A class of nonlinear adaptive controller for a continuous anaerobic bioreactor

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1 480 Journal of Scientific & Industrial Research J SCI IND RES VOL 71 JULY 2012 Vol. 71, July 2012, pp A class of nonlinear adaptive controller for a continuous anaerobic bioreactor Vicente Peña-Caballero 1, Pablo A López-Pérez 1, M Isabel Neria-González 2 and Ricardo Aguilar-López 1 * 1 Department of Biotechnology & Bioengineering CINVESTAV-IPN, Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Mexico, DF 2 Chemical and Biochemical Engineering Division, Tecnológico de Estudios Superiores de Ecatepec, Tecnológico, 55210, Valle de Anáhuac, Ecatepec de Morelos, Estado de Mexico Received 17 January 2012; revised 04 May 2012; accepted 08 May 2012 This study proposed a proportional-integral (PI) control law for tracking of sulfate concentration trajectories in a continuous anaerobic bioreactor, where a sulfate-reducing bacterium (Desulfovibrio alaskensis 6SR) is considered for different operation purposes. Proposed controller, applied to a mathematical bioreactor s model, described dynamics of biomass, sulfate and sulfide concentrations. Proposed control law improves performance of a well tuned PI controller. Keywords: Anaerobic bioreactor modeling, PI, Adaptive proportional gain, Robust performance Introduction Proportional-integral and derivative controllers (PID) are widely employed in chemical and biochemical processes. Studies on robust control have proposed the tuning of PID controllers by using information related to the model structure, such as internal model control (IMC). Proper tuning of a PID has same effect as the use of another more efficient controller 1. High rate anaerobic treatment requires robust, flexible, and efficient industrial operation modes, where corresponding control strategies play important roles. A number of studies 2-7 dealing with new controllers design under the framework of gain scheduling, predictive, optimal, and nonlinear control theories have been published. However, because of mathematical complexity, most of such studies cannot be applied to industrial plants. Aguilar et al 8 proposed novel approaches to design nonlinear PI and PID type controllers using more sophisticated techniques that allow for new friendly tuning rules for controller s gains and assuring semi-global robust performance. Biochemical reactors are a typical example of processes that exhibit non-linear behaviour and time varying parameters. This study proposed a proportional-integral (PI) control law *Author for correspondence raguilar@cinvestav.mx for tracking of sulfate concentration trajectories in a continuous anaerobic bioreactor, where a sulfatereducing bacterium (Desulfovibrio alaskensis 6SR) is considered for different operation purposes. Experimental Section Desulfovibrio alaskensis 6SR, isolated from a biofilm sample, was identified by 16S rrna gene sequencing and analysis 9. It was routinely cultivated and maintained on Postgate C medium 9. Batch Cultures For preparation of a congenital water medium, a sample of congenital water (CW) was obtained from oil pipeline located in Mexican Southeast region. Chemical analysis of CW (ph 8.8) gave: chlorides, ; sulfur, 178; and sulfate, g/l. A 1000 mlaliquot of CW was saturated with N 2 for 1 h and was enriched with sodium lactate (6 ml), yeast extract (0.5 g), and reducing solution, 5 ml (ascorbic acid, 1 g/l; and sodium thioglicolate, 1 g/l). ph was adjusted to 7 with 1N KOH. Then, CW medium (90 ml) was distributed in serum bottles (160 ml) using Hungate s technique 10 and autoclaved at 120 C for 15 min. Cultures of D. alaskensis 6SR in Postgate C medium 11 were used to inoculate CW medium (45 ml). Culture was incubated for 20 days at 37 C. A 10 ml aliquot of this culture inoculated three

