# An Application of Different Mixing Systems for Batch Cultivation of Saccharomyces cerevisiae. Part II: Multiple Objective Optimization and Model Predictive Control

**ABSTRACT** Multiple objective optimization of the initial conditions, maximal rotation speed and amplitude for a batch Saccharomyces cerevisiae cultivation using impulse and vibromixing systems is developed in this paper. The single objective function corresponds to the process productiveness and the residual glucose concentration. The multiple objective optimization problems are transformed to a single objective function with weight coefficients. A combined algorithm is applied for solving the single optimization. After this optimization the useful process productiveness increases and the residual glucose concentration at the end of the process decreases. The developed optimization and obtained results have shown that the impulse mixing systems have a better productiveness and better glucose assimilation. In addition, this system is easier for realization. The combined algorithm does not have a feedback and it does not guarantee robustness to process disturbances. For that purpose model predictive control for guarantee robustness to process disturbances is developed. The developed control algorithm - combined multiple objective optimization problem and model predictive control ensures maximal production at the end of the process and guarantees a feedback on disturbance as well as robustness to process disturbances.

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**ABSTRACT:**A new method for solving a type of fuzzy optimization problems is proposed. It concerns fuzzy optimization problems with crisp parameters and soft (flexible) constraints and objective(s) under certain additional conditions. For this special case of fuzzy mathematical programming (FMP) the necessary and sufficient conditions for analytical solving the problem are formulated. A comparison between the results derived by this method and by the widely used Zimmermann’s method is presented.Control and cybernetics 01/1995; 24(3). · 0.38 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Decision making where goals or constraints are not sharply defined boundaries and fuzzy using dynamic programmingManagement Science 06/1970; · 2.52 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Model predictive control was emerging into the process industries during the 1980's. Today it is commonplace and, in some sense, mature. Commercial packages are available on a variety of platforms and “do it yourself” implementations are also readily found. This paper takes a look at where this technology has been and where it is, and tries to predict important future developments. Some trends are clear but the range of possibilities is wide. There are many buzzwords that could describe aspects of future model predictive controllers: adaptive, non-linear, embedded, object oriented, open systems and many more. How these might fit into future model predictive controllers is explored in this paper.ISA Transactions 09/1994; 33(3-33):235-243. · 2.26 Impact Factor

Page 1

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

1

An Application of Different Mixing Systems

for Batch Cultivation of Saccharomyces cerevisiae.

Part II: Multiple Objective Optimization

and Model Predictive Control

Mitko Petrov1*, Uldis Viesturs2, Tatiana Ilkova1, Andrejs Bērziņš3,

Juris Vanags2,3, Stoyan Tzonkov1

1Centre of Biomedical Engineering, Bulgarian Academy of Sciences

105 Acad. George Bonchev Str., 1113 Sofia, Bulgaria

E-mail: {mpetrov, tanja, tzonkov}@clbme.bas.bg

2Latvian State Institute of Wood Chemistry

27 Dzerbenes St., LV-1006 Riga, Latvia

E-mail: koks@edi.lv

Website: http://www.lza.lv/scientists/viestursu.htm

3Institute of Microbiology and Biotechnology, University of Latvia

4 Kronvalda Blvd., LV-1586 Riga, Latvia

E-mail: lumbi@lanet.lv

*Corresponding author

Received: November 19, 2009 Accepted: March 12, 2010

Published: April 15, 2010

Abstract: Multiple objective optimization of the initial conditions, maximal rotation speed

and amplitude for a batch Saccharomyces cerevisiae cultivation using impulse and

vibromixing systems is developed in this paper. The single objective function corresponds to

the process productiveness and the residual glucose concentration. The multiple objective

optimization problems are transformed to a single objective function with weight

coefficients. A combined algorithm is applied for solving the single optimization. After this

optimization the useful process productiveness increases and the residual glucose

concentration at the end of the process decreases. The developed optimization and obtained

results have shown that the impulse mixing systems have a better productiveness and better

glucose assimilation. In addition, this system is easier for realization. The combined

algorithm does not have a feedback and it does not guarantee robustness to process

disturbances. For that purpose model predictive control for guarantee robustness to process

disturbances is developed. The developed control algorithm – combined multiple objective

optimization problem and model predictive control ensures maximal production at the end of

the process and guarantees a feedback on disturbance as well as robustness to process

disturbances.

