Ind. Eng. Chem. Res. 2008, 47, 7715–7720
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PROCESS DESIGN AND CONTROL Robust Control of Volatile Fatty Acids in Anaerobic Digestion Processes Hugo O. Me´ndez-Acosta,*,† Bernardo Palacios-Ruiz,† Vı´ctor Alcaraz-Gonza´lez,† ´ lvarez,† and Eric Latrille‡ Jean-Philippe Steyer,‡ Vı´ctor Gonza´lez-A Departamento de Ingenierı´a Quı´mica, CUCEI-UniVersidad de Guadalajara, BlVd. M. Garcı´a Barraga´n 1451, C.P. 44430 Guadalajara, Jal, Me´xico, and INRA, UR050, Laboratoire de Biotechnologie de l’EnVironnement, AVenue des Etangs, Narbonne, F-11100, France
This paper is focused on the experimental implementation of a robust control scheme for the regulation of volatile fatty acids (VFA) in continuous anaerobic digestion processes. The robust scheme is made of an output feedback control, and an extended Luenberger observer is used to estimate the uncertain terms of the process (i.e., influent concentration and process kinetics). The control scheme is implemented in a pilot plant up-flow fixed-bed reactor that is treating industrial wine distillery wastewater. The performance of the robust scheme 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 that the VFA concentration can be effectively regulated over a wide range of operating conditions. In addition, it is shown that the control scheme has a structure that improves its performance in the presence of noisy measurements and control input saturations. 1. Introduction Anaerobic digestion (AD) has regained the interest of the wastewater treatment scientific and industrial community to reduce and transform the organic matter from industrial and municipal effluents into a gaseous mixture called biogas,1 which is composed mainly by methane and carbon dioxide. Nevertheless, its widespread application has been limited, because of the difficulties involved in achieving the stable operation of the AD process, which cannot be guaranteed by regulating temperature and pH, because the microbial community within the AD process is quite complex2 (composed of more than 500 species). In addition, the behavior of such a process may be affected by the substrate composition, inhibition by substrates or products, and the type of bioreactor. Moreover, it is wellknown that, to guarantee the so-called operational stability3 and to avoid the eventual breakdown of the anaerobic digester, the organic matter in the liquid phase must be kept in a set of predetermined values, depending on factors such as the reactor configuration and the characteristics of the wastewater to be treated.4 However, the complex nonlinear and nonstationary nature of the AD process, the feed composition overloads, and the presence of toxic and inhibitory compounds enhance the control problems that are associated with the regulation of the organic matter and the compliance of the stringent environmental policies. Over the past decade, the regulation of the organic matter has been addressed by proposing many control techniques to keep certain operating variables which are readily available (such as the chemical oxygen demand (COD) and the biogas production) at a predetermined value.4-7 Classical proportional integral/ proportional integral differential (PI/PID) control has been recognized as a good alternative for AD control when there is * To whom correspondence should be addressed. Fax: 52 33 39425924. E-mail address:
[email protected]. † Departamento de Ingenierı´a Quı´mica, CUCEI-Universidad de Guadalajara. ‡ INRA, UR050, Laboratoire de Biotechnologie de l’Environnement.
