Artificial Neural Network Based Modeling and Control of Bioreactor

Transcription

1 Artificial Neural Network Based Modeling and Control of Bioreactor Ballekallu Chinna Eeranna* Subba Rao**,G. Prabhaker Reddy** *Dept.of petroleu Engineering, Lords institute of engineering and Technology **Dept. of Cheical Engineering, University College of Technology, Osania University, Hyderabad, Abstract: In this paper presents about control of Bioreactor useing Artificial Neural Network. bioreactor has becoe an active area of research in recent years. This is partially attributable to the fact that bioreactors can be extreely difficult to control. Their dynaic behavior is invariably non-linear and odel paraeters vary in an unpredictable anner. Accurate process odels are rarely available due to coplexity of the underlying biocheical processes. A feedback controller is needed to account for disturbances and tie-varying behavior. Neural network based odel predictive controller designed for the control of bioreactor. In the first step the neural network odel of bioreactor is obtained by levenburg- arquard training the data for the training the network generated using atheatical odel of bioreactor. Keywords: Neural network odel predictive control, bioreactor,productivity. INTRODUCTION A control syste is defined as a syste in which deliberate guidance or anipulation is used to achieve a prescribed value of a variable. In the last two decades, a new direction to control has gained considerable attention. This new approach to control is called Intelligent control. The ter conventional control refers to theories and ethods that are eployed to control dynaic systes whose behavior is priarily described by differential and difference equations. The ter intelligent control addresses to ore general control probles. It ay refer to systes, which cannot be adequately described by a differential equations fraework. There are three basic approaches to intelligent control knowledge-based experts systes, fuzzy logic and neural networks..fermentation: Most of the processes in the biotechnology industry have tie-varying paraeters and are inherently non-linear. Because of that, the ipleentation of the classical odeling and control techniques is very difficult. Moreover, it has been recognized for soe tie, that the observed cell population at a certain tie-instant is the cobined effect if various biological processes that had been initiated at different oents in the past. The processes are affected by the instantaneous environental conditions prevailing at each particular past tie. Hence the kinetics of ferentation process should be considered as depending not only on the current Process State, but also on the weighted average of the states at the past oents, i.e., of the culture eory. The ain factors contributing the difficulty in odeling and control of bioreactors are: 1) Their dynaic behavior is inherently non-linear. ) Accurate process odels are not available due to the coplexity of the underlying biocheical process. 3) Model Paraeters vary with in an unpredictable anner. 4) Reliable biosensors to easure intercellular activities are rarely available, aking the Process State very difficult to characterize. 3. CONTINUOUS BIOREACTORS: In ost of the continuous ferentation processes, one of the output variables is chosen as the controlled variable (bioass concentration or product concentration) and its estiated optial open loop profile of a constant set point is tracked. A continuous stirred tank ferenter (CSTF) is an ideal reactor, which is based on the assuption that the reactor contents are well ixed 4. PROBLEMS WITH THE CONVENTIONAL CONTROLLER: The control of non-linear process like ferentation by conventional controller does not give satisfactory results. This is due to the change in process gain and tie constant with operating conditions. In certain processes, ore than one value of a anipulated variable (u) produces the sae value of an output variable. Such situation is called as input ultiplicities. The value of the steady-state gain of the process changes as the anipulated variable changes and after certain value of u the sign of the gain value also changes. The controller tuned at one operating condition ay even destabilize the syste at another operating point. Di Biasio et al., (1994) have reported that the global stability of the reactor depends on the existence and stability of the other steady conditions. The perforance on the closed syste is copared with that of a linear P1 proposed by Henson and Seborg any constraint on the anipulated variable (which is often unavoidable in practice) can result in a total of 5 steady states (three stable 117