Keywords: Multiple objective optimization, Combined algorithm, Random search with back

steps, Fuzzy sets theory, Model predictive control.

Introduction

Multiple objective optimization is a natural extension of the traditional optimization of a

single objective function. On one hand, if the multiple objective functions are commensurate,

minimizing single objective function, it is possible to minimize all criteria and the problem

can be solved using traditional optimization techniques. On the other hand, if the objective

functions are incommensurate or competing, then the minimization of one objective function

requires a compromise in another objective function. The competition between multiple

Page 2

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

objective functions is a key distinction between the multiple objective optimization and

traditional single objective optimization [10].

Zhou et al. [16] have used of a Pareto optimization technique to locate the optimal conditions

for an integrated bioprocessing sequence and the benefits of first reducing the feasible space

by the development of a series of windows of operation to provide a smaller search area for

the optimization.

Vera et al. [13] have illustrated a general multi objective optimization framework of

biochemical systems and they have applied it optimizing several metabolic responses

involved in the ethanol production process by using Saccharomyces cerevisiae strain. The

general multiple objective indirect optimization method (GMIOM) is based on the use of the

power law formalism to obtain a linear system in logarithmic coordinates. The problem is

addressed with three variants within the GMIOM: the weighted sum approach, the goal

programming and the multi-objective optimization. We have compared the advantages and

drawbacks of each of the GMIOM modes. The results obtained have shown that the

optimization of biochemical systems was possible even if the underlying process model was

not formulated in S-system form and that the systematic nature of the method has facilitated

the understanding of the metabolic design and it could be of significant help in devising

strategies for improvement of biotechnological processes.

Tonnon et al. [12] have used interactive procedure to solve multi objective optimization

problems. A fuzzy set has been used to model the engineer’s judgment on each objective

function. The properties of the obtained compromise solution were investigated along with

the links between the present method and those based on fuzzy logic. An uncertainty, which

has been affecting the parameters, is modelled by means of fuzzy relations or fuzzy numbers,

whose probabilistic meaning is clarified by random set and possibility theory. Constraint

probability bounds that satisfy a solution can be calculated and procedures that consider the

lower bound as a constraint or as an objective criterion are presented. Some theorems make

the computational effort particularly limited on a vast class of practical problems. The

relations with a recent formulation in the context of convex modelling are also pressured.

In the papers [3, 15] a fuzzy procedure is applied to find the optimal feed policy of a fed-batch

fermentation process for fuel ethanol production using a genetically engineered

Saccharomyces yeast 1400 and the fuzzy optimization of a two-stage fermentation process

with cell recycling including an extractor for lactic acid production. By using an assigned

membership function for each of the objectives, the general multiple objective optimization

problem can be converted into a maximizing decision problem. In order to obtain a global

solution, a hybrid search method of differential evolution is introduced.

Model predictive control (MPC) is a general methodology for solving control problems in the

time domain [6]. More than 25 years after MPC appeared a theoretical basis for this technique

has started to emerge in the industry as an effective means to deal with variable constrained

control problems. In fact, that method for optimal control gives the necessary optimal profile,

but it does not give the robustness of the optimization systems. Therefore the MPC can be

used for ensuring maximal quality concentration at the end of the process and it guarantees a

feedback on disturbance and thus – the robustness to process disturbances [7].

In the second part of the work multiple objective optimization problem (MOOP) of a batch

cultivation process using the strain Saccharomyces cerevisiae has been developed. The single

2

Page 3

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

objective functions reflect the process productiveness and residual glucose concentration. A

combined algorithm has been used for the determination of MOOP and MPC has been used

for process control of the different mixing systems.