little knowledge about the plant behavior and no mathematical models are available.6,7 However, it is well-known that its performance is strongly dependent on the tuning parameters, which, in the application to nonlinear systems, are only valid around a given operating point. Moreover, the presence of input constraints (often called hard constraints) has been shown to seriously degrade the PI/PID performance limiting their practical applications. Nevertheless, the problem of the operational instability due to the accumulation of volatile fatty acids (VFA) remains open. The advent of reliable sensors8-10 for key AD variables has brought about the possibility of implementing new control alternatives to address the typical operating problems in AD processes. In this context, the regulation of the VFA concentration as a controlled variable seems to be very promising, because the operational stability of the AD process is largely dependent on the accumulation of VFA.11,12 To our knowledge, only a few contributions among those that have addressed the regulation of VFA in AD processes13-16 have been experimentally implemented.13,15 Thus, the main motivation and contribution of the present work is the experimental implementation of a simple robust control scheme that is capable of regulating the VFA concentration in continuous AD processes in the face of (i) uncertain load disturbances; (ii) model mismatch and badly known parameters due to the complex nonlinear nature of the process (i.e., uncertain kinetics), (iii) noisy measurements and (iv) control input constraints, because the dilution rate is bounded in practice to avoid undesired operating conditions, such as the washout condition.17 The paper is organized as follows. First, a brief description of a mathematical model that describes a typical continuous AD process is presented. Second, the control problem is stated in terms of the aforementioned model. Later, the robust control scheme is obtained and its closed-loop behavior is analyzed. The robust scheme then is experimentally implemented in a pilot-plant up-flow fixed-bed reactor that is treating industrial wine distillery wastewater to evaluate the controller performance and robustness under the
10.1021/ie800256e CCC: $40.75 2008 American Chemical Society Published on Web 09/13/2008
7716 Ind. Eng. Chem. Res., Vol. 47, No. 20, 2008 Table 1. Admissible Equilibrium Points of Model 1
P1 P2 P3 P4
X1*
X2*
S1*
S2*
0 (S1,in - S1*)/(Rk1) 0 (S1,in - S1*)/(Rk1)
0 0 (S2, - S2*)/(Rk3) [(S2,in - S2*) + Rk2X1*]/(Rk3)
S1,in RD*KS1/(µ1,max - RD*) S1,in RD*KS1/(µ1,max - RD*)
S2,in S2,in + {[k2(S1,in - S1*)]/k1} see eq 2 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-bed digester.
extensive research efforts are still being conducted on the modeling of AD processes18-25 for several purposes, including process control. Nevertheless, many of the AD models available in the current literature only describe particular aspects of the process resulting in complex highly dimensional models difficult to use for control purposes.26 Moreover, the identification and validation of several of these models have been restricted to stable operating conditions that are also called normal operating conditions3 (NOC). Fortunately, simpler models have been also developed and they are still being used to synthesize efficient controllers for certain bioprocess variables, such as chemical oxygen demand (COD) regulation and methane production.18-20 Recently, a generic AD model was developed in 2001 by Bernard et al.,23 which has been widely used for monitoring and control purposes, because of its simplicity and its capability to represent the dynamics of a various continuous AD bioreactors (e.g., continuous stirred tank, fixed-bed, expanded-bed, or fluidized-bed reactors). In this paper, a reduced version of the AD model proposed by Bernard et al.23 is used in the design of the control scheme and it is given by the following set of ordinary differential equations (ODEs): ˙ ) (µ (S ) - RD)X X 1 1 2 1 ˙ X ) (µ (S ) - RD)X 2
2
2
2
˙ S1 ) (S1,in - S1)D - k1µ1(S1)X1 ˙ S2 ) (S2,in - S2)D + k2µ1(S1)X1 - k3µ2(S1)X2
Figure 3. Response of the VFA concentration when the robust control scheme that is described by eq 4 is implemented. Table 2. Set-Point Changes at Various Times during the AD Experimental Run 0h *
127 h 192 h 242 h 533 h 600 h 868 h
S2 (mg VFA/L) open loop 1400
1000
1800
2500
3500
1500
influence of the aforementioned factors (i-iv). Finally, some concluding remarks are given. 2. Model Description The success of designing and applying most of the control techniques to biological processes is dependent strongly on the accuracy of the underlying dynamics and representation of the process, in terms of control relevant properties. In this regard,
