Simulation of Feedforward-Feedback Control of Dissolved Oxygen (DO) of Microbial Repeated Fed-batch Culture

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1 Simulation of Feedforward-Feedback Control of Dissolved Oxygen (DO) of Microbial Repeated Fed-batch Culture ing Gao 1,, Huibin in 2 1 Shandong Provincial Key ab for Distributed Computer Software Novel Technology School of Information Science and Engineering Shandong Normal University Jinan, China 2 Shandong Academy of Chinese Medicine Jinan, China Abstract Fed-batch culture is often used in industry, and dissolved oxygen (DO) concentration control is important in fermentation process control. DO control is often applied by using feedback (FB) control strategy. But, feedforward-feedback (FF- FB) control has the advantage in dealing with the time-varying characteristics resulting from cell growth during the fermentation process. Mathematical modeling and computer simulation is a useful tool in the analysis of the control system. In this paper, we model and simulate the FF-FB DO control and FB substrate control of repeated fed-batch culture process. The results show the feasibility of the control strategy and are useful for control system development and process analyses and optimization. Keywords - Batch culture; dissolved oxygen (DO) ; feedforward-feedback control; modeling and simulation; bioreactor I. INTRODUCTION Bioproducts, like antibiotics, amino acids, ethanol, organic acids et al., are produced by microbial fermentation processes. In order to produce the bioproducts more efficiently, fed-batch and high cell density culture is often applied [1-3]. Dissolved oxygen (DO) concentration control is important for aerobic fermentation process control, especially for high cell density culture [1-4]. During the aerobic fermentation process, the optimal DO concentration needs to be maintained in order to obtain high productivity, bioproduct concentration and substrate conversion yield. As the oxygen solubility in water is very low and the microbial respiration rate is quite high especially at high cell density, DO control becomes a hard task for fermentation process control. DO is normally controlled by the agitation speed, aeration rate and oxygen content. It can be controlled in a manual mode by maintaining the manipulated variables constant, or controlled automatically. Feedback (FB) control is often used for automatic DO control [2]. But, feedback control works only when the error occurs, which control strategy has the room to be further improved. In order to decrease the control error and increase the control performance, feedforward-feedback (FF-FB) control is a good choice [5-7]. In the FF-FB control system, the timevarying characteristics resulted from the cell growth will be considered and handled by the FF contribution, and FB control is used to compensate the control error. By using this strategy, a robust and quick response control system is expected. In this research, modeling and simulation of FF- FB control of repeated fed-batch culture will be made, and mathematical modeling of the time-varying characteristics of DO utilization will be applied in the DO FF control. II. RESUTS A. The Structure of the Control System The schematic diagram of the control system is shown in Fig. 1. The block diagram of the FF-FB DO control system is shown in Fig. 2A. In this system, the oxygen consumption of the microbial cells is considered the disturbance to the control system and is estimated by using the mathematical model and compensated by the FF control action. In order to confirm the robustness of the control system, possible inaccuracy of the mathematical model and randomized noise are considered and tested in the later simulations. As the cell growth curve may vary from batch to batch, the model predicted cell growth curve and the real cell growth curve of a certain cultivation round can t be identical. A 20% error and 5% noises are used in the model predictions, and tested by simulation. In order to compare the DO FF-FB control system, simulations with only the DO FB control is also made. The substrate concentration is feedback controlled by repeated pulse fed of certain amount of the concentrated feeding solution to make the substrate concentration reach 30 g/ when the substrate concentration in the bioreactor is lower than the set-point of 5 g/. The block diagram is shown in Fig. 2B. Repeated pulse fed is simpler and safer (less chance of contamination) than continuous feeding. DOI /IJSSST.a ISSN: x online, print

