Fuzzy Supervisory Control System for a Fed-batch ...

Proceedings of the 13th IFAC Symposium on Information Control Problems in Manufacturing Moscow, Russia, June 3-5, 2009

Fuzzy Supervisory Control System for a Fed-batch Baker's Yeast Fermentation Process George H. Riad*. Ahmed H. Yousef**. Mohammed A. Sheirah*** *Computers and Systems Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt (e-mail: [email protected]). ** Computers and Systems Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt (e-mail: [email protected]) *** Computers and Systems Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt (e-mail: [email protected])} Abstract: In this paper, a study is given on how fuzzy logic can be used as a Supervisory Controller, to improve industrial control. The application of fuzzy logic in control is illustrated by a case study, in which a Fuzzy Supervisory Control System (FSCS) is added to a fed-batch baker’s yeast fermentation process, previously controlled by a conventional PID controller. The biomass concentration (Cx) was used as the controller input and flow rate of glucose (substrate) solution (F) was controlled to maximize conversion of glucose to biomass. The objective was to preserve the final biomass concentration, as nearly as possible to its ideal final value, even if the process input is subjected to changes, taking into consideration the Respiratory Quotient (RQ). The new proposed control scheme was found to be stable throughout the production period. Keywords: Engineering Applications of Artificial Intelligence, Real-time Artificial Intelligence, Fuzzy Logic, Supervisory Control, Fed-batch, Baker’s Yeast, Fermentation. highly nonlinear, as mentioned by Verbruggen and Bruijn (1997).

1. INTRODUCTION Complex processes involve many process variables, and operators faced with the tasks of monitoring, control, and diagnosis of these processes often find it difficult to effectively monitor the process data, analyze current states, detect and diagnose process anomalies, and/or take appropriate actions to control the processes, as stated in the work of Uraikul, et al. (2007). The same authors found that fuzzy logic, as a mechanism for representing uncertain knowledge, has been widely adopted in many engineering applications in recent years. It provides a mechanism for approximation using graded statements instead of ones that are strictly Boolean. Verbruggen and Bruijn (1997) declared that the main reason to introduce fuzzy logic is to mimic the control actions of the human operators in the fuzzy controller. In this case, a prior knowledge is used and the final controller performs as well as the best operators. Ketata, et al. (1995) stated that if the process model is known, fuzzy techniques can be used to improve the closed-loop performances for linear or nonlinear plants. If the process model is unknown, fuzzy techniques are useful for modelling human operator knowledge. Fuzzy control in this sense fits well when the system to be controlled is only partly known, is difficult to be described by a white box model, has few available measurements, or is

978-3-902661-43-2/09/$20.00 © 2009 IFAC

Uraikul, et al. (2007) said that fuzzy logic supports representation of variables and relationships in linguistic terms. A linguistic variable is a variable with linguistic meaning which takes fuzzy values and is often based on a quantitative variable in the process. Fuzzy logic systems handle the imprecision of input and output variables directly by defining them with fuzzy memberships and sets that can be expressed in linguistic terms. Van der Wal (1995) stated that fuzzy logic is nowadays applied in virtually all sectors of industry and science in the western world, especially in the field of control. There are three main reasons for the present popularity and application of fuzzy logic in industry. First of all, fuzzy logic can be combined with existing methods. Second, process control often deals with uncertainties, due to change in parameters and/or difficult measurements. Classically, these uncertainties are to be handled by human operators. Finally, fuzzy logic is suitable for rapid prototyping, yielding a shorter time-tomarket. During manual operation, a human operator is normally responsible for assigning set points to regulatory controllers, performing discrete control actions, process monitoring and taking corrective measures when an abnormal situation is detected. These activities are collectively called ‘supervision’ or ‘supervisory control’. This view has been supported in the work of Muthuswamy and Srinivasan (2003).

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10.3182/20090603-3-RU-2001.0085

13th IFAC INCOM (INCOM'09) Moscow, Russia, June 3-5, 2009

In an earlier research, we applied a control system to the fermentation process, to control the substrate feeding; to make the process reaches the ideal final biomass concentration, even if the system was exposed to huge changes in its ideal initial biomass concentration. This paper is organized as follows: section 2 introduces a general description of the supervisory control system. Section 3 presents the case study, which is the fermentation process. Section 4 introduces the conventional vs. the new proposed solutions. Section 5 discusses the results got from the experiments. 2. SUPERVISORY CONTROL SYSTEM Jantzen (1998) defined the Supervisory Control System as a system that evaluates whether local controllers satisfy prescribed performance criteria, diagnoses causes for deviation from the performance criteria, plans actions, and executes the planned actions. Typical goals for Supervisory Control System are safe operation, highest product quality, and most economic operation. During plant running, the operator performs actions based on his knowledge of the components and how they interact. The operator actions can be categorized as follows: a.

