Multi-input multi-output control of a continuous fermenter using nonlinear model based controllers

Internal Model Control (IMC) and Model Predictive Control (MPC), the two most important members of model based controllers, are favourable alternatives for control of nonlinear processes. However, the performance of these controllers deteriorates drastically in the presence of substantial process-model mismatch. Hu and Rangaiah (1998) proposed feedback augmentation for nonlinear IMC (hence named Augmented IMC, AuIMC) for improving control in the presence of modelling errors, and demonstrated its success on a neutralization process. In the present study, IMC, MPC and AuIMC strategies are tested in a more difficult case of multi-input multi-output (MIMO) operation of a highly nonlinear continuous fermenter. A new control configuration is introduced as the conventional configuration is not applicable. Simulation results for different modelling errors show that IMC is better than MPC for fermenter control. The advantage of augmentation as in AuIMC manifests in the significantly improved regulatory control of the fermenter.     

Optimizing control of a continuous stirred tank fermenter using a neural network

Feedforward neural networks are a general class of nonlinear models that can be used advantageously to model dynamic processes. In this investigation, a neural network was used to model the dynamic behaviour of a continuous stirred tank fermenter in view of using this model for predictive control. In this system, the control setpoint is not known explicitly but it is calculated in such a way to optimize an objective criterion. The results presented show that neural networks can model very accurately the dynamics of a continuous stirred tank fermenter and, the neural model, when used recursively, can predict the state variables over a long prediction horizon with sufficient accuracy. In addition, neural networks can adapt rapidly to changes in fermentation dynamics.List of Symbols F Dimensionless flow rate (F/ V₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective cost function - K _i Dimensionless constant in Eq. (3) (k _i /s₀) - k _i kg/m³ Substrate inhibition constant in Haldane model - k _m Dimensionless constant in Eq. (3) (k _s /s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - n prediction horizon - S Dimensionless substrate concentration (s/s₀) - s kg/m³ Substrate concentration - t h Time - v Dimensionless volume (V/V₀) - V m³ Liquid volume in fermenter - W _ij , W _jk Weight matrices in neural network - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ) - 1/h Maximum specific growth rate - 1/h Specific growth rate - Dimensionless time ( t)     

Optimization and control of a continuous stirred tank fermenter using learning system

A variable structure learning automaton is used as an optimization and control of a continuous stirred tank fermenter. The algorithm requires no modelling of the process. The use of appropriate learning rules enables to locate the optimum dilution rate in order to maximize an objective cost function. It is shown that a hierarchical structure of automata can adapt to environmental changes and can also modify efficiently the domain of variation of the control variable in order to encompass the optimum value.List of Symbols f Random number - F Dimensionless flow rate (F/V ₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective function - K _i Dimensionless constant in Eq. (3) (k _i/s₀) - k _i · kg/m³ Substrate inhibition constant in Haldane model - K _m Dimensionless constant in equation (3) (k _s/s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - L Number of levels of the hierarchical system of automata - N Number of possible control actions - p Probability - S Dimensionless substrate concentration (s/s ₀) - s kg/m³ Substrate concentration - T Dimensionless sampling period - t h Time - v Dimensionless volume (V/V ₀) - V m³ Liquid volume in fermenter - W Input to the stochastic automaton - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ^*) - ^* h^–1 Maximum specific growth rate - h^–1 Specific growth rate - Dimensionless time ( t)     

Nonlinear adaptive optimization of biomass productivity in continuous bioreactors