(1)
where X1, X2, S1, and S2 denote, respectively, the concentrations of acidogenic bacteria (g/L), methanogenic bacteria (g/L), primary organic substrate (expressed as chemical oxygen demand (COD, g/L)), and volatile fatty acids (VFA, mmol/L). The subscript in denotes the influent concentration of each component. The dilution rate, D (h-1), is defined by the ratio D ) Q/V, where Q (L/h) is the feeding flow and V (L) the digester volume, while k1, k2 (mmol/g), and k3 (mmol/g) are constant yield coefficients. The introduction of R in Model (1) has made possible to describe the dynamic behavior of various continuous bioreactor configurations. It is evident that by setting R ) 1, Model (1) describes the dynamics of the classical continuous stirred tank reactor (CSTR) where the biomass is completely suspended in the liquid phase. Model (1) has been also used to describe the dynamics of fluidized-bed reactors or fixed-bed reactors (FBRs). Although it is well-known that FBRs are usually modeled by partial differential equations (PDEs), it has been demonstrated that, under good mixing and recycling conditions, together with generous biogas production, it is possible to neglect the axial dispersion.27 Moreover, as a consequence, one may use Model (1), with 0 < R < 1, to describe the dynamics of the aforementioned bioreactors with biomass suspended in the liquid phase. Finally, the biomass growth rates (µ1 and µ2) are assumed to be described by the Monod and Haldane expressions, i.e.,
(
µ1(S1) ) µ1,max
S1 S1 + KS1
)
(
µ2(S2) ) µ2,max
S2 S2 + KS2 + (S2 ⁄ KI2)
2
)
-1
where µ1,max (h ), KS1 (g/L), µ2,max (h-1), KS2 (mmol/L), and KI2 (mmol/L) are the maximum bacterial growth rate and the half-saturation constant associated to the substrate S1, the maximum bacterial growth rate in the absence of inhibition, and the saturation and inhibition constants associated to substrate S2, respectively. 3. Controller Design 3.1. Control Problem Statement. As previously noted, one of the main control objectives when dealing with AD processes is to guarantee process stability.1-6 As a first contribution, this paper focuses on the VFA regulation, because its behavior can be directly linked to the digester stability. Thus, the control problem can be stated as follows: the proposal of a robust control scheme capable of regulating the VFA concentration (S2) around a desired setpoint (S2*) in the face of the aforementioned factors (i-iv) for AD processes operating under stable conditions (NOC) and whose dynamic behavior can be represented by Model (1). In other words, the objective of this work is the proposal of a robust scheme capable of preserving the process stability in continuous AD processes via the regulation of the VFA concentration, where the stable operating conditions (NOC) are defined in terms of Model (1) as those operating conditions where the following inequalities are fulfilled (see also section 3.2): (a) X1(t), X2(t) > 0 (b)
0 < β1 e
∫
t+δ1
t
∀tg0
∆S1,in(τ) dτ
∀tg0
where ∆S1,in(t) is defined as ∆S1,in(t) ≡ S1,in(t) - S1(t) and, β1 and δ1 are positive constants.
(c)
0 < β2 e
|∫
t+δ2
t
|
∆S2,in(τ) dτ
Ind. Eng. Chem. Res., Vol. 47, No. 20, 2008 7717
evidence, it is nonrestrictive to assume that these functions are smooth, bounded, and positive-definite.28 (A3) The substrate influent concentration Sj,in for j ) 1, 2 is min max assumed to be unknown but bounded (i.e., Sj,in e Sj,in e Sj,in ). (A4) R is assumed to be uncertain but does vary in the open interval 0 < R < 1. (A5) The inlet flow rate Q, which is the manipulated variable, is constrained because of the capacity of the pumps used in the AD processes.28-30 Consequently, the manipulated variable given by the dilution rate is bounded by the following saturation function:
{
Dmax (if D g Dmax) sat(D) ) D (if Dmin < D < Dmax) Dmin (if D e Dmin) where the upper and lower bounds of the dilution rate (Dmax and Dmin, respectively) are known and D ∈ R+. 3.2. Admissible Setpoints under NOC. To regulate the VFA concentration around desired and admissible set-point values, it is necessary to analyze the operating conditions where natural stable conditions naturally occur. Thus, by analyzing the openloop behavior of Model (1) and by solving the steady-state mathematical model, four possible solutions are attained (see Table 1). Table 1 clearly shows that the equilibrium point P4 is the only one that can be attainable under stable conditions (NOC), because the other three equilibrium points lead to the breakdown of the AD process via the elimination of at least one of the microbial populations (i.e., the bioreactor exhibits washout conditions). Furthermore, it can be demonstrated that Model (1) presents two steady-state solutions for the VFA concentration, but only one of them is physically attainable under NOC;30 it is given by S∗2 ) -