2 AGUILAR-LÓPEZ et al: A NONLINEAR ADAPTIVE CONTROLLER FOR CONTINUOUS ANAEROBIC BIOREACTOR 481 bottles with CW medium for different time periods (0, 24 and 36 h) under same conditions. Bacterial growth was followed through optical density (OD) measurements, consumption of sulfate and production of sulfide. Samples from cultures were taken anaerobically every 1 h. Sulfate in the medium was measured by turbidimetric method based on barium precipitation 12. Production of sulfide was measured by a colorimetric method 13. OD reading for cell growth was transformed to dry weight (mg/l) through a standard growth curve. Data were analyzed and only the points that adjusted to a straight line (exponential phase) were used to determine growth kinetics parameters according to Monod model 14. Mathematical Model of Bioreactor High rate anaerobic treatment technologies can be used to treat organic wastewaters (distillery, brewery, paper manufacturing, petrochemical, etc.) Anaerobic digesters are large fermentation tanks, where sludge digestion and settling occur simultaneously. Sludge stratifies and forms different layers (digested sludge, actively digested sludge, supernatant, scum layer, and gas) from bottom to top of the tank. Higher sludge loading rates are achieved in high-rate version, in which sludge is continuously mixed and heated; anaerobic digestion is affected by temperature, retention time, ph, chemical composition of wastewater, presence of toxics, and competition between methanogenic bacteria and sulfatereducing bacteria. For control purposes, a reduced order model that can describe dynamic behavior of the main state variables is adequate. Therefore, following mathematical model (Fig. 1) is proposed, based on classical mass balances for biomass, sulfate (substrate) and sulfide (product) concentrations, considering continuous operation: For sulfate (S t ), (1) For biomass ( ), (2) For sulfide ( ), (3) Where specific growth rate is considered to obey Monod s model 14 as, and Here is dilution rate (control input), is specific growth rate, is sulfate coefficient yield, and is sulfide coefficient yield. In accordance with specific experimental setup, following initial conditions were considered for batch culture and model validation purposes:,,. Employing bioreactor s model, an open-loop stability analysis was done in accordance with a linear approach, evaluating Jacobian matrix on selected operation points (MatLab ). Equilibrium Point for Sulfate Removal Taking ; ; ), Jacobian matrix evaluated in equilibrium point and ) is Therefore, equilibrium point is unstable. Equilibrium Point for Heavy Metal Removal Taking ; ; Jacobian matrix evaluated in equilibrium point and ) is ; (4) ; ), (5) Therefore, equilibrium point is unstable. With these results, it is concluded that open-loop operation would be hard to achieve, such that any disturbance arriving to bioreactor leads the process to an undesirable operation point, justifying closed-loop operation with the proposed feedback controller. Controller Design Proposed control law is aimed at controlling sulfate concentration in bioreactor by employing input flow

3 482 J SCI IND RES VOL 71 JULY 2012 (dilution rate) as control input. Proposed controller is related with PI contributions of the named regulation error [difference between sulfate trajectory and corresponding set point ( )]. This is considered for easyness of its possible real-time implementation. Considering a canonical control form of controlled sulfate state equation as (6) (9) Where and. Note that matrix is Hurwitz stable with an adequate choosing of control gain dξ. Therefore, dt L + A ξ, which on solving gives Where and (10). Also, is vector of state; is control action; is a nonlinear field that consists of continuosly differentiable known vectors;. Now, control law is proposed as when Matrix A is stable, hence the first term tends to zero t, hence (11) (7) Where dynamic equation for is an adaptation algorithm to update time-varying control gain, is proportional gain, and is integral time. To prove closedloop stability of bioreactor, consider dynamic equation of regulation error as or Now, supposing that function continuous function on integration interval is maximum of the function on domain considering is bounded as for large enough.. Under the assumptions, A1. (8) with is a positive, then M ; thus, such that, Therefore, and A2. taking norms to both sides of Eq. (8) and applying A1 and A2, it is obtained If in the last inequality, the term refers to integral tending to zero in finite time, reducing difference between set point and measured value. Therefore, closed-loop process should exhibit stable behavior during operating time. Results and Discussion Kinetic model validation on experimental data (Figs 1 & 2) shows adequate performance of kinetic model, describing sulfate-reducing process for D. alaskensis 6SR. On the other hand, rigorous simulations show the performance of proposed controller. A policy for reactor s operation is that sulfate concentration at the outlet should be maximum permissible. Therefore, criteria to control sulfate concentration was that sulfate concentration be at the exit of reactor. According to simulations for different dilution rates, a concentration was obtained of sulfate in reactor outlet stream for (Fig. 3). Bioreactor is operated in open-loop mode from 0 to when controller is tuning up, and shows behavior of three set points ( ). In this last control action, bioreactor operates according to the maximum allowable residual concentration of sulfate ( ). To compare performance of proposed controller, a linear PI controller was implemented. It was tuned by IMC guidelines 19 ; corresponding tuning was done via a step disturbance of 5% in the nominal value

4 AGUILAR-LÓPEZ et al: A NONLINEAR ADAPTIVE CONTROLLER FOR CONTINUOUS ANAEROBIC BIOREACTOR 483 Fig. 1 Model validation with experimental data: a) biomass; b) sulfate; and c) sulfide [Error bars represent standard error of mean (8 replicates)] Fig. 2 Model validation with experimental data: a) Comparison of experimental sulfate, biomass and sulfide with model prediction for batch experiment; and b) Plot between residual and corresponding state variables

5 484 J SCI IND RES VOL 71 JULY 2012 Fig. 3 Behavior of states for different dilution rates ( ) for the model in Eqs (1-3): a) biomass concentration; b) sulfate concentration; and c) sulfide concentration Fig. 4 Closed-loop trajectory of sulfate concentration Fig. 5 Closed-loop performance of uncontrolled X t and P t concentrations