Materials and methods

The experimental investigations for the different mixing systems were carried out in a

bioreactor with total volume 5 litres and working volume V0 = 3 litres. The impulse mixing

system included a double Rushton turbine with baffles. Maximum rotation speed of the stirrer

is nm = 260 rpm with frequency f1 = 0.5 s-1 and period T = 2 s (Fig. 1a). The vibromixing was

realised by replacing the turbine stirrer with vibrator plate 1 (Fig. 1b), where D is the

bioreactor diameter. The maximum amplitude is Am = 10 mm, frequency f2 = 10 s-1, and

period T = 0.l s [14].

The parameter identification of the batch models of Saccharomyces cerevisiae is examined in

[14], using the different mixing systems. The models were developed based on the functional

state approach [8] and they are shown in Table 1, where X1,2, S1,2 – cell and glucose

concentration for different mixing systems, g·l-1; K1 ÷ K9 and k1 ÷ k10 – the parameters of the

models for different mixing systems; t – time, h.

The process is in Phase I, when S1 ≥ 9.6, in Phase II – when S1 < 9.6 for the impulse mixing

and in Phase I, when S2 ≥ 12.81, in Phase II – when S2 < 12.81 for the vibromixing.

3

n, rpm

0 T 2T 3T 4T t

nm, rpm

z, mm

D

r

Am

1

a) impulse mixing b) vibromixing

Fig. 1 Impulse and vibromixing realised

The maximal values of the rotation speed nm and amplitude Am influence the specific grown

rate by the Monod constants – coefficients

2

K ,

recalculated by the following dependences:

nKK/

2

,

m

nKK/

5

,

m

Akk/

2

, and k

The experimental investigations have shown a decrease of the biomass concentration at the

end of the process. This is because there is an insufficient mass exchange in the so-called

dead zones of the bioreactor [14]. This is reflected in the models (1) – (4) by a coefficient K6.

Now we will specify the coefficient and we will made the model validation at

K6 = 0. The obtained parameter values of the models (1) – (4) are:

''

5

K ,

'

2k , and

'

7k (Table 1). They have been

m

'

2=

'

5=

'

2=

m

Ak/

7

'

7=

.

Page 4

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

K1 = 0.238,

K6 = 0.0, K7 = 0.778, K8 = 4.286 and K9 = 0.106.

These values are not significantly different from the values shown in Table 1. The model at

K6 = 0 showed good statistical indexes. The statistic λ value [14] is λ = 1739 at a theoretical

value

model, and this will not significantly influence the simulation results.

Table 1. Models of the different mixing systems

Mixing systems Phase I

2

111

X

SK dt

+

1

X

SKKdt

+

4

'

2

K = 1158.3, K3 = 0.122, K4 = 0.641,

'

5

K = 621.14,

'

T F = 6.9, i.e. the model is adequate and the coefficient K6 can be removed from the

Phase II

SK

+

1

KK

Impulse mixing

1

2

1

K

'

2

SKdX

=

(1)

1

2

1

'

2

2

11

3

1

SdS

−=

(2)

2

161

1

'

5

1

S

41

XKX

K dt

dS

dX

−=

(3)

1

119

17

8

1

X

SX

S

+

K

dt

−=

(4)

Initial conditions X1(0) = 0.89, S1(0) = 13.80.

Parameters

K1 = 0.254,

K6 = 0.035, K7 = 0.907, K8 = 0.113, K9 = 5.200.

2

212

X

Skdt

+

1

X

SXkkdt

+

9 .1160

'

2=

К, K3 = 0.161, K4 = 0.714,

'

5

638.51

K =

,

Vibromixing

2

2

2

'

2

SkdX

=

(5)

2

225

23

4

2

Sk

dS

−=

(6)

2

2

'

7

2

S

62

X

k

Sk

dt

dX

+

=

(7)

2

2210

2

+

8

9

2

1

k

X

SXk

Sk

dt

dS

−=

(8)

Initial conditions: X2(0) = 1.20, and S2(0) = 15.75.