2 Figure 2. The block diagram of the control system. Figure 1. The schematic diagram of the bioreactor control system. T, transmitter; C, controller; M, motor; F, feeding rate; N, agitation speed; G, aeration rate. B. The Mathematical Model for the FF-FB Control The FF DO control actions of agitation speed and aeration rate for compensation of the time-varying disturbance on DO consumption resulted from the growing cells utilization are predicted by the mathematical model developed in the following. The specific cell growth rate is modeled using double substrate Monod equation (Eq. (1)). The specific glucose consumption rate modeled by Eq. (2) includes two parts, one for the net cell growth, the other for the maintenance. The specific oxygen consumption rate is 6 times of mole ratios of the glucose consumption rate modeled by Eq. (3). The oxygen uptake rate (OUR) is the product of the specific oxygen consumption rate and the cell concentration modeled by Eq. (4). The oxygen transfer rate (OTR) is proportional to the product of the volume oxygen transfer coefficient of ka and the driving force for oxygen transfer, C= (C - C), modeled by Eq. (5). The mass balance equations are modeled by Eqs. (6) (9). ka is related with the agitation speed (N) and aeration rate (G) as described by Eq. (10). (A) DO FF-FB control, (B) substrate FB control GC.N, GC.G, GP, Gd, Gf, GC are the transfer functions of agitation control, gas rate control, process dynamics, disturbance, feedback signal, and substrate feeding control, respectively. m S C (1) k S k C m O2 qs ms YG (2) M O2 qo q 6 2 S M Gluc (3) OUR q X (4) O 2 OTR k a C C (5) where, C, and C are the DO and the saturated DO concentrations, respectively; X, and S are the cell and glucose concentrations, respectively; and m are the specific growth rate and its maximum value, respectively; km, and ko2 are the substrate and oxygen affinity constants, respectively; YG is the net cell growth yield; ms is the substrate maintenance coefficient; qs, and qo2 are the specific consumption rates of substrate and O2, respectively;, are the constants for uedeking-piret equation; OUR and OTR are oxygen uptake rate and oxygen transfer rate, respectively; ka is the volume oxygen transfer coefficient; MO2 and MGluc are the molecular weights of O2 and of glucose, respectively. The mass balance equations for the repeated fed-batch culture are described by Eqs. (6) (9). dx F X X dt V (6) ds F qs X SF S dt V (7) DOI /IJSSST.a ISSN: x online, print

3 dc F OTR OUR C dt V dv F dt where, SF is the substrate concentration in the concentrated feeding solution; V is the liquid volume; F is the feeding rate, the manipulated variable for substrate FB control in a repeated pulse fed mode. The substrate feeding solution is concentrated so that the volume change resulted from the substrate feeding can be neglected in Eqs. (6) (8). For FF control of DO, in order to compensate the DO disturbance resulted from the cell growth, OTR should be equal to OUR according to Eq. (8) after the dilution effect of the feeding being neglected, to ensure C unchanged (dc/dt = 0) and remained at the set-point. As the oxygen transfer driving force, C = (C - C), is relatively constant as discussed in the discussion section, ka should meets Eq. (10) to compensate the time-varying DO utilization by the cell respiration according to Eqs. (5), (8), and dc/dt = 0. OUR ka (10) C C The value of ka is controlled by agitation speed (N) and aeration rate (G) descried by Eq. (11) ka kn G (11) Between the two manipulated variables, N is more effective than G in controlling ka [2]. Therefore, 70% of the control effort is assigned to N and 30% is assigned to G by using Eqs. (12) and (13), respectively, which are drawn from Eqs. (10) and (11). OUR 1 N FFt 70% (12) 0.5 C C kg t1 2 OUR 1 GFF t 30% (13) 3 C C k N t1 Where, the subscripts t and t-1 are the current and last time points, respectively. So, N and G control actions should be finished in several control rounds. Eqs. (12) and (13) are used in the FF control. As model predictions may not be very accurate, FB control is used to eliminate the control error and ensure the control accuracy. In the case of FB control, the error between DO setpoint and process variable is calculated by Eq. (14). ec C. sp (14) Where, C.sp is DO set-point. The proportional and integration (PI) control strategy is used for FB control by using Eqs. (15) (16) for N and G control, respectively. Similarly, 70% of the control action is assigned to NFB and 30% is assigned to GFB. 1 3 (8) (9) 70% N FBt kpn e kin e (15) GFB t kp G eki G e30% (16) Then, the total DO control action N and G are as follows: Nt N0 NFF t NFB t (17) Gt G0 GFF t GFBt (18) where, N0 and G0 are the initial values of N and G, respectively. The self-programmed software using Visual Basic (Microsoft Co., USA) is used in solving the mathematical model and the simulation. The Runge-Kutta method of order four was used in solving the differential equations. C. Simulation of the FF-FB Control The substrate concentration is controlled by pulse feeding of the concentrated feeding solution until the substrate concentration in the bioreactor reaches 30 g/l when its concentration is lower than the set-point. The substrate feeding stops at 85th h. For DO control, FF-FB control is applied using the agitation speed and aeration rate as the manipulated variables as described earlier. In order to compare the control processes with or without DO FF control, the simulation only with FB DO control was made. The simulation results are shown in Fig. 3. The simulation results indicated that FF-FB control of DO was better for cell growth compared with FB control. -D. Simulation of the FF-FB Control with Prediction Errors and Noises In order to confirm the robustness of the control system under model prediction errors and noises, 5% randomized noises and 20% over or under estimate of the cell growth were added in the mathematical model predictions in the FF- FB control. Then, simulations were made with the above noises and prediction errors and the results were compared with the control. The simulation with 5% randomized noises and 20% over estimate of cell growth was made, and the control without the noise and overestimate of cell growth was also made. The results were shown in Fig. 4. The results indicated that the process variables of the above two cases were almost identical except the cell concentration and the OUR. The reason is that FB control finally compensated the control action resulted from the overestimated FF control. The simulation with 5% randomized noises and 20% underestimate of cell growth was also made and similar results were obtained. III. DISCUSSION DO control is one of the major difficulties in fed-batch fermentation process control. As oxygen has low solubility in water while its consumption speed is high, DO control is much challenging. In DO control, OTR should be equal to the time-variant OUR so as to ensure C unchanged and DOI /IJSSST.a ISSN: x online, print