6 AGUILAR-LÓPEZ et al: A NONLINEAR ADAPTIVE CONTROLLER FOR CONTINUOUS ANAEROBIC BIOREACTOR 485 Fig.6 Control input effort Fig. 7 Performance index (ITSE) for controllers of control input ( ), steady-state gain was calculated as, characteristic time, time delay as and corresponding proportional gain as, and integral time for closed-loop time constant. Integral timeweighted squared error ( ) measures 20 impact of control error. ITSE provides the advantage of heavy penalization of large errors at long term; therefore, it is an adequate measure of resilience of considered controllers 21. Proposed controller (solid line) is better (Fig. 4) than linear PI controller (dashed line), as proposed controller acts immediately, leading sulfate trajectory to the corresponding set points (1.8 g/l, 1.0 g/l, and 0.5 g/l). Under the scheme for sulfate control, behaviors of other uncontrolled states (biomass and sulfide) are shown as stable (Fig. 5). Therefore, corresponding control effort is shown in Fig. 6. Under performance comparison (Fig. 7) of proposed controller with resilience of simulated controllers, ITSE was evaluated for dynamic system under the influence of two controllers. Proposed controller has been found able to stabilize the system in long term, whereas for linear PI controller, this error increases limitless. This is due to the ability of proposed controller to eliminate offset, a property that is not exhibited by classic controller.

7 486 J SCI IND RES VOL 71 JULY 2012 Conclusions A nonlinear PI controller for a continuous anaerobic bioreactor is designed and developed to control supply of sulfate. Proposed controller is able to provide adequate performance for regulation and tracking purposes in a better way than standard PI controller. Acknowledgment Authors (V Peña-Caballero & P A López-Pérez) thank CONACYT for scholarship. References 1 Morari M &Zafiriou E, Robust Process Control (Prentice Hall, Englewood Cliffs, NJ) 1989, Aguilar-Lopez R & Alvarez-Ramirez J, Sliding-mode control scheme for a class of continuous chemical reactors, IEE Proc Contr Theory & App, 149 (2002) Maya-Yescas R, Aguilar-López R, Gonzalez-Ortiz A, Mariaca- Dominguez E, Rodriguez-Salomon S et al, Impact of production objectives on adiabatic FCC regenerator control, Petrol Sci Technol, 22 (2004) Galán O, Romagnoli J & Palazoglu A, Robust H control of nonlinear plants based on multi-linear models: application to bench-scale ph neutralization reactor, Chem Engg Sci, 55 (2000) Schmid R & L Ntogramatzidis, A unified method for the design of non overshooting linear multivariable state-feedback tracking controllers, Automatica, 46 (2010) Quan Q & Cai K Y, A Filtered Repetitive Controller for a Class of Nonlinear Systems, IEEE Trans Automat Cont, 56 (2011) Nie M W & Tan W W, Stable adaptive fuzzy PD plus PI controller for nonlinear uncertain systems, Fuzzy Set Syst, 179 (2011) Aguilar R, González J, Barrón M, Martínez-Guerra R & Maya- Yescas R, Robust PI 2 controller for continuous bioreactors, Process Biochem, 36 (2001) Neria-González I, Wang E T, Ramirez F, Romero J M & Hernández-Rodriguez C, Characterization of bacterial community associated to biofilms of corroded oil pipelines from southeast of Mexico, Anaerobe, 12 (2006) Hungate, R E, A roll tube method for cultivation of strict anaerobes Methods in microbiology, vol 3B, edited by J R Norris and D W Ribbons (Academic Press Inc., New York) 1969, Postgate J R, The Sulphate-Reducing Bacteria (Cambridge University Press, Cambridge, New York) 1984, Kolmer A, Wikström P & Hallberg K, A fast and simple turbidimetric method for the determination of sulfate in sulfate-reducing bacteria cultures, J Microbiol Meth, 41 (2000) Cord-Ruwisch R A, A quick method for determination of dissolved and precipitated sulfide in cultures of sulfate-reducing bacteria, J Microbiol Meth, 4 (1985) Monod J, The growth of bacterial cultures, Ann Rev Microbiol, 3 (1949) Nagpal S, Chuichulcherm S, Peeva L & Livingston A, Microbial sulfate reduction in a liquid-solid fluidized bed reactor, Biotechnol Bioeng,70 (2000) Veeken A H M, Akoto L, Look W H P & Weijma J, Control of sulfide (S 2- ) concentration for optimal zinc removal by sulfide precipitation in a continuously stirred tank reactor, Water Res, 37 (2003) Sahinkaya E, Biotreatment of zinc-containing wastewater in a sulfidogenic CSTR: performance and artificial neural network (ANN) modeling studies, J Haz Mater, 164 (2009) Hammack R W & Edenborn H, The removal of nikel from mine waters using bacterial sulfate reduction, Appl Microbiol Biotech, 37 (1992) Rivera E D, Morari M & Skogestad S, Internal model control 4. PID controller design, Ind Eng Chem Process Des Dev, 25 (1986) Ogunnaike, B A & Ray W H, Process Dynamics, Modeling, and Control (Oxford University Press, New York) 1994, Krohling R A & Rey J P, Design of optimal disturbance rejection PID controllers using genetic algorithm, IEEE Trans Evol Comput, 5 (2001)