2 and two saddle points) even though a sufficient control action is present. 5. CONTROL OF BIOREACTORS USING NEURAL NETWORK: The inherent non-linearity of the ferentation process often renders control difficult. Neural network has becoe popular tool for odeling and control of dynaic process, deonstrating the ability of handling non-linearity. Many neural network controllers are of the rule-based type where the controller s output response is described by a series of control rules. The unique features of this neural network control technique include: A wide operation range for handling a non-linear process. Robustness for dealing with rando disturbance and possible syste paraeter Drafting. Relatively siple ipleentation. In the present work, neural network control is designed and evaluated for the continuous bioreactor with one input and one output to overcoe the control probles associated with linear P1 controller due to the input ultiplicity. 6. MATHEMATICAL MODELLING OF A CONTINUOUS BIOREACTOR A scheatic of a continuous bioreactor is shown in figure 3.1-We assue that the bioreactor has constant volue, its contents are well ixed, and the feed is sterile. The dilution rate D and the feed substrate concentration Sf are available as anipulated inputs. The effluent cell-ass or bioass concentration X, substrate concentration S and product concentration P are the process state variables. In ethanol production, for exaple, X, Y, and P represent yeast, glucose, and ethanol concentrations, respectively. Many odels have been proposed for ferentation processes. Structured odels attept to describe the individual organiss in detail but are usually atheatically too coplex to be useful for controller design. Significantly sipler unstructured odels can be obtained by assuing that the bioreactor culture consists of a single, hoogeneously growing organis. These odels usually consist of a few nonlinear ordinary differential equations and are particularly well suited to the nonlinear control strategies. 6.1 MODEL DERIVATION: The dynaic odel is developed by writing aterial balances on the bioass (cells), the substrate (feed source for cells) and the product. Bioass grows by feeding on the substrate results in generation of product. Bioass Material Balance We write bioass aterial balance as: Rate of accuulation = i/p o/p + generation d(vx)/dt=fxf FX + Vr1 (1) Substrate Material Balance: The substrate aterial balance is written as: d(vs)/dt = F Sf FS Vr () Product Material Balance: Finally, the product aterial balance is written as: D (VP)/dt = F P + Vr3 (3) The reaction rate (ass of the cells generation/volue/tie) is norally written in the following for: r1 = µx (4) As yield Y = r1/r, r = r1/y And hence r = µ X/Y (5) Siilarly r3 = (αµ+β) X (6) Defining F/V as D, the dilution rate, and assuing bioass feed concentration as Zero,Finally, the odel equations can be written as; X = -DX + µx (7) S = D (Sf - S) µx/y (8) P = -DP + (αµ +β ) X (9) This unstructured odel can describe a variety of ferentations. Because Y, and P are assued to be independent of the operating conditions, above odel is called a constant yield odel. The specific growth rate odel is allowed to exhibit both substrate and product 1 P / P inhibition: K S S / K1 (1) This odel contains four odel paraeters: the axiu specific growth rate, the product saturation constant P, the substrate saturation constant K, and the substrate inhibition constant K1. Model equation of the syste on which the study is based: In practice, the odel paraeters in equations (7)-(1) are chosen to fit experiental data (Munack and Thoa, 1986; Enfors et a!., 199). If the bioreactor deviates significantly fro the operating conditions where the data was collected, the odel paraeters previously deterined ay no longer be valid. The cell-ass yield Y and the axiu specific growth rate t tend to be especially sensitive to changes in the operating conditions. Fro a process control X = DX + µx S S = D (S f S) µx/y P = DP+ (αµ+ β) X K 1 P / P S S / S K 1 118

3 perspective, these two odel paraeters can be viewed as uneasured disturbances because they ay exhibit significant tie-varying behavior. Many types of ferentations can be odeled by choosing the odel paraeters appropriately. For instance, the product is totally growth-associated if a α, β =, totally non growth-associated if a =, β, and a cobination of the two if α, β. Siple Monod kinetics (Johnson, 1987) can be obtained by setting P = K1 =α c. In any ferentations such as penicillin production, cell growth is inhibited by high substrate concentrations so that < K1 < cc. If the growth rate approaches zero at high product concentrations then <P < α. Noinal odel paraeters and operating conditions used throughout the study are listed below: Variable Y Α Noinal value.4 g/g. g/g Β. h -1 µ.48 h -1 P 5 g/1 K 1. g/1 K 1 g/1 S f g/1 If the bioass and substrate are of negligible value when copared to that of the product, the productivity Q can be defined as the aount of product cells produced per unit tie: Q = DP (11) 7. DESIGN OF NEURAL NETWORK MODEL PREDICTIVE CONTROLLER OF BIOREACTOR The neural network predictive controller that is ipleented in the neural network toolbox software uses a neural network odel of a nonlinear plant to predict future plant perforance. The controller then calculates the control input that will optiize plant perforance over a specified future tie horizon. Predictive control The odel predictive control ethod is based on the receding horizon technique. The neural network odel predicts the plant response over a specified tie horizon. The predictions are used by a nuerical optiization progra to deterine the control signal that iniizes the following perforance criterion over the specified horizon. (11) Where N1, N, and Nu and define the horizons over which the tracking error and the control increents are evaluated. The u' variable is the tentative control signal, yr is the desired response, and y is the network odel response. The p value deterines the contribution that the su of the squares of the control increents has on the perforance index. The following diagras illustrates the odel predictive control process. The controller consists of the neural network plant odel and the optiization block. The optiization block deterines the values of u' that iniize J, and then the optial u is input to the plant. The controller block is ipleented in Siulink, as described in the following section. 8. SIMULATION RESULTS & DISCUSSIONS The perforance of proposed neural network controller and conventional PI controller to the continuous bioreactor with input ultiplicities in dilution rate is evaluated using the closed loop block diagra as shown fig. this block diagra essentially is prepared in the siulation MATLAB, its associated tool siulink and the NEURAL NETWORK toolbox have been used. The siulation studies for regulatory and servo proble have been presented below. 8.1 LOWER DILUTION RATE (D =.9368HR-1) Servo proble: The servo response has been studied by giving a step change in set point of productivity with direct inverse neural network and PI controller. At lower dilution rate the servo proble has been analyzed by giving step change in set point of productivity fro 3. to 3.1 and the corresponding responses are shown fig.6.model predictive e control shows stable response at about 1hrs. Whereas PI reaches after 1 hrs.its corresponding control action in ters of dilution rate is shown in fig. 7. Fig 8 shows the step change in the set point of productivity fro 3. to.9.in this response the NNMPC reaches the set point at around hrs without any offset whereas PI is reaching the set point at 3 hrs.the corresponding anipulated variable in ters of dilution rate versus tie behavior is shown fig Regulatory proble: The regulatory response in productivity of odel predictive neural network controller and PI controller for dilution rate input of disturbance in feed substrate concentration have been studied and they are stated below: The regulatory response in productivity of odel predictive neural network and conventional PI is shown in fig 1 for a step change in feed substrate concentration fro to 4(+%).This fig shows that the response of the odel 119