4 remained at the set-point. OTR is proportional to ka and the oxygen transfer driving force, C = (C - C), according to Eq. (5). As C is fixed when air is used for aeration, C is fixed. Then, OTR can only be controlled by ka in such a case. ka is related with agitation speed and the aeration rate, which are the most often used manipulated variables for bioreactor DO control, according to Eq. (11). ka includes two components, k and a, which are the oxygen transfer coefficient and the specific area, respectively. On the gas/liquid surface, a relatively stable liquid membrane is absorbed on the surface of the gas bubbles, which is the major resistance (R=1/k) for oxygen transfer. By increasing the agitation speed, the thickness of the absorbed liquid membrane is decreased leading to the increase of k, in the mean time, the bigger bubbles are split into smaller ones leading to the increase of a. By increasing aeration rate, only a is increased. Of the above two manipulated variables, agitation speed is more effective than aeration rate in controlling DO [2]. Therefore, agitation speed is assigned 70% of the control task while aeration rate the rest 30% control task. In some cases, pure oxygen is used to increase the oxygen content and C in order to increase the oxygen transfer driving force C and OTR [3], but it will increase the production cost, is not the first choice for DO control. In bioreactor DO control, FB control is most often used for its acceptable performance and ease of application. But, FF-FB control can improve the performance of the DO control system which also be confirmed in this simulation studies. In real applications, the time delay may be serious and the advantage of FF-FB control will be more obvious. As the activities of the microbes may vary from batch to batch, it will make the model prediction and FF control inaccurate. Combining FF and FB in the DO control, the error of FF control resulted from the inaccurate model prediction can be compensated by the FB control so that both fast response and good control accuracy can be obtained by using FF-FB control. To measure the cell concentration on-line can avoid the prediction error of the mathematical model [7], but it will make the system sophisticated and increase the cost of hardware. The substrate control is also satisfactory shown by Fig. 3 and 4, on the next page. This research also showed that mathematical modeling and computer simulation is useful in bioprocess analysis and control system design and evaluation [8,9]. IV. CONCUSION For the reason of lack of reliable sensors for bioprocesses, model predictions of bioprocess variables The model predictions with or without 5% randomized noises and 20% over estimate of the cell growth in FF-FB control are often used, which may lead to large errors in the predicted variables. Automatic control based on ill predicted process variables may be fatal in real applications. Combination of FF and FB control is an ideal way to overcome the above problem in using FB control to compensate the control errors of the FF control action. Computer simulation of FF-FB DO control of bioreactor made in this research showed that this control method is ideal and applicable. In addition, mathematical modeling and simulation method is confirmed an efficient and useful way in designing and evaluating the control strategies. ACKNOWEDGMENT This work was partially supported by the National Natural Science Foundation ( , , , , ), the Science and Technology Development Project of Shandong (2015GSF121016, 2014GSF119018, 2013GGX10125), the National Traditional Chinese Medicine Industry Project ( ), the Chinese Medicine Science & technology Development Project (2011Z-003-2), the National Key Technology Research and Development Program (2011BAC02B04), the National Program on Key Basic Research Project (2010CB630902, 2004CB619202), Twelfth Five-Year Plan for Science and Technology Research (2011BAI06B01), the National High Technology Research and Development Program (2007AA05Z455), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No ), the Natural Science Foundation of Shandong (ZR2010FM021), and the Taishan Scholar Project of Shandong, China. REFERENCES [1]. G. Potvin, A. Ahmad, Z. 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Femat, V. Gonz alez-alvarez, A robust feedforward/feedback control for an anaerobic digester, Computers and Chemical Engineering, No. 29, pp , [7]. Q. Guo, G. iu, N. Dong, Q. i, J. in, J. in, Model predictive control of glucose feeding for fed-batch Candida utilis biomass production, Research J. BioTechnol., No. 08, pp. 3-7, [8]. K. Schügerl, Progress in monitoring, modeling and control of bioprocesses during the last 20 years, J. Biotechnol., No. 85, pp , [9]. Y. in, G. iu, H. in,. Gao, J. in, Analysis of batch and repeated fedbatch productions of Candida utilis cell mass using mathematical modeling method, Electronic J. Biotechnol., vol. 16, No.04, pp ,, DOI /IJSSST.a ISSN: x online, print

5 Figure 3. Simulation of the model based FF-FB control compared with FB control. DOI /IJSSST.a ISSN: x online, print

6 Figure 4. Simulation of the model based FF-FB control with prediction error and noise. DOI /IJSSST.a ISSN: x online, print