Parameters

k1 = 0.161,

k6 = 0.367,

76

, k8 = 0.339, k9 = 0.113, k10 = 1.521.

. 132

. 9

'

2=

'

7=

k

k

, k3 = 0.312, k4 = 0.161, k5 = 9.280,

19

Formulation of the multiple objective optimization problem

Selection of the control variables

Control variables were used in the initial condition of the different mixing systems for solving

optimization problems, such as X1(0), X2(0), S1(0), S2(0), two time dependent variables

rotation speed nm(t) for impulse mixing, and maximal amplitude Am(t) for vibromixing.

The control variables intervals for the different mixing systems are:

0.5 ≤ X1,2(0) ≤ 1.5 g·l-1, 12 ≤ S1,2(0) ≤ 17 g·l-1, 100 ≤ nm ≤ 500 rpm, and 5.0 ≤ Am ≤ 15 mm.

The vector of the control variables has the type:

for impulse mixing: u = [X1(0), S1(0), nm(t)]T

for vibromixing:

u = [X2(0), S2(0), Am(t)]T

Page 5

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

Criterion for optimization

The objective of the problem is to find optimal initial conditions of the biomass, glucose

concentration, maximal rotation speed, and amplitude for the different mixing systems in

which the following objective functions have maximum values:

tV))((

max

1

Q

u

5

f

f

t

S

00

XX

−

=

(9)

) 0 (S

)( ) 0 (S

max

u

where Q1, Q2, X0, S0, X(tf), and S(tf) – vectors of the objective functions, initial conditions,

and kinetics variables for the different mixing systems; tf – final time.

The first objective function corresponds to the process productiveness. The second objective

function corresponds to the residual glucose concentration.

The aggregate optimization criterion has an additive type [5]:

maxQQJ

u

where JS – vectors of aggregate criteria; w1, w2 – weight coefficients, w1 = w2 = 0.5.

Combined algorithm for optimization

Random search with back step algorithm

The random search algorithm is well-known from the literature [11]. Its rate of congruence,

which is also valid for other algorithms, depends on the selection of a starting point. For

augmentation of the congruence rate, a preliminary choice of a random set is used in the

following scheme:

A starting point in the admissible space is generated in an accidental method:

(

0,min,max,min,

,1, 2, ...,;

iiiii

iM

ξ

=+−=

uuuu

2

Q

ft

−

=

(10)

2211

ww

S

+=

(11)

)

2

2

4

4

at

at

3

3

m

m

m

M

m

⎧

+

+

≤

>

=⎨

⎩

where

The point with the best result concerning some criterion JS is chosen as a starting point. After

that a random search with back step algorithm is applied.

Fuzzy algorithm

Fuzzy sets theory [2] allows the possibility to develop a “flexible” model that reflects possible

values of the criterion in more details all , as well as the control variables under the developed

model. The model of the batch process (1) - (8) for different mixing systems is considered the

most appropriate but deviations (εi) are admissible with small degree of acceptance. It is

represented by fuzzy set of the following type X and S come into view approximately by the

following relations:

)(IYURAND

i=

ξ

. URAND(IY) is a random generator of random numbers [0 ÷ 1].

Page 6

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

η

where i = 1, 2; εi – deviation from the models.

The prepositional “flexible” model of the process reflects better influence of all values of the

kinetics variables.

A fuzzy criterion from the following type: “JS to be in possibility higher” is formulated and

presented with the subsequent membership function:

1 for

SS

⎧

<

⎪

−

⎪

=≤≤

⎨

−

⎪

⎪

>

⎩

where

min

S

J

and

max

S

J

– minimal and maximal values of criteria.

The fuzzy set of the solution is presented by a membership function of the criterion η0 and

model ηi [1]:

⎫

⎩

==

00

ii

where γ – parameter characterized the compensation degree; θi – the weights of ηi.