Binary Actions: change in the structure of the plant and switching to other plant configurations. Examples are on/off valves.

b.

Prepare Actions: prepare the whole plant, or part of the plant, for closed loop control, with set points selected by the operators. An example is to start a pump in order to obtain a minimum flow rate of steam before switching to automatic control.

c.

Control Actions: closed loop control around proper set points. An example is control of steam flow rate by automatically adjusting pump speed.

d.

Corrective Actions: take actions when malfunction occurs. An example is servo valve that does not function because it sticks.

Jantzen (1998) also found that a high level controller (like Supervisory Controller) works on the same level as the human operator. It takes over a part of, or the operator’s entire job of controlling the process. A Fuzzy Supervisory Control System (FSCS) is integrated with other controllers in various schemes, as seen in Fig. 1. In Fig. 1, PID is an example of a conventional control scheme, while Fuzzy refers to high level control strategy, or Supervisory Control System. Often, the conventional loops represent an existing control scheme, which has been controlling the process before installation of the Supervisory Control System. In Fig. 1(a), the operator may select between the Supervisory Control System and the conventional control loops. The operator has to decide which of the two alternatives is the most likely to produce the best control performance. In Fig. 1(b), the original Supervisory Control idea is presented, in which the manual control carried out by a human operator is replaced by automatic control. Again, it is

up to the operator to decide whether manual or automatic control will result in the best possible operation of the process. In Fig. 1(c), the Supervisory Control is used for the adjustments of the parameters of the conventional control loops. A common problem with PID controllers is that the set of controller parameters produces satisfactory performance only when the process is within a small operation window. Outside this window, other parameters or set points are necessary, and these adjustments may be done by the Supervisory Control. In Fig. 1(d), conventional PID controllers are capable of controlling the process when the operation is steady and close to normal conditions. However, if sudden changes occur, or if the process enters abnormal situations, then this configuration may be useful to bring the process back to normal operation as fast as possible. This configuration is used here in this research.

Figure 1. Fuzzy Supervisory Control System (FSCS) configurations 3. CASE STUDY: FERMENTATION Muthuswamy and Srinivasan (2003) mentioned that fermentation requires a high level of operator involvement, like other batch and fed-batch processes. In addition to runto-run variability, this could lead to abnormal situations, in which any deviation from desired operating regimes could result in product quality variations. This provides a strong motivation for automating batch operation supervision. The most important performance index involved in the yeast production is the final biomass concentration. It is a must to make the process reaches the highest possible biomass concentration at the end of the fermentation process. The Respiratory Quotient (RQ) was taken into consideration in this research. 3.1 Fermentation Model The fermentation model, the model state variables and the model equations are given by Pertev, et al. (1997) and were studied in details in our earlier research (2009). 3.2 Control of Biomass Concentration Fig. 2 shows how the initial biomass concentration can affect the final result.

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3.3 Problem Statement The ideal initial condition for the biomass concentration is 0.54 C-mol/L (1 C-mol of biomass = 24.2 g). One of the main goals of the fermentation process is to maximize this concentration as much as possible. The ideal final biomass concentration with this ideal initial biomass concentration was 2.4147 C-mol/L. Reed (1981) defined the Respiratory Quotient (RQ) as the ratio between the moles of carbon evolved per moles of oxygen consumed. It has been a general method used to determine indirectly the lack of substrate in the growth medium. The RQ is often analyzed to study the carbon flux, that is, the feed should be conditioned in such a way that it should prevent excess of carbon dioxide evolution caused by unnecessarily severe substrate limitation. The objective is thus to control RQ as near to 1 as possible. If RQ is not about 1, ethanol is formed from the fermentable sugar and the yeast becomes alcoholic.

Figure 3. Structure of the model for the experiments

2.5

2

1.5

However, this final concentration is very much degraded whenever the initial biomass concentration decreases, for example 0.5 C-mol/L or 0.4 C-mol/L. Fig. 3 shows how the model was structured for the experiments. Fig. 4 and Fig. 5 show the degradation of the final biomass concentration and the RQ respectively, when the initial biomass concentration was changed from the ideal value (0.54 C-mol/L) to a lower value (0.3 C-mol/L).

Ideal Cx Cx when Cx(0) = 0.3 and w/o any control

Cx

If the initial biomass concentration is higher than the ideal, for example 0.6 C-mol/L or 0.7 C-mol/L, there will be no problem because the final biomass concentration in this case will be higher than the ideal.