∀tg0
where ∆S2,in(t) is defined as ∆S2,in(t) ≡ S2,in(t) - S2(t) and, β2 and δ2 are positive constants. (d) x ° ) x(t ) 0) > 0 where x ) [X1,X2,S1,S2]′. Condition (b) implies that, even when it is possible in practice to have load organic charges for which S1,in(t) e S1(t), condition ∆S1,in(t) > 0 eventually will be re-established. Moreover, even in the situation at which S2,in(t) ) 0, for short periods of time, condition (b) establishes a sufficient condition to guarantee a permanent supply of substrate for methanogenic bacteria. On the other hand, condition (c) implies that the situation in which ∆S2,in(t) may be identically equal to zero (or even less than zero) but it will not prevail for long periods of time. Implications of these conditions on the steady-state and closed-loop robustness will be discussed in the following subsections. On the other hand, the controller design takes also into account the following assumptions: (A1) The outlet VFA concentration (S2) is readily available from online measurements.8-10 (A2) For controller design purposes, the growth functions that are associated with the acidogenic and methanogenic steps are assumed to be unknown but can be represented by µ1( · ) and µ2( · ), respectively. Furthermore, based on biological
2 KI2 2
{(
1-
µ2,max /
RD
) ( +
1-
µ2,max /
RD
) ( )} 2
-4
KS2 2 KI2
(2)
where S2* represents the admissible setpoints under NOC for all D*, such that Dmin e D* e Dmax. 3.3. The Robust Control Scheme. In the past decade, the control based on differential geometry has emerged as a powerful tool to deal with a great variety of dynamic nonlinear systems. However, to obtain input-output linear dynamic behavior, this control tool becomes dependent on the exact cancellation of the nonlinear terms, which requires, as a consequence, the perfect knowledge of the system. This means that the presence of modeling errors, unmeasured disturbances, and parametric uncertainties cannot be taken into account in the typical controller design based on differential geometry, preventing its application in a large number of complex dynamical processes such as AD.29 Here, to overcome the aforementioned difficulties associated to the design of geometric control, a robust control scheme is proposed to regulate the VFA concentration in AD processes from the extension of the previously reported ideas by Alvarez-Ramirez et al. from the late 1990s.31,32 Therefore, model mismatch, unmeasured disturbances and parameter uncertainties are taken into account in the controller design by defining an uncertain but observable function, whose dynamic behavior is estimated from available measurements by using a simple nonlinear state estimator: an extended Luenberger observer (ELO). The robust scheme then is obtained from the combination of the nonlinear state estimator and an output feedback control with a linearizing-like structure. For robust control design purposes, let us consider, without any
7718 Ind. Eng. Chem. Res., Vol. 47, No. 20, 2008
loss of generality, that the influent VFA concentration can be described as follows: S2,in ) Sj2,in + ∆S2, where ∆S2 is an uncertain and bounded function that is related to the variation of the influent composition around a well-known nominal value Sj 2,in, which can be determined using a single VFA offline measurement of the wastewater to be treated. A new function that lumps the system uncertainties then is defined as η ≡ k2µ1(S1)X1 - k3µ2(S2)X2 + ∆S2D. After this function is defined, Model (1) can be rewritten in the following extended state-space representation by means of a nonlinear coordinate transformation:16 z˙1 ) η + (S2,in - z1)D ˙ ) Π(z,D) η z˙i ) γi(z) (for i ) 2, 3, 4)
(3) 33
where two important properties can be highlighted: (a) the extended state-space (eq 3) is equivalent to eq 1, and therefore, if a control law is applied to eq 3 to attain certain control objectives, such a law can also achieve the same control objectives when applied to eq 1 and, (b) the dynamics of the uncertain state η can be reconstructed by using an ELO and readily available information: the dilution rate, the VFA concentration, its time derivative and its influent nominal value (i.e., η ) z˙1 - Sj2,in - z1)D). Thus, one can devise the following output feedback control, which has a linearizing-like structure: 16
zˆ˙1 ) η ˆ + (S2,in - zˆ1)D + Γg1(z1 - zˆ1) ˙ ˆ ) Γ2g2(z1 - zˆ1) η 1 D ) sat ˆ - KC(zˆ1 - S/2)] [-η (S2,in - zˆ1)
{
}
(4)