The solution was obtained by using the common defuzzification method BADD [4]:

θ

η

===

∑

∑

6

(

1

)

1

2

i

−

+=

i

ε

(12)

min

min

minmax

maxmin

max

0

for

0for

SS

SSS

SS

SS

η

JJ

JJ

JJJ

JJ

JJ

(13)

⎭

⎬⎨

⎧

−−+−=

∏∏

22

D

)1 (1) 1 (

ii

ii

θθ

ηγηγη

(14)

0

1

1

,1, ..., ;1, ...,

i

i

i

j

q

D

m

i

p

i

D

j

iqjq

θ

η

=

=

uu

(15)

where q – number of discrete values of control variables; m – number of control variables.

An effective algorithm for process optimization is synthesized by using the random search

and fuzzy sets [9]. The combined algorithm includes a method of random search for finding

an initial point and a method based on fuzzy sets theory which are combined in order to find

the best solution of the optimization problem.

All programs were written using a FORTRAN 77 programming language version 5.0. All

computations were performed on a Pentium IV 1.8 GHz computer using Windows XP

operating system.

Results after fuzzy optimizations and optimal control

Since the maximal rotation speed nm(t) and amplitude Am(t) are time dependent variables, the

optimal control problem can be considered for an infinite dimensional problem. To solve this

problem efficiently, the two control variables are represented by a finite set of control

parameters in the time interval tj-1 < t < tj as follows nm(t) = nm(j) and Am(t) = Am(j) for

j = 1 ÷ K, where K – number of time partitions.

Page 7

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

The optimization problem (12) - (15) is determined in two stages – a static problem for

determination of the optimal values of the initial conditions X1(0), S1(0), X2(0), S2(0), nm(1),

and Am(1) for different mixing systems is defined on the first stage. A dynamic problem for

determination of the optimal profiles of nm(j) and Am(j), (j > 1) is defined on the second stage.

The obtained results of the control variables, kinetics variables, and criteria before and after

optimization are shown in Table 2.

Table 2. Optimal values of control variable, kinetics variables and criteria

Mixing systems Variables X1(0) S1(0)

Before 0.890 13.800

Impulse mixing

After 1.35913.398

Variables X2(0) S2(0)

Before 1.20015.750

Vibomixing

After 1.21212.918

The optimization results have shown (Table 2) that the biomass concentration increases by

more than 49% in the impulse mixing and only by 1% for the vibromixing. Respectively, the

process productiveness (criterion Q1) increases by more than 48% in the impulse mixing and

only by 1% in the vibromixing. The glucose concentration decreases more than 4 times in the

impulse mixing and more than 19 times in the vibromixing. The residual glucose

concentrations (criterion Q2) are insignificant in the impulse mixing and decrease by more

than 6% in the vibromixing. These results indicate the process impulse mixing productivity is

better than the vibromixing and the residual glucose concentration is better in the

vibromixing.

The optimal initial values of biomass and glucose concentration (Table 2) for the different

mixing systems are distinguished materially for biomass > 12% and glucose > 3.5%. The

optimization problem is now decided in the intervals, determined by the optimal values

(shown in Table 2): 1.212 ≤ X1,2(0) ≤ 1.359 and 12.918 ≤ S1,2(0) ≤ 13.398 with the purpose to

validate the optimal initial values for both mixing systems in order to choose t. The intervals

of change nm and Am are not changed. This will allow a comparative analysis to be made.

The results are presented as follows: X1(0) = 1.334 and S1(0) = 13.122; X2(0) = 1.304 and

S2(0) = 13.049.

The differences between the new optimal values are insignificant (for the initial biomass

concentration it is < 2.5%, for the initial glucose concentration it is < 0.7%). And for general

initial condition X(0) = 1.3 g⋅l-1 and S(0) = 13.0 g⋅l-1 are chosen. With these initial conditions

a fuzzy optimal control is made for determining nm(j) and Am(j) (j > 1). The obtained results

for the kinetics variables and criteria are shown in Table 3.