A novel on-line adaptive optimization algorithm is developed and applied to continuous biological reactors. The algorithm makes use of a simple nonlinear estimation model that relates either the cell-mass productivity or the cell-mass concentration to the dilution rate. On-line estimation is used to recursively identify the parameters in the nonlinear process model and to periodically calculate and steer the bioreactor to the dilution rate that yields optimum cell-mass productivity. Thus, the algorithm does not require an accurate process model, locates the optimum dilution rate online, and maintains the bioreactors at this optimum condition at all times. The features of the proposed new algorithm are compared with those of other adaptive optimization techniques presented in the literature [1–5]. A detailed simulation study using three different microbial system models [3, 6–7] was conducted to illustrate the performance of the optimization algorithm.List of Symbols A(q ^–1) polynomial in q ^–1 - b bias term - c _F nutrient cost term - B(q ^–1) polynomial in q ^–1 - C(q ^–1) polynomial in q ^–1 - CMPR kg/(m³ · h) cell mass productivity - D 1/h dilution rate - D _opt 1/h optimum dilution rate - E(q ^–1) polynomial in q ^–1 - h exponential filter constant - J objective function - k time index - K _m Monod's constant - n optimization interval - P covariance matrix - q ^–1 backward shift operator - r defined by equation (28) - S kg/m³ substrate concentration - S _F kg/m³ feed substrate concentration - T _s h sampling period - u vector containing previous input values - V dm³ fermenter volume - X kg/dm³ cell mass concentration - Y output variable - Y vector containing previous output values - Y _x/s g/g yield coefficient - optimization tuning constant - vector linear or nonlinear combination of u and Y - denominator covariance matrix update equation - forgetting factor - parameter vector - 1/h specific growth rate - _m 1/h maximum specific grow rate     

Experimental adaptive on-line optimization of cellular productivity of a continuous bakers' yeast culture

An adaptive on-line optimization method that utilizes dynamic model identification has been applied to maximize the cellular productivity of a continuous bakers' yeast culture. Experiments were conducted on a sophisticated computerized fermentation system. Experimental results show that the adaptive on-line optimization method requires very little a priori information, is easy to implement, converges quickly, adapts to changes in the process, and is stable even when operational difficulties are encountered.     

Production of mouse monoclonal antibodies using a continuous cell culture fermenter and protein G affinity chromatography

The production of anti--fetoprotein monoclonal antibodies for diagnostic use was carried out in a stirred tank fermenter equipped with a double membrane stirrer for bubble free aeration and continuous medium perfusion. A serum-free medium supplemented with 4 mM L-glutamine and 2.0 g/l glucose with a protein content of only 780 g/ml was used for the production process. The harvested antibodies were concentrated 50-fold using a tangential ultrafiltration system and were then purified in a one step purification process by protein G affinity chromatography. The purity of the final product (90%) was controlled by SDS-polyacrylamide gel electrophoresis, gel exclusion chromatography and isoelectric focussing. For further quality controls of the product the immunoglobulin subclass and the isoelectric point were determined and the specificity of the purified mAb was tested by RIA using¹²⁵I labelled -fetoprotein.1.87 g of purified monoclonal antibodies were produced (90% purity) within 2 weeks. It was found that the use of this type of stirred tank fermenter combined with a one step purification process using protein G affinity chromatography represents a suitable method for the fast production of medium scale quantities (500 mg–5 g) of monoclonal antibodies for diagnostic use.Abbreviations AFP -Fetoprotein - BSA bovine serum albumine - FCS Fetal calf serum - HRP horseradish peroxidase - OPD o-phenylenediamine dihydrochloride - I.P. isoelectric point - IEF isoelectric focussing - PBS Phosphate buffered saline     

Computer control of pH and DO in a laboratory fermenter using a neural network technique

In this contribution, the advantages of the artificial neural network approach to the identification and control of a laboratory-scale biochemical reactor are demonstrated. It is very important to be able to maintain the levels of two process variables, pH and dissolved oxygen (DO) concentration, over the course of fermentation in biosystems control. A PC-supported, fully automated, multi-task control system has been designed and built by the authors. Forward and inverse neural process models are used to identify and control both the pH and the DO concentration in a fermenter containing a Saccharomyces cerevisiae based-culture. The models are trained off-line, using a modified back-propagation algorithm based on conjugate gradients. The inverse neural controller is augmented by a new adaptive term that results in a system with robust performance. Experimental results have confirmed that the regulatory and tracking performances of the control system proposed are good.     

Maximizing the productivity of the microalgae <Emphasis Type="Italic">Scenedesmus</Emphasis> AMDD cultivated in a continuous photobioreactor using an online flow rate control

In this study, production of the microalga Scenedesmus AMDD in a 300 L continuous flow photobioreactor was maximized using an online flow (dilution rate) control algorithm. To enable online control, biomass concentration was estimated in real time by measuring chlorophyll-related culture fluorescence. A simple microalgae growth model was developed and used to solve the optimization problem aimed at maximizing the photobioreactor productivity. When optimally controlled, Scenedesmus AMDD culture demonstrated an average volumetric biomass productivity of 0.11 g L^?1 d^?1 over a 25 day cultivation period, equivalent to a 70 % performance improvement compared to the same photobioreactor operated as a turbidostat. The proposed approach for optimizing photobioreactor flow can be adapted to a broad range of microalgae cultivation systems.     

