Self-Tuning GMV Control of Glucose Concentration in Fed-Batch ...

Appl Biochem Biotechnol (2014) 172:3761–3775 DOI 10.1007/s12010-014-0794-5

Self-Tuning GMV Control of Glucose Concentration in Fed-Batch Baker’s Yeast Production Zeynep Yilmazer Hitit & Havva Boyacioglu & Baran Ozyurt & Suna Ertunc & Hale Hapoglu & Bulent Akay

Received: 1 November 2013 / Accepted: 10 February 2014 / Published online: 26 February 2014 # Springer Science+Business Media New York 2014

Abstract A detailed system identification procedure and self-tuning generalized minimum variance (STGMV) control of glucose concentration during the aerobic fed-batch yeast growth were realized. In order to determine the best values of the forgetting factor (λ), initial value of the covariance matrix (α), and order of the Auto-Regressive Moving Average with eXogenous (ARMAX) model (na, nb), transient response data obtained from the real process wereutilized. Glucose flow rate was adjusted according to the STGMV control algorithm coded in Visual Basic in an online computer connected to the system. Conventional PID algorithm was also implemented for the control of the glucose concentration in aerobic fed-batch yeast cultivation. Controller performances were examined by evaluating the integrals of squared errors (ISEs) at constant and random set point profiles. Also, batch cultivation was performed, and microorganism concentration at the end of the batch run was compared with the fed-batch cultivation case. From the system identification step, the best parameter estimation was accomplished with the values λ=0.9, α=1,000 and na =3, nb =2. Theoretical control studies show that the STGMV control system was successful at both constant and random glucose concentration set profiles. In addition, random effects given to the set point, STGMV control algorithm were performed successfully in experimental study.

Z. Y. Hitit (*) : H. Boyacioglu : B. Ozyurt : S. Ertunc : H. Hapoglu : B. Akay Faculty of Engineering, Department of Chemical Engineering, Ankara University, Tandogan, 06100 Ankara, Turkey e-mail: [email protected] H. Boyacioglu e-mail: [email protected] B. Ozyurt e-mail: [email protected] S. Ertunc e-mail: [email protected] H. Hapoglu e-mail: [email protected] B. Akay e-mail: [email protected]

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Keywords Self-tuning generalized minimum variance control (STGMV) . Bioreactor . Saccharomyces cerevisiae . Baker’s yeast . System identification . Glucose concentration control

Introduction Fed-batch operations are used in a wide range of industrial fermentation processes [1–3]. In this type of operation, substrate feed rate is varied during the process, and the final product is removed at the end of the process. By regulating the substrate feed rate in a predetermined manner or by using feedback control, the main cost in the process is decreased and the productivity is increased. Therefore, the overflow metabolism and/or accumulation of toxic substrates is avoided. In all cases, the main problem is to find the optimal feeding profile in order to produce the desired product [4]. In the literature, lots of feeding strategies for different types of fermentation processes have been developed. Glucose feed rate was adjusted to follow the increasing amount of yeast [5]. Henes and Sonnleitner (2007) presented a feed strategy based on a simple exponential function for Saccharomycescerevisiae, Escherichia coli and Pichia pastoris in a fed-batch fermenter [6]. Klockow C. et al. (2008) developed a model-based substrate control system for S. cerevisiae fed-batch cultivations to maintain the concentration of substrate glucose at a fixed selected set point [7]. Yüzgeç U. et al. (2009) developed a novel search technique based on genetic algorithm (GA) to find the optimum feed flow rate profile during the industrial-scale baker’s yeast fermentation [8]. S.cerevisiae microorganisms known as baker’s yeasts are used in various applications such as production of ethanol, β-glucan and invertase enzyme. From the point of process economy requirements, a high volumetric efficiency of cells should be obtained in the growth phase of microorganisms. Microorganisms used as biocatalysts are affected by lots of parameters like pH, temperature, dissolved oxygen concentration, airflow rate, agitation speed, substrate concentration etc. They contain the highest enzyme activity at the selected operating condition. These bioreactor operating parameters must be selected carefully and controlled at the optimum values. The composition of growth medium and the substrate concentration have considerably high effect on the microorganism growth. High substrate concentrations may cause inhibition on microorganism production. Ethanol production also occurs in the same condition because of the oxygen deficiency. This situation is also known as ‘Crabtree effect’ [9], which is undesired because of the yeast production aim. Substrate levels which prevent production of yeast mainly depend on the cell and substrate types. Glucose concentration over 200 g/L inhibits the microorganism growth in yeast production. For this reason, control of glucose concentration in fed-batch yeast production is essential. Glucose concentration control is a difficult task, especially in fed-batch fermentation because of time-varying conditions, variable time delays and difficulties encountered in glucose concentration measurement. Also, operating temperature, media composition, agitation speed, cell growth and aeration rate are the other important operational difficulties of the glucose concentration control in an aerobic fermentation process [10, 11]. Some applications of glucose control in fermentation processes are presented in literature. There are two ways to control glucose concentration in fed-batch fermentation. The first one is to choose glucose flow rate as the manipulated variable and glucose concentration as the controlled variable [7]. The second way is to choose glucose flow rate as the manipulated variable as in the first one and controlled

