ТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИ, 2013, том 47, № 5, с. 566-572
УДК 66.011
NONLINEAR CONTROLLER DESIGN WITH APPLICATION TO A CONTINUOUS BIOREACTOR
© 2013 г. P. A. López-Péreza, c, M. I. Neria-Gonzálezb, R. Aguilar-Lópeza
aDepartment of Biotechnology and Bioengineering, CINVESTAV-IPN Av. Instituto Politécnico Nacional, No. 2508, San Pedro Zacatenco, D.F. México bChemical and Biochemical Engineering Division, Tecnológico de Estudios Superiores de Ecatepec. Av. Tecnológico S/N. CP 55120, Ecatepec, Edo.de México, México
raguilar@cinvestav.mx
cDepartment of energy Universidad Politécnica Metropolitana de Hidalgo, Boulevard de acceso a Tolcayuca N° 1009
Exhacienda San Javier, Tolcayuca, Hgo. C.P. 43860 Received 30.11.2011
The goal of this work is to present a mathematical model of a sulfate-reducing bioreactor where a proposed nonlinear controller is applied to regulate the dynamics of the process. The corresponding kinetic model, experimentally corroborated, is extended to simulate continuous operation, and a class of smooth controllers, under the frame of sliding modes, is proposed to control the sulfate concentration into the bioreactor employing the dilution rate as control input, with successes. The proposed controller avoids the named chattering phenomena for its smooth structure, and its performance is compared with a well tuned proportional-integral and high-order sliding-mode controllers in order to analyze their corresponding closed-loop behavior. A sketch of proof of the closed-loop stability is provided.
DOI: 10.7868/S0040357113050060
INTRODUCTION
The processing of biological materials and employing biological agents such as cells, enzymes, or antibodies have been recognized since thousands of years. Bioprocesses are currently used to produce some chemical compounds synthesized by a microorganism, cultivate a biomass for its utilization, extract its metabolites, and degrade a pollutant.
Several problems arising from this industrialization are generally the same as those encountered in any processing industry, in the field of bioprocessing, almost all of the problems that are being tackled in automatic control. Thus, system requirements for supervision, control and monitoring of the processes in order to optimize operation or detect malfunctions are on the increase [1—3]. However, in reality, few installations are provided with such systems.
The majority of the key variables associated with these systems (concentrations of biomass, substrates and products) can be measured only using analyzers on a laboratory scale, where they exist, which are generally very expensive and often require heavy and expensive maintenance. Thus, the majority of the control strategies used in industries is very often limited to indirect control of fermentation processes by control loops of the environmental variables such as dissolved oxygen concentration, temperature, pH, etc. [4].
The early successful application control strategy in process control is in evolution of the proportional-integral-derivative (PID) controller and Ziegler—
Nichols tuning method [5]. However, as (i) the industrial demands, (ii) the computational capabilities of controllers, and (iii) complexity of systems under control increase, so the challenge is to implement advanced control algorithms [6, 7].
Since achievable controller performance in a model-based control scheme is dependent on the quality of the process model [8], a controller based on a model that captures events occurring at both the general considerations for control of bioreactors.
On the other hand, the difficulty of implementing a feedback control is twofold. First, response of sensors tends to be slower than many of the processes they monitor. Second, the sensors are generally not available for measurement of substrate with rapid dynamics for feedback application [9]. Given the above objectives there are, broadly speaking, two ways to design an appropriate control system. The most frequently used method is to pre-select a controller structure and then to tune the parameters of this controller so that the desired closed-loop response is obtained. This is referred to as a parameter optimized control system, the most well-known example of which is probably the PID controller [10]. The other approach is the use of structure optimal control systems, where both the structure and parameters of the controller are adapted to those of the process model [11]. In practice, however, the use of the latter method is severely restricted because exact dynamic term cancellation is required in order to produce the optimal controller structure. This is
usually not possible for various reasons, e.g., the lack of an appropriate process model, non-linearities and physical constraints on the process variables.
From the above, in this work a class of smooth controllers is proposed which is close to sliding-mode frame, where a smooth reaching law is proposed to lead to the bioreactor to stable surface, where the process is robust against some disturbances and model uncertainties (as classical sliding-mode controllers) avoiding the named chattering problem improving the closed-loop performance of the system.