Experimental multivariable adaptive optimization of the steady-state cellular productivity of a continuous baker's yeast culture

A multivariable adaptive optimization algorithm that uses transient data to improve the optimization speed was successfully implemented on-line to maximize the steady-state cellular productivity of a continuous culture of baker's yeast. The algorithm was shown to be stable even during periods of oscillatory growth and was able to reoptimize the culture when planned disturbances were introduced. Although adaptive tuning of the forgetting factor improved the performance, further refinements in the adaptive forgetting factor algorithm are necessary for completely satisfactory results.     

L-Sorbose production in a continuous fermenter with and without cell recycle

The kinetics of continuous l-sorbose fermentation using Acetobacter suboxydans with and without cell recycle (100%) were investigated at dilution rates (D) of 0.05, 0.10, 0.15 and 0.3 h^–1. The biomass and sorbose concentrations for continuous fermentation without recycle increased as the dilution rate was increased from 0.05 to 0.10 h^–1. A maximum biomass concentration of 8.44 g l^–1 and sorbose concentration of 176.90 g l^–1 were obtained at D=0.10 h^–1. The specific rate of sorbose production and volumetric sorbose productivity at this dilution rate were 2.09 g g^–1 h^–1 and 17.69 g l^–1 h^–1. However, on further increasing the dilution rate to 0.3 h^–1, both biomass and sorbose concentrations decreased to 2.93 and 73.20 g l^–1 respectively, mainly due to washout of the reactor contents. However, the specific rate of sorbose formation and volumetric sorbose productivity at this dilution rate increased to 7.49 g g^–1 h^–1 and 21.96 g l^–1 h^–1 respectively. Continuous fermentation with 100% cell recycle served to further enhance the concentration of biomass and sorbose to 28.27 and 184.32 g l^–1 respectively (in the reactor at a dilution rate of 0.05 h^–1). Even though, there was a decline in the biomass and sorbose concentrations to 6.8 and 83.40 g l^–1 at a dilution rate of 0.3 h^–1, the specific rates of sorbose formation and volumetric sorbose productivity increased to 3.67 g g^–1h^–1 and 25.02 g l^–1 h^–1.     

Multilayer adaptive control of continuous bioprocesses using optimising control technique. Case study: Bakers' yeast culture

High costs associated with many fermentation processes in an increasingly competitive industry make any prompt application of modern control techniques to industrial bioprocesses very desirable. However, this is often hampered by the lack of adequate mathematical models, on the one hand, and by the absence of continuous, on-line measurement of the most relevant process variables, on the other hand. This paper addresses these problems and offers a new strategy to control continuous bioprocesses using a hierarchical structure such that neither structured process models nor continuous measurement of all relevant variables have to be available. The control system consists of two layers. The lower layer represents a dynamic adaptive follow-up control of a continuously measured output — in our case dissolved oxygen concentration. This variable is supposed to be strongly correlated with the key output variable — in our case cellular concentration which is not continuously available for measurement. The higher layer is then designed to maintain a desired profile of the process key output using a set-point optimising control technique. The Integrated System Optimisation and Parameter Estimation method used operates on an appropriately chosen steady-state performance criterion. A prerequisite for successful application of the proposed approach is an approximate steady-state model, describing the relationship between the measured output and the process key output variable. Furthermore, occasional in situ, off-line or laboratory measurement values of the key output variable are needed. Promising simulation results of the biomass concentration control, by manipulating the air flow-rate in the continuous bakers' yeast culture are presented.     