1

0.5

0

0

5

10

15

Time

Figure 4. Difference between the ideal Cx and Cx when the initial biomass conc. was not ideal (0.3 C-mol/L not 0.54 Cmol/L)

It is clear that the final ideal concentration reduced from 2.4147 C-mol/L to 2.2317 C-mol/L. Although it appears that the degradation is about 7.5%, this has a very huge effect economically, knowing that the fermentor volume is 100,000 liters (100 m3). The loss in the final product due to the bad initial concentration is about 443 kg, which affects the production economically. So, the conclusion is to minimize the difference between ‘Cx_Ideal’ and ‘Cx_Mod’, while preserving the RQ as nearly as possible to 1.

1.28

1.26

1.24

1.22

RQ

1.2 Ideal RQ RQ when Cx(0) = 0.3 and w/o any control

1.18

1.16

1.14

1.12

1.1

1.08

0

5

10

15

Time

Figure 2. Effect of the initial biomass concentration on the final result

Figure 5. Difference between the ideal RQ and the RQ when the initial biomass conc. was not ideal (0.3 C-mol/L not 0.54 C-mol/L) 4. CONVENTIONAL VS. FSCS SOLUTIONS Two solutions were presented to solve the problem of the different initial biomass concentration. They were

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implemented based on the Model Reference Adaptive Control methodology. 4.1 Conventional Solution A conventional PI controller was implemented to solve this problem. Fig. 6 depicts how the system was structured for the experiments. The values of P and I were chosen optimally for each initial biomass concentration. They were auto tuned such that the final biomass concentration is equal to or greater than the ideal final biomass concentration, whatever the Cx profile is all over the simulation period. 4.2 FSCS Solution A Fuzzy Supervisory Control System (FSCS) was implemented over the conventional PI controller to solve this problem. Fig. 7 depicts how the system was structured for the experiments. The values of P and I are the same values reached through the auto tune in the previous experiments. The fuzzy logic controller consists of three rules as follows:

Figure 7. Structure of the FSCS solution

Low

Medium

High

1

IF (error) is low, THEN (Added Feed) is low. Degree of membership

0.8

IF (error) is medium, THEN (Added Feed) is medium. IF (error) is high, THEN (Added Feed) is high. Fig. 8 shows the input “error” membership, while Fig. 9 shows the output “added feed” membership functions, when the initial biomass concentration was 0.3 C-mol/L. It is seen from these three fuzzy rules that the output is directly proportional with the error. It is logical that if the error is high, the compensation in the substrate feed must be also high to compensate this large error, and vice versa. The error represents the difference between the model output of the ideal initial conditions and that of the different initial conditions.

0.6

0.4

0.2

0 -0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Error

Figure 8. Input “Error” membership function

Low

Medium

High

1

Degree of membership

0.8

0.6

0.4

0.2

0 -280

-260

-240

-220

-200

-180

-160

-140

-120

-100

-80

-60

Added Feed

Figure 6. Structure of the conventional solution implemented as a PI controller

Figure 9. Output “added substrate feed” membership function

5. RESULTS AND DISCUSSIONS First the simulation was run when the initial biomass concentration decreased from 0.54 C-mol/L to 0.3 C-mol/L.

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The results are shown in Fig. 10, Fig. 11 and Fig. 12. It is shown that the conventional PI controller increased the final biomass concentration from 2.2317 C-mol/L to 2.4161 Cmol/L. Adding the FSCS increased the final biomass concentration to 2.3128 C-mol/L.

Closed Loop Model with Fuzzy Supervsiory Control System over a conventional PI Controller 2.5

2

The great effect was depicted in the RQ parameter. The conventional PI controller worsened the RQ profile to the degree that the Integrated Square Error (ISE) between the ideal RQ and the resulted RQ from the PI controller was nearly infinity, because the run-time values were floating from -2000 to +3000. Adding the FSCS improved the RQ profile so much as seen in Fig. 11. To ensure the solution generality, the simulation was repeated several times at different initial biomass concentrations. The results of the experiments are shown in Table 1. Table 1 shows the numerical values of the experiments results, in each trace of simulation, with various biomass concentrations. Each trace was simulated once without any control, once with the conventional PI controller and finally with the FSCS.

Cx

1.5

1

0.5 Ideal Cx Cx when Cx(0) = 0.3 and w/o any control Cx when Cx(0) = 0.3 with conventional PI controller Cx when Cx(0) = 0.3 with FSCS 0

5

10

15

Time

Figure 10. Difference between the various biomass conc. profiles when the initial biomass conc. was not ideal (0.3 Cmol/L)

Inspecting the results in Table 1, it can be seen that the conventional PI controller increased the final biomass concentration to the ideal one. In the same time, the RQ profile was very much negatively affected by this kind of control.