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variable as glucose concentration depending on respiratory quotient (RQ) [12] which is defined as the moles of CO2 produced per mole of O2 consumed. Different types of optimal and adaptive control strategies are applied to control the substrate concentration in fed-batch fermentation [13–17]. In the present work, after the system identification step, the glucose concentration level was controlled at different set profiles by applying both theoretical and experimental self-tuning generalized minimum variance (STGMV) control algorithm with time-delay compensation. Glucose flow rate is chosen as the manipulated variable. Self-tuning techniques were used to improve the control performance and to increase the product yield by using different set profiles. As a means of comparing the models and the performance of the controller, the integrals of squared errors (ISEs) were used.

Theory of GMV Production and safety are one of the most important operation goals in chemical processes. Another goal is to make the operation more economical. Operating conditions of the system are changed both automatically and manually in order to make the profit maximum. Control systems are based on the cost function which is similar to the economic goal. Minimum variance (MV) technique was presented by Aström and Wittenmark in 1973 to minimize the cost function shown below [18]. h i ð1Þ Jðu; tÞ ¼ E ðyt þ k−rt þ k Þ2 Output variable, set point and manipulated variables are represented by y, r and u respectively. Cost function is minimized by choosing u value at time t. There are some difficulties faced in the applications of an MV technique. These are the following:

& & &

Lack of online tuning parameters Weakness on control of non-minimum phase systems Poor control on changing or unknown time-delayed systems.

Clarke and Gawthrop modified the MV technique in 1972 in order to overcome these difficulties [10]. The cost function of this technique is shown below. h i ð2Þ Jðu; tÞ ¼ E ðyt þ k−rt þ k Þ2 þ λu2t This expression is also modified in order to reach zero steady state under non-zero set point; this is shown below. h i ð3Þ Jðu; t Þ ¼ E ðyt þ k−rt þ k Þ2 þ λðΔutÞ2 GMV technique which uses this cost function depends on staying close to the goal by carrying out a minimum output change in order to take λ value as little as possible to maintain closed-loop stability. In general, this cost function can be expressed as follows:   ð4Þ Jðu; t Þ ¼ E ϕ2 ðt þ k Þ In order to obtain the φ(t+k) pseudo-system output as shown in Fig. 1, a system output expression y(t+k) should be defined. This requires the system model, which is defined in the

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next section. The expression for φ(t+k) is effectively the addition of two independent terms. The first term can be defined as.
1 b t þ kjt ¼ ½ðBE þ QCÞuðtÞ þ GyðtÞ−CRrðtÞ þ Ed Š φ C

ð5Þ

and represents the best forecast of φ(t+k) established on data up to time t. The second term is. Eeðt þ k Þ ¼ φ ðt þ k Þ−b φ t þ kjt




ð6Þ

which is the output prediction error originating from the noise sources e(t+1), e(t+2) and e(t+ k). These latter sources cannot be removed by the control signal u(t). GMV approach uses a pseudo-system output to minimize the cost function above, and this is expressed in the equation below.
b t þ kjt ¼ 0 φ

ð7Þ

This minimization gives the control law: ðBE þ QC ÞuðtÞ þ GyðtÞ−HrðtÞ þ Ed ¼ 0

uðtÞ ¼

HrðtÞ−Gy−Ed ðBE þ QCÞ

ð8Þ

ð9Þ

The controller contains a feed-forward term (Q). This GMV algorithm is implicit, i.e. the evaluated parameters are employed precisely in the control law computation. However, due to the implicit character of this algorithm, it can be shown that the controller design parameters cannot be varied online without degrading the parameter estimates [10]. Recursive least square (RLS) method is used for the evaluation of the parameters.