Maximizing biomass productivity and cell density of Chlorella vulgaris by using light-emitting diode-based photobioreactor

Green microalgae have recently drawn attention as promising organisms for biofuel production; however, the question is whether they can grow sufficient biomass relative to limiting input factors to be economically feasible. We have explored this question by determining how much biomass the green microalga Chlorella vulgaris can produce in photobioreactors based on highly efficient light-emitting diodes (LEDs). First, growth results were improved under the less expensive light of 660nm LEDs, developing them in the laboratory to meet the performance levels of the traditional but more expensive 680nm LEDs by adaptive laboratory evolution (ALE). We then optimized several other key parameters, including input superficial gas velocity, CO(2) concentration, light distribution, and growth media in reference to nutrient stoichiometry. Biomass density thereby rose to approximately 20g dry-cell-weight (gDCW) per liter (L). Since the light supply was recognized as a limiting factor, illumination was augmented by optimization at systematic level, providing for a biomass productivity of up to 2.11gDCW/L/day, with a light yield of 0.81 gDCW/Einstein. These figures, which represent the best results ever reported, point to new dimensions in the photoautotrophic performance of microalgal cultures.     

Multilevel control of multistage continuous culture using a microprocessor

This paper describes the implementation of multilevel techniques using a microprocessor to control multistage continuous culture systems. A system which produces gramicidin S is taken as an example. The single level technique using the conjugate gradient method is applied to solve the two-stage and the three-stage continuous culture and is compared with the multilevel one. The results show that the application of multilevel techniques is more advantageous and suitable for this system than any other method which has been utilized so far. The advantages of using a microprocessor will be stated.     

Maximizing productivity of CHO cell-based fed-batch culture using chemically defined media conditions and typical manufacturing equipment

A highly productive chemically defined fed-batch process was developed to maximize titer and volumetric productivity for Chinese hamster ovary cell-based recombinant protein manufacturing. Two cell lines producing a recombinant antibody (cell line A) and an Fc-fusion protein (cell line B) were used for development. Both processes achieved product titers of 10 g/L on day 18 under chemically defined conditions. For cell line B, the use of plant derived hydrolysates combined with the optimized chemically defined medium increased the titer to 13 g/L. Volumetric productivities were increased from a base line of about 200 mg/L/d to about 500 mg/L/d under chemically defined conditions and as high as 700 mg/L/d with cell line B using plant derived hydrolysates. Peak cell densities reached greater than 20E6 vc/mL, and cell viabilities were maintained above 80% on day 18 without the use of antiapoptotic genes or temperature shift. A rapid compound screening method was developed to effectively test positive factors within 72 h. Peak volumetric oxygen uptake rates (OUR) more than tripled from the baseline condition. Oxygen demand continued to increase after maximum cell density was reached with a maximal OUR of 3.7 mmol/L/h. The new process format was scaled up and verified at 100 L pilot scale using reactor equipment of similar configuration as used at manufacturing scale.     

Maximizing recovery of native protein from aggregates by optimizing pressure treatment

Recovering native protein from aggregates is a common obstacle in the production of recombinant proteins. Recent reports have shown that hydrostatic pressure is an attractive alternative to traditional denature-and-dilute techniques, both in terms of yield and process simplicity. To determine the effect of process variables, we subjected tailspike aggregates to a variety of pressure-treatment conditions. Maximum native tailspike yields were obtained with only short pressure incubations (<5 min) at 240 MPa. However, some tailspike aggregates were resistant to pressure, despite multiple cycles of pressure. Extending the postpressure incubation time to 4 days improved the yield of native protein from aggregates from 19.4 +/- 0.9 to 47.4 +/- 19.6 microg/mL (approximately 78% yield of native trimer from nonaggregate material). The nearly exclusive conversion of monomer to trimer over the time scale of days, when combined with previous kinetic data, allows for the identification of three postpressure kinetic phases: a rapid phase consisting of structured dimer conversion to trimer (30 min), an intermediate phase consisting of monomer conversion to aggregate (100 min), and a slow phase consisting of conversion of monomer to trimer (days). Optimizing the production of structured dimer can yield the highest level of folded protein. Typical refolding additives, such as glycerol, or low-temperature incubation did not improve yields.     