7

nm(1)

260

332

Am(1)

10.0

10.4

X1(tf)

3.267 0.162 1.426 0.988

4.885 0.038 2.115 0.997

X2(tf) S2(tf)

3.968 0.957 1.661 0.939

4.011 0.049 1.679 0.996

S1(tf) Q1,1

Q2,1

Q1,2

Q2,2

Table 3. Optimal values of kinetics variables and criteria

Variables nm(1) X1(tf)

Before 488 3.899

After 428 4.837

Variables Am(1) X2(tf)

Before 14 4.025

After 13 4.332

Mixing systems

S1(tf)

0.037

0.035

S2(tf)

0.044

0.043

Q1,1

1.56

2.21

Q1,2

1.64

1.82

Q2,1

0.9972

0.9973

Q2,2

0.9966

0.9967

Impulse mixing

Vibromixing

Page 8

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

The optimization results with identical initial conditions (Table 3) have shown that the

biomass concentration increases by more than 24% in the impulse mixing and by more than

7% in the vibromixing. Respectively, the process productiveness (criterion Q1) increases by

more than 38% in the impulse mixing and by more than 12% in the vibromixing. The glucose

concentrations decrease by more than 6% in the impulse mixing, and by more than 4% in the

vibromixing.

The results for the biomass concentrations for different mixing systems before and after

optimization are shown in Fig. 2.

8

012345

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

X 1 - before

X 1 - after

X 2 - before

X 2 - after

Biomass concentration, g.l

- 1

t, h

Fig. 2 Biomass concentration before and after optimization

The optimal profiles of maximal rotation speed and amplitude are shown in Fig. 3.

012345

360

370

380

390

400

410

420

430

440

450

460

470

480

490

Maximal rotation speed, rpm

t, h

012345

12,0

12,5

13,0

13,5

14,0

14,5

Maximal amplitude, mm

t, h

a) impulse mixing b) vibromixing

Fig. 3 Optimal profile of rotation speed and amplitude

The obtained results show the impulse mixing is preferable to vibromixing. Another

advantage is that expensive special equipment is not required. It can be realized easily in each

bioreactor which has control systems equipped with a generator for a saw impulse.

Model predictive control

In order to understand MPC algorithm see Fig. 4. The figure and the notation used in the

description are adapted from [6, 7]. The first part of the MPC algorithm is the specification of

the reference trajectory which may be as simple as a step change to a new set point or as it is

common for batch processes – a trajectory that the system must follow. At the present time k,

the reference trajectory has a value r(k).

Page 9

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

Also at k, consider the predicted process output over a future prediction horizon p. A suitable

controller model of the process is used to obtain the projected behavior of the output over the

prediction horizon by simulating the effects of the past inputs applied to the actual process

(value y ˆ (k) at the current time) [7].

9

-10

0

10 20

3040

0

10

20

30

40

reference trajectory

project output

process output

Measured Profile

Manipulated

variable profile

r (k)

y ˆ(k)

ym (k)

u(k)

u(k+m-1)

k Time k+m-1 k+p

past future

Fig. 4 MPC algorithm scheme

However, due to unmodeled disturbances and modelling errors there might be some

deviations between the actual observed output ym(k) and the predicted output behaviour. Due

to these deviations, the computed future manipulated variable moves are no longer

appropriate and hence only the first of the computed manipulated variable moves ∆u(k) is

implemented on the actual process. The error d(k) = ym(k) – y ˆ (k) is calculated and it is used to

update the future measurements.

The optimization is carried out again based on this new horizon and using the updated system

information and the process continues. Since the horizon recedes at the next time step, this is

also known as a receding horizon control problem. However, in the case of batch systems

where the final time of the process operation is specified the available prediction horizon and

the window of opportunity for control shrink as the batch is close to completion.

Consequently, the value of the prediction horizon in the control algorithm successively

decreases as the end of batch is near [7].