Fig. 1 Pseudo system output

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System Model In practice, generation of proper process models is difficult. Mostly, a system model that includes all the parameter effects on the system is too complicated to handle for control purpose. A simple system model is defined as a linear input-output model [19]. yðt Þ þ a1 yðt−1Þ þ … þ ana yðt−na Þ ¼ b0 uðt−k Þ þ b1 uðt−k−1Þ þ … þ bnb uðt−k−nb Þ

ð10Þ

This model is described as a discrete transfer function. yð t Þ ¼

B uðt−k Þ A

ð11Þ

Here, B and A polynomials are system’s poles and zeros respectively. If a pole of the process is outside of the unit circle, the system is unstable, or a zero of the process is outside the unit circle, then the system has a non-minimum phase property. The system model equation given above does not contain load effect in system output y(t), but the random disturbances that affect the system should also take place. Accordingly, the Auto-Regressive Moving Average with eXogenous (ARMAX) model that includes the random load expression is given below. yðtÞ ¼

B C uðt−k Þ þ eðtÞ A A

ð12Þ

Material and Methods Culture and Media The yeast S. cerevisiae NRRL-Y-567 obtained from the Northern Regional Research Centre, ARS Culture Collection (Peoria, IL, USA), was used. Growth medium

Fig. 2 Experimental system

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Fig. 3 Process response to the positive step input given to glucose flow rate from 4.4 to 84 mL/min

consists of 2 % glucose, 0.6 % yeast extract, 0.3 % K2HPO4, 0.335 % (NH4)2SO4, 0.376 % NaH2PO4, 0.052 % MgSO4 · 7H2O, and 0.0017 % CaCl2 · 4H2O. Stock cultures were maintained on agar slants containing 2 % agar in addition to the same growth medium. The media were sterilized by autoclaving; salt and glucose solutions were autoclaved separately to prevent caramelization and mixed after cooling. Inoculation ratio of 1:10 was used for scale enlargement. The cell growth was determined turbid metrically at 580 nm with a Shimadzu (Tokyo, Japan) model UV-160A spectrophotometer. Experimental System All the experiments were operated with a fed-batch laboratory scale bioreactor which has a volume of 5 L using a heating jacket for the production of baker’s yeast production. Experimental system was shown in Fig. 2. The bioreactor was equipped with an oxygen sensor (WTW, Microprocessor Oximeter, Oxi96), a pH sensor (WTW, pH340i), an ethanol sensor (Cetotech Biotechnologie Gmbh, Alcocontrol), a glucose sensor (The Electron Machine Corporation, SSP/E-Scan), a thermocouple (J-type, Elimko Ltd.), a sparger and a four-bladed turbine type impeller, heating water pump, a circulator, air supply, an I/P transducer, a V/I converter, gas flow metre, microbiological filters, data acquisition system (PCM 9901, Commat Instrument Company) and an online computer control system. The optimum temperature, pH values, agitation speed, airflow rate of growth medium and bioreactor operating conditions were found at 32 °C 5, 600 rpm, and 2.6 L/min respectively. In order to obtain high cell efficiency, these values should be maintained.

Table 1 Choice of forgetting factor and order of system for initial value of covariance matrix

Forgetting factor, λ

Order of system

Condition 1

0.9

na =2

nb =2

Condition 2

1

na =3

nb =2

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Table 2 Choice of initial value of covariance matrix and order of system for forgetting factor

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Initial value of covariance matrix, α Order of system Condition 3