4 predictive neural network controller is faster than that of the linear PI. Proposed neural network control has less deviation of 3% whereas conventional PI controller has a larger deviation of about 8%. odel predictive neural network controller has low settling tie than the PI controller. The corresponding control actions for anipulated variable in ters of dilution rate versus tie behavior are shown in fig 11. The regulatory response in productivity of odel predictive neural network and conventional PI is shown in fig 1 for a step change in feed substrate concentration fro to 18(- 1%).This fig shows that the response of the odel predictive neural network controller is faster than that of the linear PI. Proposed neural network control has less deviation of % whereas conventional PI controller has a larger deviation of about 6%. odel predictive neural network controller has low settling tie than the PI controller. The corresponding control actions for anipulated variable in ters of dilution rate versus tie behavior are shown in fig Plant Input tie (s) Plant Output tie (s) Fig. 3. Data generation of the neural network Model Predictive Controller Fig.1. Block diagra of neural network odel predictive controller Input Error tie (s) 3 1 Plant Output NN Output tie (s) Fig.4. Trainig data for neural network predictive controller Fig.Block diagra of the subsyste of Bioreactor Tie, hr Fig 5. Closed loop response of productivity for step change in set point fro 3. to 3.1 (+1%) at lower input 1

5 Tie, hr Fig 6 Control action in Dilution rate Vs tie as shown in fig 5 Tie, hr Fig 9 Productivity Versus tie for change in Sf fro to 18 g/l at lower input Tie, hr Fig 7. Closed loop response of productivity for step change in set point fro 3. to.9 (-1%) at lower input Tie, hr Fig 1 Control action in Dilution rate Vs tie as shown in fig 9 Tie, hr Fig 8 Control action in Dilution rate Vs tie as shown in fig 7 Tie, hr Fig 11 Productivity Versus tie for change in Sf fro to 4 g/l at lower input 11

6 Tie, hr Fig 1 Control action in Dilution rate Vs tie as shown in fig 11 CONCLUSIONS In the present work, the perforance of conventional PI controller and Neural Network based controller is studied for the set point changes at lower input dilution rates. Based on the above studies the following conclusions are ade. At lower input dilution rate, response of PI controller for set point change fro 3 to 3.1 g/l/h is stable with offset and for another set point change of 3 to.9 g/l/h is stable with offset response due to input ultiplicities. Whereas proposed neural network based odel predictive controller is giving stable REFERENCES [1]. Chidabara,M and Reddy, G.P. (1995) Nonlinear control of systes with input ultiplicities, Coputers and Cheical Engineering, 19 pp49-5. []. Abonyi, J,.Babuska, R. and Ayala Botto, M and Szeifert, F L. Nagy and Nagy () Identification and control of nonlinear systes using fuzzy haerstein odels, Industrial & Engineering cheistry Research.39 pp [3]. Dash, S.K. and Koppel, L.B.(1989) Sudden destabilization of controlled cheical Processes Cheical Engineering Counications, 84, pp [4.] Koppel,L.B. (198) Input ultiplicities in nonlinear ultivariable control systes AIChE Journal.8 pp [5.] Koppel, L.B.(1983) Input ultiplicities in process control, Cheical Engineering Education, pp58-63, & [6]. D.B.Anuradha, G.Prabhaker Reddy and, J.S.N.Murthy, Direct Inverse Neural Network Control of A Continuous Stirred Tank Reactor, Proc. IMECS,., Hong Kong,36-41,9. [7] M. A. Henson &.D.E. Seborg, Nonlinear control strategies for continuous ferenter, Cheical engineering Science, 47,81-835,