where Γ is a tuning parameter and the constants g1 and g2 are chosen such that the polynomial s2 + g2s + g1 ) 0 is the Hurtwitz polynomial, which is the characteristic polynomial of the linear part of the estimation error dynamics, and e is the estimation error vector, which is defined as e ) [z1 - zˆ1,η ηˆ ]. In this way, it is possible to guarantee that e f ε as t f ∞, where ε is an arbitrarily small neighborhood around the origin.31-33 Figure 1 shows the block diagram of the robust control scheme described by eq 4, where DC ) 1/(Sj2,in - zˆ1)[-ηˆ - KC(zˆ1 - S2*)] and D ) sat(DC) are the computed and actual control inputs. 3.4. Closed-Loop Behavior. Now let us analyze the closedloop behavior of the robust control scheme that is described by eq 4 under the following two possible situations: (I) The control input does not saturate (i.e., D ) DC); then, zˆ˙1 ) Γg1(z1 - zˆ1) - KC(zˆ1 - S/2)
(5)
By taking eq 5 into the Laplace domain, the following transfer function is obtained: Γg1 zˆ1(s) ) z1(s) s + Γg1 + KC
(6)
Clearly, in this situation the ELO acts as a first-order low-pass filter; in fact, the cutoff frequency of the low-pass filter (eq 6) depends on the observer and control gains Γ, KC, and, as a consequence, the effect of noisy measurements can be properly handled by selecting adequate values for both these parameters. (II) The control input does saturate (i.e., D ) Dmax, min, where Dmax, min is a constant value denoting the upper or/and lower limit of the saturation function defined in assumption A5; thus,
zˆ˙1 ) η ˆ + (S2,in - zˆ1)Dmax,min + Γg1(z1 - zˆ1)
(7)
whose Laplace domain representation is given by Γg1s + Γ2g2 zˆ1(s) ) 2 z1(s) s + (Γg + D )s + Γ2g 1
max,min
(8)
2
which shows that ELO has a structure of a second-order lowpass filter with an feed-forward action, which allows the continuous estimation of the uncertain state η, even when the control input saturates. In fact, by looking at the block diagram of the control scheme described by eq 4, one can clearly see that this structure resembles an antiwindup bumpless transfer (AWBT) feedback scheme,34 which has been shown to suppress the influence of significant external disturbances that typically requires large control actions but limited by the presence of input constraints. In the particular situation in which ∆S2,in(t) may become identically equal to zero (or even less than zero), it is clear that the control law that is described by eq 4 may saturate; however, the antiwindup structure of the robust control that is described by eq 4 is designed to drive the process to the setpoint as smoothly and quickly as possible, such that the computed control effort does not exceed their bounds. 4. Experimental Implementation The performance and robustness of the control law that is described by eq 4 was experimentally tested in a 0.528 m3 fully instrumented AD pilot-scale plant that was used to treat wine distillery wastewater (which is also known as vinasses; see Figure 2). The experimental implementation of the proposed control scheme was performed one month after the AD process was restarted, following seven months of inactivity (that is, under the most highly uncertain conditions). The sensors and actuators information was supplied to an input-output device that allowed the acquisition, treatment, and storage of data in a personal computer (PC). The proposed scheme was implemented by using software developed in Matlab. The automatic titrimetric analyzer Anasense, commercialized by the Belgian company Applitek, which was placed at the output of the process, was used to measure the outlet VFA concentration online every 30 min.10 This means that the robust control scheme that is decribed by eq 4 was calculated every 30 min, maintaining the control input constant until the next measurement was available (see Figure 4b, given later in this paper). However, because the sampling time was sufficiently fast, compared to the process residence time (which was >20 h), the assumption of continuous control was assumed to be valid over the entire experimental time period. The influent constraints were fixed as Dmin ) 0.0019 h-1 and Dmax ) 0.04167 h-1. The tuned control parameters used in the real-time pilotplant application were Kc ) 0.4 h-1, Γ ) 0.7, g1 ) 2 h-1, and g2 ) 1 h-1. These parameters were determined from the a priori off-line numerical implementation of the control scheme that is decribed by eq 4, using experimental data from the aforementioned AD pilot-scale plant. Different diluted vinasses (i.e., H2O + vinasses) were used during the experimental run. However, S˜2,in was fixed at 7500 mgVFA/L which corresponds to a single VFA off-line measurement of the raw vinasses to be treated to induce a significant error and to test the robustness of the proposed control law under the influence of load disturbances. Finally, six set-point changes were induced during the experimental run to test the output tracking capabilities of the proposed control scheme. These changes are listed in Table 2.