1,000

na =2

nb =2

Condition 4

1,000

na =3

nb =2

Batch Experiments To produce S. cerevisiae yeast in a batch process, a 5-L bioreactor is sterilized and filled with 20-g/L growth medium for batch case. In order to maintain the operating temperature at 32 °C, heating water was passed through the jacket of the bioreactor. The pH value of growth medium was adjusted to 5 with 0.1 M NaOH, and all the sensors listed above were installed. Glucose concentration was measured with glucose sensor, and analogue signals collected from this sensor were converted to digital signals and delivered to the computer simultaneously. A circulator was used to pump 20 °C cooling water throughout the system in order to achieve the sensitive operating condition of glucose sensor. For a 1:10 scale enlargement, 330-mL liquid growth medium with microorganisms was inoculated to the 3,000-mL growth medium, which filled the bioreactor. VISIDAQ computer program was used to observe the changes. Samples were taken with time intervals of 30 min, and the concentration of microorganisms was determined with UV160A. Fed-Batch Experiments To control glucose concentration in a fed-batch bioreactor, a 5-L bioreactor is sterilized and filled with 4-g/L growth medium for batch phase. A 100-g/L concentration of glucose solution (CS) was prepared for fed-batch phase and pumped through the system by a peristaltic pump which is connected to the computer via process control modules. Process parameters are adjusted to the optimum values, which are given in “System Identification”.

0,04355 0,04350 0,04345 0,04340 0,04335 0,04330

ISE

NORM

0,04360

0,0160 0,0158 0,0156 0,0154 0,0152 0,0150 0,0148 0,0146 0,0144 0,0142 0,0140

-0,6674 ISE NORM M

-0,6675 -0,6676 -0,6677 -0,6678 -0,6679 -0,6680

400

500

600

700

800

900

1000

-0,6681 1100

Initial value of covariance matrix

Fig. 4 Performance comparison of initial value of covariance matrix (na =2, nb =2, λ=1)

M

0,04365

0,01015

-0,66935

0,01010

-0,66940

0,01005

-0,66945

0,01000

-0,66950

0,00995

-0,66955

ISE NORM M

0,00990

-0,66960

0,00985 400

500

M

0,050 0,045 0,040 0,035 0,030 0,025 0,020 0,015 0,010 0,005 0,000

ISE

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NORM

3768

600

700

800

900

1000

-0,66965 1100

Initial value of coveriance matrix

Fig. 5 Performance comparison of initial value of covariance matrix (na =2, nb =2, λ=0.9) heat given the immersed heater is the manipulated variable

Results and Discussion System Identification During the microorganism growth in a fed-batch bioreactor at optimum operating conditions, a positive step change was applied to glucose concentration from 4.4 to 84 mL/min. As a result, the glucose concentration increased from 1.7 to 2.5 g/L. This process response was shown in Fig. 3. Experimental data obtained were used for system model identification. Determination of Initial Values of Covariance Matrix and Forgetting Factor Using the experimental data, model parameters were estimated at conditions given in Tables 1 and 2 by means of an RLS algorithm. Parametric model estimation results for different α (covariance matrix) and λ (forgetting factor) values are shown in Figs. 4, 5, 6, 7, 8 and 9. By considering minimum ISE, mean of ISE (M) and norm values, optimal parameters were determined as α = 1,000 and λ = 0.9.

0,0155

-0,6049

0,0150

0,05775

0,05765 0,05760

ISE

NORM

0,05780

0,05770

ISE NORM M

-0,6050 -0,6051

0,0145

-0,6052

0,0140

-0,6053 -0,6054

0,0135

-0,6055

0,05755 0,05750

0,0130 400

500

600

700

800

900

1000

-0,6056 1100

Initial value of covariance matrix

Fig. 6 Performance comparison of initial value of covariance matrix (na =3, nb =2, λ=1)

M

0,05785

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0,0088

0,059

-0,6066 ISE NORM M

0,0087

0,058

-0,6067 -0,6068

0,0085

-0,6069

0,055

0,0084

-0,6070

0,054

0,0083

M

0,0086

0,057

ISE

NORM

3769

0,056

400

500

600

700

800

900

1000

-0,6071 1100

Initial value of covariance matrix

Fig. 7 Performance comparison of initial value of covariance matrix (na =3, nb =2, λ=0.9)

