TWO TIME STEPS PREDICTIVE CONTROL APPLICATION TO A BIOPROCESS SIMULATOR

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1 TWO TIME STEPS PREDICTIVE CONTROL APPLICATION TO A BIOPROCESS SIMULATOR S Altuntaş (a), H Hapoğlu (b) (a) Provincial Directorate of Environment and Urbanization, Samsun, Turkey (b) Department of Chemical Engineering, Ankara University, Ankara, Turkey (a) seminaltuntas@hotmail.com, (b) hapoglu@eng.ankara.edu.tr ABSTRACT The control of batch bioreactors to maintain the ph at a constant set point is quite different from the continuous system applications, because acid and base simultaneous addition has a strong effect on the closed loop performance which may never reach desired value. While it is most desirable to use approximate models based on the chemistry of the system, this may not always be possible for batch bioprocesses. The present paper discusses usage of a simulator with appropriate input and output data obtained from the real batch bioprocess without control. The real process ph behaviour was simulated by using 7M citric acid flowrate changes in the face of constant base addition. Two time steps predictive control was applied to the bioprocess simulator by coordinating 0.5M citric acid and 0.5M sodium bicarbonate flow rates. The best control weighting factor magnitude was determined. The constant set point following was achieved successfully. Keywords: predictive control, bioprocess simulator, ph control, constant desired ph 1. INTRODUCTION The ph control of batch bioprocesses is considered quite difficult. These processes may move from one operating point to another operation point or never reach a predetermined point. The batch system identification and a small amount addition of controller manipulating variables and determination of weighting factor magnitude are the most important and time consuming tasks in the proper implementation of control. Bharathi, Sivakurnar and Shanmugam (2006) applied model based ph control algorithm to highly nonlinear systems such as fed-batch reactors. They noted that proportional integral derivative (PID) controllers are not adequate to obtain efficient ph control of such processes with extra nonlinear features. It is also proved with the simulation results in the same work that model based PI controller gives better performance and robustness. Meenakshipriya, Saravanan, Somasundaram and Kanthabhabha (2011) investigated a ph neutralization system control by using PI and P algorithm based on the coefficient diagram method. Simulation results showed that the performance of these controllers was good when compared to other techniques. Pekel, Zeybek, Hapoglu and Alpbaz (2010) reported successful generalized predictive ph control application to textile wastewater treatment batch process. Camcıoglu, Ozyurt and Hapoglu (2015) applied proportional integral derivative ph control to paper mill wastewater treatment batch process. The coordinated ph control application was achieved properly by using acid and base flow rates as manipulated variables. For the food quality, the output variable measurements are compared to the desired values which can be converted into instrumental process set points. Paraskevopoulou, Athanasiadis, Blekas, Koutinas, Kanellaki and Kiosseoglov (2003) investigated the stability of kefir type drink production by adding kefir granules into cheese whey mixture containing fructose, black raisin extract and milk. A continuous low alcohol drink production by using whey mixture with kefir yeast was proposed by Kourkoutas, Psarianos, Koutinas, Kanellaki, Banat and Marchant (2002). The self-tuning proportional integral and derivative ph control and generalized predictive ph control algorithm were theoretically applied to discrete-time modelling of the cheese whey drink production respectively (Altuntaş, Ertunç, Hapoglu and Alpbaz 2011; Altuntaş, Ertunç, Hapoglu and Alpbaz 2012). In this work, the appropriate citric acid flow rate changes introduced into the simulator from out of the system stands for the dynamic ph behaviour of the cheese whey batch kefir-type drink production in the face of constant 0.5M sodium bicarbonate addition. Two time steps predictive control was applied to the bioprocess simulator to hold the mixture ph value at a constant desired value. The ph value and the coordinated acid and base flow rates were chosen as the controlled and the manipulating variables respectively. One of the manipulating variables was kept at a small constant value, while the other was changed versus time by using control algorithm. The best control tuning parameter values were chosen according to performance criteria. 162