Closed Loop Model with Fuzzy Supervsiory Control System over a conventional PI Controller 1.4

1.35

1.3

Adding the FSCS, the final biomass concentration increased than the one without control but still below the one with the conventional PI controller. Noting the RQ parameter, it can be seen that the FSCS enhanced the RQ profile, compared with the one with the conventional PI controller. Note also that the FSCS decreased the glucose substrate feed rate in some cases, so that it can solve the problem. The most interesting matter is that moving the output “added substrate feed” membership function range positively to the right enhances the final biomass concentration at the expense of the RQ profile, and moving the range negatively to the left enhances the RQ profile at the expense of the final biomass concentration. It is left to the operator to decide which profile the fed-batch baker’s yeast fermentation process goes.

0

1.25

RQ

Ideal RQ RQ when Cx(0) = 0.3 and w/o any control RQ when Cx(0) = 0.3 with FSCS 1.2

1.15

1.1

1.05

0

5

10

15

Time

Figure 11. Difference between the various RQ profiles when the initial biomass conc. was not ideal (0.3 C-mol/L) 4 Closed x 10Loop Model with Fuzzy Supervsiory Control System over a conventional PI Controller

0.5

0

RQ

-0.5

-1

-1.5

-2 Ideal RQ RQ when Cx(0) = 0.3 with conventional PI controller -2.5

0

5

10

15

Time

Figure 12. Difference between the ideal RQ and the RQ profiles under the conventional PI controller when the initial biomass conc. was not ideal (0.3 C-mol/L)

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Table 1A. Results of the Experiments (without any control) Without Control Initial Biomass Conc.

Final Cx

0.5

2.3934

0

0.4

2.3303

0.0803

0.3

2.2317

2.3025

ISE of RQ

Table 1B. Results of the Experiments (with PI controller) With PI controller Initial Biomass Conc.

Final Cx

0.5 0.4 0.3

ISE of RQ

Optimal P

Optimal I

2.4154

0

600

120

2.4177

0.505

650

130

2.4161

Infinity

700

140

of industrial yeast fermenters, Computers & Chemical Engineering, Volume 21, Supplement 1, pp.S739-S744. Reed G., 1981, Industrial Microbiology. 4th ed. London, UK: Chapman & Hall. Riad, G.H., Yousef, A.H. & Sheirah, M.A., 2009, Supervisory Control System for a Fermentation Plant, unpublished. Uraikul, V., Christine, W.C. & Tontiwachwuthikul, P., March 2007, Artificial intelligence for monitoring and supervisory control of process systems, Engineering Applications of Artificial Intelligence, Volume 20, Issue 2, pp.115-131. Van der Wal, A.J., 25 August 1995, Application of Fuzzy Logic Control in Industry, Fuzzy Sets and Systems, Volume 74, Issue 1, pp.33-41. Verbruggen, H.B. & Bruijn, P.M., 1 September 1997, Fuzzy control and conventional control: What is (and can be) the real contribution of Fuzzy Systems?, Fuzzy Sets and Systems, Volume 90, Issue 2, pp.151-160.

Table 1C. Results of the Experiments (with FSCS) With FSCS Output “added feed” membership function range

Initial Biomass Conc.

Final Cx

ISE of RQ

Input “error” membership function range

0.5

2.4589

0

-0.005 to 0.045

0 to 135

0.4

2.3619

0.435

-0.02 to 0.16

-180 to 40

0.3

2.3128

4.2708

-0.05 to 0.3

-280 to -60

6. CONCLUSIONS Although the fermentation process is very sensitive to the initial biomass concentration, this work ensures that the use of Fuzzy Supervisory Control System (FSCS) solved the problem. This FSCS adjusts the glucose (substrate) feeding rate – by increasing or decreasing it – when a change is detected in the output of the process. It shows superior results on the conventional PI controller. REFERENCES Jantzen, J., 1998, Fuzzy Supervisory Control, technical report no 98-H-875 (proc), Denmark: Technical University of Denmark. Ketata, R., De Geest, D. & Titli, A., 14 April 1995, Fuzzy controller: design, evaluation, parallel and hierarchial combination with a PID controller, Fuzzy Sets and Systems, Volume 71, Issue 1, pp.113-129. Muthuswamy, K. & Srinivasan, R., August 2003, Phasebased supervisory control for fermentation process development, Journal of Process Control, Volume 13, Issue 5, pp.367-382. Pertev, C., Turker, M. & Berber, R., 20 May 1997, Dynamic modeling, sensitivity analysis and parameter estimation

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