EXPERIMENTAL
Organism, culture maintenance and purity test.
Desulfovibrio alaskensis 6SR was isolated of a developed biofilm inner face of oil pipeline [12]. The strain was maintained routinely in Hungate tubes with 5 mL of Postgate's B medium. Decimal dilution was made in plates of anaerobic agar supplemented with 6 mL of lactate (60% w/w), 4.5 g of Na2SO4, 0.004 g of FeSO4, and 27.5 g of NaCl to evaluate the purity of organism. The plates were placed in anaerobic jar (BBLTMGasPakTM anaerobic systems) and were incubated until to appear colonies. The presence of black colonies indicates growth of sulfate-reducing bacteria. One black colony well definite and isolated was picked and quickly transferred at 45 mL sterile Postgate's C medium in anaerobic conditions [13], and subcultures ware made subsequently. The media were inoculated with 5 mL of culture and incubated at 37°C. Each medium was prepared and dispended in anaerobic conditions under a N2 (99.998% purity) atmosphere, 120 and 160 mL serum bottles were filled with 45 and 95 mL of medium, respectively, and autoclaved at 121°C. The inoculum for kinetics was cultured in 45 mL of Post-gate's C medium for 25 h at 37°C (logarithmic phase). A 5-mL aliquot was taken to inoculate 95 mL of fresh medium at 37°C. Two independent cultures for triplicate and incubated with 12 h apart were monitored to measure biomass, sulfate, sulfide and extracellular polymeric substances (EPS) for 72 h.
Analytic methods. The bacterial growth was followed through optical density methodology, consumption of sulfate and production of sulfide. Samples of cultures were taken, avoiding contact with oxygen, between 3 and 4 h. Sulfate in the medium was measured by the turbid metric method based on the precipitation of barium [14]. Also, the production of sulfide was measured by a colorimetric method [15]. The optical density reading for cell growth was transformed into dry mass (mg/mL) through a standard growth curve. The EPS was extracted using heat treatment and filtration. Bottle containing the bacterial culture was opened and put in water bath at 50° C for 15 min, the sample was vortexed once or twice, then the cellar suspension was passed through a 0.45- ^m nylon membrane, the filtrate was collected in 250 mL centrifuge bottle and EPS was then precipitated from it, adding
an equal volume of cold ethanol overnight at —20°C, followed by centrifugation at 2500g for 10 min at 4°C (Hettich Zentrifugen UNIVERSAL 320R). The pelleted EPS was transferred at micro-centrifuge tube and washed in 70% (v/v) ice-cold ethanol. EPS was dried on oven (ECOSHEL DOV23A) at 70°C for 24 h and dry weight was recorded.
BIOREACTOR MODELLING
For biological systems, the unstructured models are the simplest of all modeling philosophies used to describe the biological model. They consider the cell mass as a single chemical species and do not consider any intracellular reactions occurring within the cell. Unstructured models typically describe the growth phenomena based on a single limiting substrate and consider only substrate uptake, biomass growth, and product formation in the modeling framework. Thus, the biological component of the system depends directly on the macroscopic reactor variables. These models give an adequate representation of the biological growth phenomena in relatively simple cases, when the cell response time to environmental changes is either negligibly small or much longer than the batch time.
The response state variables data (biomass, sulfate, sulfide, extracellular polymeric substances and inactivate biomass) of the three series of sulfate-reducing batch culture were analyzed and the average value of each measurement point was calculated. In graphic of the average experimental data for each response variable, the product in the bacterial development showed a negative effect. Then the specific growth rate follows the product inhibition model. In this work, the growth kinetics was described with the product inhibition model as follows:
ф = Ф (i. p)-»_ (, - p)' (-kS-S )
(i)
where 9 is the specific biomass growth rate, P is the sulfide concentration, S is the sulfate concentration and Ks is the affinity constant. This equation represents an unstructured kinetic model proposed by Levenspiel [16]. Figure 1 is related with the model validation with experimental data, where a satisfactory agreement between the predicted and experimental data is observed. POLYMATH 6.0 Professional software was used in order to fit the optimum parameter's set, the program allows applying effective numerical analysis techniques. Table 1 contains the parameter's set obtained from the above methodology. A linear regression between the experimental data and the predicted data was
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