Selisteanu, D., Petre, E., R?svan, V. (2007).Sliding mode and adaptive sliding-modecontrol of a class of nonlinear bioprocesses.International Journal of Adaptive Controland Signal Processing 21, 795-822.
www.amidiq.com 145
M.I. Neria-Gonzalez et al./ Revista Mexicana de Ingenierıa Quımica Vol. 10, No. 1 (2011) 137-146
Soroush, M. (1997). Nonlinear state-observerdesign with application to reactors.Chemical Engineering Science 52, 387-404.
Tejeda, P. A. (2007). Estadıstica para CienciasSociales, del comportamiento y de la salud.Edit. CENGAGE Learning, 3a Edicion,
Mexico.
Vester, V. y Ingvorsen, K. (1998). Improvedmost-probable-number method to detectsulfate reducing bacteria with natural mediaand a radiotracer. Applied EnvironmentalMicrobiology 64, 1700-1707.