At the next time instant k + 1, the process measurement is taken again and the horizon is

shifted forward by one step. The optimization is carried out again based on this new horizon

and using the updated systems information and the process continues. Since the horizon

recedes at the next time step it is also known as a receding horizon control problem.

The 2nd hour is chosen as a first control point. As it may be noted that there is a diversion

from the reference profile, accordingly the optimal profile is changed. The second point is at

3rd hour. The third point is at 4th hour. The obtained control guarantees the robustness and

stability of the optimization criterion. The optimization criterion is criterion (11). This is

represented in Fig. 5.

Page 10

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

10

Fig. 5 MPC to Saccharomyces cerevisiae cultivation

1,0

500

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

D

F

G

E

C

360

500

370

380

390

400

410

420

430

440

450

460

470

480

490

012345

360

370

380

390

400

410

420

430

440

450

460

470

480

490

X optimized

Trajectory change

MPC after 2nd hour

MPC after 3rd hour

MPC after 4th hour

Maximal rotation speed with optimization Maximal rotation speed with MPC Biomass concentration, g.l-1

Page 11

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

Conclusions

1. The multiple optimization results with identical initial conditions have shown that the

process productiveness increases by more than 38% for the impulse mixing and by

more than 12% for the vibromixing. The glucose concentration decreases by more

than 6% for the impulse mixing, and by more than 4% for the vibromixing. These

results have shown that the impulse mixing is preferable to the vibromixing.

2. The different initial conditions have shown the biomass concentration increases by

more than 49% for the impulse mixing, and only by 1% for the vibromixing.

Respectively, the process productiveness (criterion Q1) increases by more than 48%

in the impulse mixing and only by 1% in the vibromixing. The glucose concentration

decreases by more than four times in the impulse mixing, and more than 19 times in

the vibromixing. The residual glucose concentration change (criterion Q2) is

insignificant in the impulse mixing and increases by more than 6% in the

vibromixing. These results have indicated the process impulse mixing productivity is

better than the vibromixing and residual glucose concentration is better in the

vibromixing.

3. The applied multiple objective optimization of the process has shown а vast increase

of their productivity, respectively decrease in the residual substrate concentration.

This result leads to a higher economical effectiveness for each of them at a smaller

outlay. The proposed combined algorithm for optimization includes a method for

random search of an initial point and a method based on fuzzy sets theory, combined

in order to find the best solution of the optimization problem. The application of the

combined algorithm eliminates the main disadvantage of the used fuzzy optimization

method, namely decreases the number of discrete values of control variables. In this

way, the algorithm allows solution of problems having a larger scale. The developed

combined algorithm can be used for the solution of other optimization problems in

the area of bioprocess systems.

4. Combined algorithm does not have a feedback and it does not guarantee robustness to

process disturbances. MPC is developed to guarantee robustness of the process

disturbances. The method is carried out with the purpose to control disturbance of the

optimal control variables. The developed control algorithm – combined CA and MPC

ensures maximum criterion at the end of the process and guarantees a feedback on

disturbance as well as robustness to process disturbances.

Acknowledgements

This work was supported by the EU FP7 Project (WOOD-NET). TP 10: Development of

Process Control Systems.

References

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Continuous Bioreactors: Dissection of Cybernetic Models, Chemical Engineering

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Academic Publishing House, Sofia.

9. Petrov M., T. Ilkova (2009). A Combined Algorithm for Multi-objective Fuzzy

Optimization of Whey Fermentation, Chem. Biochem. Eng. Q., 23(2), 153-160.

10. Sendín O., J. Vera, T. Nestor (2006). Model Based Optimization of Biochemical Systems

using Multiple Objectives: A Comparison of Several Solution Strategies, Mathematical

and Computer Modelling of Dynamical Systems, 12(5), 469-487.

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(2009). Application of Different Mixing Systems for the Batch Cultivation of the

Saccharomyces cerevisiae. Part I: Experimental Investigations and Modelling,

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Chemistry Research, 37, 3434-3443.

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INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

13

Assoc. Prof. Mitko Petrov, Ph.D.