Ind. Eng. Chem. Res., Vol. 47, No. 20, 2008 7719
Figure 4. Behavior of the control input during the experimental run.
The response of the robust scheme that is described by eq 4 is depicted in Figure 3. As is seen, the proposed control scheme satisfactorily tracked the set-point changes while attenuating the disturbances over the whole 36 days experimental run. Note the effect of the open-loop operation at the startup of the AD process: the response of the VFA concentration deteriorated but drastically changed when the control loop was closed at t ) 127 h as this variable reached the setpoint in a rather smooth and fast way. Two simultaneous disturbances were induced at t ) 240 and 242 h: the first disturbance was a change on S2,in from 5200 mg VFA/L to 6700 mg VFA/L, whereas the second consisted of a set-point change from 1000 mg VFA/L to 1800 mg VFA/L. Clearly, the robust control scheme was able to regulate the VFA concentration around the setpoint. As a result of a sensor failure, a major disturbance occurred at t ) 313 h, resulting in a rapid fall of the VFA concentration readings, which led to the decision to operate the bioreactor in an open-loop manner. However, after the sensor was fixed and the robust control loop was again closed, the VFA concentration quickly returned to the setpoint. The cleaning maintenance of the Anasense sensor also introduced two additional operation disturbances at t ) 624 h and t ) 731 h but were satisfactorily handled by the controller, which was able to regulate the VFA concentration around the setpoint without retuning the control parameters. It is evident that the control scheme performed quite well, despite these disturbances and without the knowledge of both the inlet VFA concentration S2,in and the process kinetics. Figure 3 also shows that the estimation results of the extended Luenberger observer was reasonably good, because the estimated values (black line) were closer to those measured by the online sensor (gray line) during the experiment. Figure 4a illustrates the behavior of the control input D during the experimental run. Notice that, during the entire experimental run, the dilution rate calculated by the proposed control law (black line) was different from that measured at the entrance of the digester (gray line). This error was mainly due to a calibration problem in the feeding pump which caused the small off-set between the VFA concentration and the set-point value (see Figure 3). Also note that, after the introduction of most of the set-point changes, the control input saturated (from below
or from top, depending on the magnitude and direction of the set-point change) without serious consequences on the controller performance (see Figure 4b). Figure 4b finally depicts the effect of the calculated controller action on the control input. Although the control law that is described by eq 4 was calculated every 30 min, the behavior of D was quite smooth, despite saturation. This behavior is a desirable feature from a practical point of view, to guarantee safety operating conditions and increase the lifetime of the pump. 5. Conclusions A model-based robust nonlinear control methodology for anaerobic digestion processes with uncertain dynamics, input constraints, parameter uncertainty, and load disturbances was developed. This methodology was obtained from the extension of the previously reported ideas by Alvarez-Ramirez et al.31,32 by the combination of an output feedback control with a linearizing-like structure and an extended Luenberger observer used to estimate the uncertain terms of the process. The proposed methodology was experimentally implemented over a period of 36 days under different uncertain scenarios and load disturbances in an anaerobic digester (AD) pilot-scale plant that was used for the treatment of industrial wine distillery wastewater. It was shown that the controller yields robustness in the face of parameter uncertainty, load disturbances, and variable setpoints. The performance of the proposed robust control scheme is particularly encouraging to scale it up to real-life industrial applications: (i) its