Maximizing productivity of chromatography steps for purification of monoclonal antibodies

The large scale production of monoclonal antibodies presents a challenge to design efficient and cost effective downstream purification processes. We explored a two stage resin screening approach to identify the best candidates to be utilized for the platform purification of monoclonal antibodies. The study focused on commercially available affinity resins including Protein A, mimetic and mixed-mode interaction resins as well as ion exchangers used in polishing steps. An initial screening using pure proteins was followed by a final screening where selected resins were utilized for the purification of MAbs in complex mixtures. Initial screenings aimed to measure the theoretical upper limit for dynamic binding capacity (DBC) at 1% breakthrough and productivity. We confirmed that DBC of affinity, mimetic and mixed-mode resins was a strong function of the linear velocity used for loading. Productivities >27 g/(L-h), were obtained for rProtein A FF, Mabselect and Prosep rA Ultra at 2 min residence time. For the cation exchangers, we identified UNOsphere S and Fractogel SO(3) as the best candidates for our purification based on DBC. For anion exchangers operated in flowthrough mode, Q Sepharose XL and UNOsphere Q were selected from the initial screening based on DBC and resolution of IgG from BSA. Finally, a three step purification scheme was implemented using the selected affinity and ion exchangers for the purification of IgG from complex feedstocks. We found that Mabselect followed by UNOsphere Q and UNOsphere S provided the best purification scheme for our applications based on productivity.     

Effects of air pressure oscillation amplitude on oxygen transfer rate and biomass productivity in a solid-state fermenter

The modified sulfite oxidation method was adapted for estimation of the overall oxygen transfer rate in a pressure oscillating, solid-state fermenter. At 4.5 atm and 30 °C, the oxygen transfer rate reached 717 mmol kg^–1 initial dry matter h^–1 in this system against 37 mmol kg^–1 initial dry matter h^–1 in a static tray fermenter. At 30 °C and 3 atm, Azotobacter vinelandii grew on wheat straw and reached 4.7×10¹⁰ c.f.u. g^–1 substrate dry matter after 36 h, while only 8.2×10⁹ c.f.u. g^–1 substrate dry matter was obtained in a static tray system.     

Analysis of the hollow-fibre fermenter using ultrafiltration

Summary A mathematical model for the hollowfibre fermenter using ultrafiltration (Park and Kim 1985b) was developed to investigate the performance of the fermenter. The model describes the behavior of the reactor well, using three parameters: the Stanton number, the Damköhler number, and the ratio of ultrafiltration rate to outlet tube-side flow rate. The experimental result was compared with the model after adjustment of parameters.     

Neural adaptive control of nonlinear multivariable systems with application to a class of inverted pendulums

In this paper multilayer neural networks (MNNs) are used to control the balancing of a class of inverted pendulums. Unlike normal inverted pendulums, the pendulum discussed here has two degrees of rotational freedom and the base-point moves randomly in three-dimensional space. The goal is to apply control torques to keep the pendulum in a prescribed position in spite of the random movement at the base-point. Since the inclusion of the base-point motion leads to a non-autonomous dynamic system with time-varying parametric excitation, the design of the control system is a challenging task. A feedback control algorithm is proposed that utilizes a set of neural networks to compensate for the effect of the system's nonlinearities. The weight parameters of neural networks updated on-line, according to a learning algorithm that guarantees the Lyapunov stability of the control system. Furthermore, since the base-point movement is considered unmeasurable, a neural inverse model is employed to estimate it from only measured state variables. The estimate is then utilized within the main control algorithm to produce compensating control signals. The examination of the proposed control system, through simulations, demonstrates the promise of the methodology and exhibits positive aspects, which cannot be achieved by the previously developed techniques on the same problem. These aspects include fast, yet well-maintained damped responses with reasonable control torques and no requirement for knowledge of the model or the model parameters. The work presented here can benefit practical problems such as the study of stable locomotion of human upper body and bipedal robots.     

High productivity ethanol fermentations with Zymomonas mobilis using continuous cell recycle

Summary Cell recycle studies have been carried out with a strain of Zymomonas mobilis selected for its improved ethanol tolerance and faster rates of glucose uptake and ethanol production. As part of the investigation a capilliary cross-flow microfiltration unit with polyamide membranes has been evaluated in view of its potential advantages (low cost and ability to withstand repeated cleaning with caustic soda). The results demonstrate that ethanol concentrations of 60–65g/l can be sustained at productivities ranging from 120–200g/l/h.