Determination of Parametric Model Order Various orders of parametric model were investigated on the basis of ISE and the mean value of mean of ISE (M) and norm criteria. In this way, the polynomials' order in the ARMAX model was determined as na =3 and nb =2 by taking the minimum criteria values into consideration. Time variations of the glucose concentration and its estimated values determined by using the model with optimal parameters were given in Fig. 10. By using the RLS Method which was coded in MATLAB, ARMAX model parameters were obtained from process transient response, which is glucose concentration profile subjected to step changes in glucose flow rate. The system model parameters can be written as a1 =−1.6871, a2 =0.9175, a3 =−0.2226, b0 =0.0001 and b1 =0.0002. Identified model parameters were used in both theoretical and experimental STGMV control studies as initial values. Control Results

0,015 0,0434

0,014 0,013

0,0432 0,0431 0,0430

ISE

NORM

0,0433

ISE M NORM

0,012 0,011

0,0429 0,0428 0,0427

0,010 0,009 0,88

0,90

0,92

0,94

0,96

0,98

1,00

-0,6678 -0,6680 -0,6682 -0,6684 -0,6686 -0,6688 -0,6690 -0,6692 -0,6694 -0,6696 -0,6698 1,02

Forgetting factor

Fig. 8 Performance comparison of forgetting factor (condition 3, na =2, nb =2, α=1,000)

M

Conventional PID and STGMV algorithms were used to maintain the glucose concentration at different set profiles in order to increase the product yield. As means of comparing ARMAX models with different parameter values and polynomial orders and the performance of the controller, the ISE criteria values were computed from the closed-loop process output.

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0,0574 0,0573 0,0572

ISE

NORM

0,0575

-0,6054 -0,6056

ISE M NORM

-0,6058 -0,6060 -0,6062

0,011

-0,6064 -0,6066

0,010

0,0571 0,0570 0,0569

-0,6068

0,009 0,008 0,88

M

0,0576

-0,6070 -0,6072 0,90

0,92

0,94

0,96

0,98

1,00

1,02

Forgetting factor

Fig. 9 Performance comparison of forgetting factor (condition 4, na =3, nb =2, α=1,000)

Theoretical Control Results In this work, PID and STGMV control algorithms were tested in order to obtain the most efficient performance for substrate concentration control. A system model with constant model parameters determined by the RLS algorithm described above was used to perform theoretical PID control. Theoretical studies were used as a base for the experimental work. Although the system identification was achieved, it is not possible to prepare two experimental set-ups under exactly the same conditions, and thus, an RLS algorithm is needed to be applied to the control algorithm to obtain the best model that defines the process. Constant and random set trajectories were used to examine the theoretical PID and STGMV controller performances. ISE values were also calculated for performance evaluations. In STGMV control studies, the same set point trajectories were used to observe how much more success is achieved by STGMV control than by PID control. ISE values were also calculated for this algorithm and used for performance comparisons. Results of the theoretical control studies are given in Figs. 11 and 12. ISE values of the controllers are compared in Table 3. As can be seen from Table 3, performance of the STGMV controller is better than that of the PID controller. Experimental Control Results Experimental STGMV control study was carried out by an online computer connected to the system, and control algorithm was coded in Visual Basic. Microorganism growth was performed at the optimal operating conditions which were determined previously. Glucose flow rate which is the most effective on the output variable was selected as the manipulated variable. Control experiments for fed-batch glucose concentration were performed at different set profiles. These were used during the substrate (glucose) concentration control in a bioreactor in which S. cerevisiae NRRL-Y-567 was produced under aerobic conditions. The intention is to keep the concentration of substrate glucose at different set points during the fermentation. This set point profile is also the same as the one used in theoretical studies. STGMV control is one of the adaptive control strategies which have variable control parameters and constant model parameters. In baker’s yeast production,

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physical, chemical and biological properties of growth medium have been changing during the fed-batch fermentation process. Due to this dynamic behaviour, with using initial model values obtained by the system identification, the model and control parameters were calculated in the control algorithm for each sampling time and applied to the experimental system. In this experimental study, model parameters changing according to the dynamic behaviour of the system were used in the control algorithm, and so, on GMV control, structure was made self-tuning. Results of the experimental control study were given in Fig. 13. ISE values for the