E-mail: mpetrov@clbme.bas.bg

Mitko Petrov (born 1959) was graduated from the Technical University –

Sofia in 1987 as a mechanical engineer. He has worked as a Research

Associate at the Centre of Biomedical Engineering – Bulgarian Academy

of Sciences since 1988. He achieved his Ph.D. degree in 2004. He has

been an Associate Professor since 2007. His scientific interests are in the

fields of modelling and optimization of apparatus of bioprocess systems

and modelling of ecological systems. He has about 120 scientific

publications with more than 20 known citations.

Prof. Uldis Viesturs, Dr. habil. Sc.

E-mail: koks@edi.lv, http://www.lza.lv/scientists/viestursu.htm

Expertise: Chemical engineering and bioengineering; bioreactor design,

process control, designing and start-up of basic equipment for classical

biotechnology, food technology. Full Member, Latvian Academy of

Sciences, Latvian Academy of Agriculture and Forestry Science;

Member, Academia Scientarum et Artium Europaea, Latvian Council of

Science Expert Committee (Molecular Biology, Microbiology, Virology,

Biotechnology 1996). More

biotechnological industry, 35 years in research and students’ training.

Supervision of 16 Ph.D. students. Courses: University of Latvia, Latvian

University of Agriculture: Biotechnology, Bioengineering, Food

biotechnology.

Assoc. Prof. Tatiana Ilkova, Ph.D.

E-mail: tanja@clbme.bas.bg

Tatiana Ilkova was born in 1970. She received the M. Sc. Degree in

Engineering of Biotechnology (1995) and Ph.D. Degree (2008) from the

Technical University – Sofia. At present she is Associate Professor at the

Centre of Biomedical Engineering – Bulgarian Academy of Sciences.

Her scientific interests are in the fields of bioprocess systems, modelling

and optimization of bioprocesses and modelling of ecological systems.

She has about 120 scientific publications with more than 20 known

citations.

than 15 years’ experience in

Page 14

INT. J. BIOAUTOMATION, 2010, 14(1), 1-14

14

Res. Andrejs Bērziņš, M.Sc. Eng.

E-mail: lumbi@lanet.lv

Andrejs Berzins (born 1954) graduated the Riga Polytechnical Institute

in 1977 as a chemist engineer-technologist and Latvia University of

Agriculture in 2001 as M.Sc. Eng. He had worked at the Institute of

Microbiology, LAS as a engineer and researcher (1977-1993), and at the

Institute of Microbiology and Biotechnology as an research assistant and

researcher (1993-). His scientific interests are bioreactor design and

influence of fermentation conditions on microorganisms. He has about

70 scientific publications.

Res. Assoc. Juris Vanags, Dr. Sc. Eng.

E-mail: btc@edi.lv

Juris Vanags (born 1954) was graduated from the University of Latvia in

1983 as a physical engineer. He had worked at the Institute of

Microbiology, LAS as a researcher (1984-1990), and at the Latvian State

Institute of Wood Chemistry (Laboratory of Bioengineering) as a

researcher (1990-). Since 1996 he has worked also as Chairman of Board

at JSC, Biotehniskais Centrs. He received his Dr. Sc. Eng. degree in 1993.

His scientific interests are process automation, bioreactor design and

bioprocess control. He has about 60 scientific publications and 2 patents.

Prof. Stoyan Tzonkov, D.Sc., Ph.D.

E-mail: tzonkov@clbme.bas.bg

Prof. Stoyan Tzonkov was graduated from the Technical University –

Sofia in 1966. Since 1984 he is a Doctor of Technical Sciences and from

1987 – Professor. Since 1994 he has been the Head of Department of

Modelling and Optimization of Bioprocess Systems, Centre of

Biomedical Engineering – BAS. He has more than 300 publications,

among those 30 books, book chapters and textbooks with more than 258

known citations. Scientific interests: modelling and optimization, control

systems, complex control systems, variable structure systems, bioprocess

engineering.

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