simple structure is easy to implement and tune (there are only two parameters to adjust: Γ and KC) and (b) it does not require the knowledge of the influent composition nor the process kinetics nor biogas production measurements. Both of these features are among the main advantages of the proposed scheme, with regard to the previously reported approaches.13-16 In other words, the proposed methodology includes the advantages of proportional integral and proportion integral differential (PI/PID) control and the robustness of the nonlinear control schemes but requires a VFA online analyzer, which is not very restrictive, because the
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technical and economical availability to acquire reliable VFA online sensors has increased drastically over the past few years. Acknowledgment This work was partially supported by Project Nos. CONACyT/J50282/Y, PROMEP/103.5/05/1705 and PROMEP/103.5/ 02/2354. B.P.-R. thanks CONACyT for financial support (under Grant No. 185382). Literature Cited (1) Henze, M.; Harremoes, P.; Jansen, J. L. C.; Arvin, E. Wastewater Treatment: Biological and Chemical Processes, 2nd Edition; SpringerVerlag: Berlin, 1997. (2) Zumstein, E.; Moletta, R.; Godon, J. J. Examination of two years of community dynamics in an anaerobic bioreactor using fluorescence polymerase chain reaction (PCR) single-strand conformation polymorphism analysis. EnViron. Microbiol. 2000, 2 (1), 69–78. (3) Hill, D.; Cobbs, S.; Bolte, J. Using volatile fatty acid relationships to predict anaerobic digester failure. Trans. ASAE 1987, 30, 496–501. (4) Ahring, B.; Angelidaki, I. Monitoring and controlling the biogas process. In Proceedings of the 8th International Conference on Anaerobic Digestion, 1997; Vol. 1, pp 40–49. (5) Schu¨gerl, K. Progress in monitoring, modeling and control of bioprocesses during the last 20 years. J. Biotechnol. 2001, 85, 149–173. (6) Olsson, G.; Nielsen, M. K.; Yuan, Z.; Lynggaard-Jensen, A.; Steyer, J. P. Instrumentation, Control and Automation in Wastewater Systems. IWA Scientific Technical Report, No. 15, 3IWA Publishing, 2005. (7) Steyer, J.; Bernard, O.; Batstone, D.; Angelidaki, I. Lessons learnt from 15 years of ICA in anaerobic digesters. Wat. Sci. Technol. 2006, 53 (4), 25–33. (8) Feitkenhauer, H.; von Sachs, J.; Meyer, U. On-line titration of volatile fatty acids for the process control of anaerobic digestion plants. Water Res. 2002, 36, 212–218. (9) Steyer, J. P.; Bouvier, J.; Conte, T.; Gras, P.; Harmand, J.; Delgenes, J. On-line measurements of COD, TOC, VFA, total and partial alkalinity in anaerobic digestion process using infra-red spectrometry. Wat. Sci. Technol. 2002, 45 (10), 133–138. (10) De Neve, K.; Lievens, K.; Steyer, J. P.; Vanrolleghem P. Development of an on-line titrimetric analyser for the determination of volatile fatty acids, bicarbonate, and alkalinity. In Proceedings of the 10th IWA World Congress on Anaerobic Digestion, Montreal, Canada, 2004; Vol. 3, pp 1316-1318. (11) Rozzi, A. Alkalinity considerations with respect to anaerobic digester. In Proceedings of the 5th Forum on Applied Biotechnology, Med. Fac. Landbouww, 1991; Vol. 56, pp 1499–1514. (12) Lahav, O.; Morgan, B. E. Titration methodologies for monitoring of anaerobic digestion in developing countries: A review. J. Chem. Technol. Biotechnol. 2004, 79 (12), 1331–1341. (13) Renard, P.; Van Breusegem, V.; Nguyen, N.; Naveau, H.; Nyns, E. J. Implementation of an adaptive controller for the start-up and steadystate running of a biomethanation process operated in the CSTR mode. Biotechnol. Bioeng. 1991, 8, 805–812. (14) Alcaraz-Gonza´lez, V.; Maloun, A.; Harmand, J.; Rapaport, A.; ´ lvarez, V.; Pelayo-Ortiz, C. Robust interval-based Steyer, J. P.; Gonza´lez-A SISO and SIMO regulation for a class of highly uncertain bioreactor: Application to the anaerobic digestion. In Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000; IEEE: Piscataway, NJ, 2000; Vol. 5, pp 4532–4537.
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ReceiVed for reView February 13, 2008 ReVised manuscript receiVed June 25, 2008 Accepted July 11, 2008 IE800256E