2,6

C S, g/L

2,4 2,2 2,0 y ye

1,8 1,6 0

5

10

15

20

25

30

35

40

0

5

10

15

20

25

30

35

40

F S , mL/min

100 80 60 40 20 0

Parameters

2 1 a2

0 a3

-1

a1

-2 0

5

10

15

20

25

30

35

40

45

50

25

30

35

40

45

50

Parameters

1,0 0,5

b1

0,0 b0

-0,5 -1,0 0

5

10

15

20

Time interval Fig. 10 Variations in the glucose concentration of the system output and estimated changes in glucose concentration from the model with optimal parameters estimated by means of RLS algorithm (na =3, nb =2, λ=0.9, P=1,000) in the face of a positive step change given to glucose flow rate

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Fig. 11 Theoretical a PID and b GMV control results which have 0.005 noises for constant set point changes

theoretical and experimental STGMV studies were calculated as 952 and 1,422 respectively. As can be seen from the results, experimental and theoretical STGMV control results are similar. UV spectrophotometer analysis carried out sequentially shows that the microorganism concentration was 4.712 and 6.034 g dry cell/L at the end of 7 h of the batch and fed-batch bioreactor operations respectively. Batch and fed-batch initial and final yeast concentrations

Fig. 12 Theoretical a PID and b GMV control results which have 0.005 noises for random set point changes

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Table 3 Comparison of ISE values obtained by using PID and STGMV controller for different set point profiles

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Type of set point profile

With PID ISE values

With STGMV ISE values

Constant set point

17.5

13.6

Random set point

73.6

44.3

are given in Table 4. Changes in the microorganism concentration with time in the controlled and uncontrolled experiment case are given in Fig. 14.

Conclusion In this work, a step change was given to glucose feed flow rate in order to obtain dynamic data of the glucose concentration in a fed-batch bioreactor for system 15 12 9 6 3 0

CS, g/L

(a) Set point Glucose

0

3000

FS, mL/min

80

6000

9000

12000

Time, s

15000

18000

21000

18000

21000

(b)

60 40 20 0 0

3000

6000

9000

12000

15000

Time, s

Control parameters

0,6

(c) f0

0,3

g1

g0

f2

0,0 f1

h0

-0,3 0

3000

6000

9000

12000

15000

18000

21000

Model parameters

Time, s

1,0

(d)

0,5

b0

b1

0,0

a2

a1

-0,5 -1,0

a3

-1,5 0

3000

6000

9000

12000

15000

18000

21000

Time, s Fig. 13 Experimental GMV control results in fed-batch fermentation for random set point changes a controlled variable (glucose concentration), b manipulated variable (glucose flow rate), c control parameters, and d model parameters

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Table 4 Comparison of initial and final yeast concentration for batch and fed-batch experiments in baker’s yeast fermentation

Initial yeast concentration

Final yeast concentration

Batch

0.517

4.712

Fed-batch

0.263

6.034

identification. Initial values of the covariance matrix, forgetting factor and the order of the model are the most important parameters in system identification studies, and optimum values of these three parameters were found by trial and error method in order to find the best model that represents the system. First, initial value of the covariance matrix provides a faster prediction and was found as 1,000 in this work. Second, forgetting factor is the indicator of the number of past data that is used in prediction calculations, and the lower values of this parameter results in a longer time taking and farther prediction; likewise, the higher values cause a heavy load in calculations and were used as 0.9 in this work. Third, order of the model determines the prediction accuracy by defining the number of parameters in the identifying equation and was chosen as na =3 and nb =2. The model found by the system identification study is used in theoretical PID and STGMV algorithms in order to compare the controller performances. ISE values show that STGMV controller is much more successful than PID controller. Then, another simulation has been done to simulate the planned set point trajectory in the bioreactor. The ISE value of this simulation is 952. After that, a random change in the glucose concentration set point trajectory was carried out in a fed-batch bioreactor by an STGMV algorithm. Concentration of 6.034 g dry cell/L of yeast was produced from an initial concentration of 0.263 g dry cell/L of yeast by this controlled fed-batch experiment in 7 h. In a previous experiment, after the seventh hour of an open-loop batch fermentation, 4.712 g dry cell/L yeast concentration was produced from an initial 0.517 g dry cell/L yeast concentration. The results clearly show that in the controlled case, glucose concentration provides a better yield for yeast production, and in this work, it has improved production yield by 22 %.

Fig. 14 Changes in the microorganism concentration with time in the controlled and uncontrolled experiments

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