2 2. TWO TIME STEPS PREDICTIVE CONTROL Two time steps predictive control is designed on the basis of generalized predictive control (Clarke, Mohtadi and Tuffs 1987) as below: J(u, t) = E{(y t+2 r t+2 ) 2 + (y t+1 r t+1 ) 2 + W(u t 1 u t 2 ) 2 }(1) Where W is a weighting factor for manipulating variable. The expectation E presents the control value u(t) that is estimated from data obtained up to and including time t and that a stochastic disturbance model is assumed. The quadratic minimization of equation (1) corresponds to a direct minimization problem. The logic for applying incremental input u t in the criterion is that Equation (1) does not allow zero static error in the case of a non-zero constant reference unless the open loop system algorithm involves an integrator, which would permit y t to stay at a constant value when the control input is zero. One feature of using u t in the control law term is that definite bounds on u t may be difficult to achieve. This particular control design seems also to be a variant of the minimum variance strategy and the idea is to maintain weighting factor (W) as small as possible in order to achieve minimum output variation while still sustaining closed loop stability. The method can handle a variable dead time but not with a model which has an over specified order. It is necessary to maintain numerical robustness to keep control weighting close to zero (Hapoglu 2002; Ertunç, Akay, Bursali, Hapoglu and Alpbaz 2003; Hitit, Boyacioglu, Ozyurt, Ertunc, Hapoglu and Akay 2014). To establish the controller algorithm it is supposed that a model of the system is expressed in terms of the following controlled autoregressive integrated moving average (CARIMA) form: y(t) = b 0 u(t 1) 1+a 1 z 1 +a 2 z 2 (2) Altuntaş, Ertunç, Hapoglu and Alpbaz (2012) obtained the coefficients of the model for the experimental open loop process of cheese whey drink production with kefir yeast using a pseudo random binary sequence as the forcing function and Bierman (1976) Algorithm. The magnitude of the coefficients were determined as a 1 =- 0.93, a 2 = and b 0 = These values were also used in the control algorithm utilized in the present work. The function of the operator ( =1-z -1 ) is to guarantee integral action in the controller which eliminate offset, i.e. a steady-state output disturbance. Definition of the vectors f and y, f = [y t+1 t y t+2 t ] T (3) G T = [g 0 g 1 ] (5) y = G u t + f (6) The future incremental control vector u t is given by: u t = [G T G + WI] 1 G T (r f) (7) In which r has been clearly described from the reference signal as: r = [r t+1 r t+2 ] T (8) The control gain computed in equation (7) stays fixed and only the vectors r and f are update at the next sampling time. In the present work, the steps used in the application of two time steps predictive control algorithm may be summarised as: 1. Apply a pseudo random binary sequence to the system as a forcing function and attain the plant output. 2. Estimate the coefficients from equation (2) using the Bierman U-D update algorithm. 3. Apply equation (7) to estimate the control signal utilizing the control procedure, and use this at every sampling time step. 3. EXPERIMENTAL PROCEDURE The bioprocess simulator is given in Figure 1. The display screen shown in Figure 2 is designed for the simulator. The bioreactor is a 1 L glass jacketed cylindrical vessel and the mixture that is mixed by a stirrer. Water is used as coolant in the jacket. For all the experiments, the manipulated variable was acknowledged as a valve opening for the coordinated acid and base flow input rates while one of these was kept at a small constant value. It was accepted that enough agitation was provided by the mixer in the simulator. During cheese whey drink production by fermentation with kefir yeast, the open loop dynamic ph behaviour was used as a sample profile which is simulated by using the acid flow rate changes introduced into the simulator from out of the system. At the beginning of the experiment, the simulator mixture which contains cheese whey, glucose, grape juice and milk was carried to the desired temperature. Then the appropriate flow rate changes of citric acid were added to the simulator in the face of constant base addition and the mixture temperature was held at the desired value by means of on-off control. Where y t+j t is the free response prediction of y t+j assuming that future control increments after time t-1 will be zero. y = [y t+1 y t+2 ] T (4) 163

3 Figure 1: The Experimental Bioprocess Simulator Figure 2: The display screen of the simulator Internal ph of the simulator was measured and transferred to the computer. A computer with A/D and D/A converters was used for data acquisition and the advance ph control algorithm was applied to the simulator. The converter modules were connected to regulate the flow rate of the pump and the heat input given to the reactor. The converter module had two outputs (pump and heater) and three inputs (mixture ph, cooling water inlet temperature and outlet temperature). Digital signals from the system were transferred into the module and these signals were sent to a computer connected on-line to the system to convert the signals into analogue signals. 4. RESULTS AND DISCUSSIONS An experimental work has been carried out to acquire the medium ph variation versus time during the open loop batch cheese whey drink production with kefir yeast. The pasteurized mixture of the reactor which contains 350ml cheese whey, 10g glucose, 70ml grape juice and 273 ml milk was used. Kefir yeast was added as 7ml inoculum. The actual ph behaviour without control was monitored throughout the fermentation process. Visidaq programming for data acquisition was advanced and applied during the experiments. In order to simulate the open loop bioprocess ph disturbance, the ph effect of citric acid flow rate variations at different concentrations has been examined to stand for the experimental ph profile while a small amount of 0.5M sodium bicarbonate flow rate was consistently introduced. The results given in Figures 3, 4, 5 and 6 indicate that the citric acid concentration and very small flow rate variations have strong effect on the ph profile obtained for simulation. Under control free condition, ph responses were compared to each other and real ph change of medium with kefir yeast to see the performance of the citric acid flow rate change pattern with various concentrations. Figure 3 presents the ph in medium with kefir yeast which ranged from 8 to 4, and the ph simulation without kefir yeast over a 28000s period. The ph simulation tested by 1M citric acid flow rate changes in the face of constant base addition was ranged from 6.8 to 2.8. The ph decreased somewhat linearly to about 8000s. Above 8000s, the ph tended to level off around ph 2.8. This simulation did not support the real ph profile obtained with kefir yeast. Figure 4 presents that if the ph signal for comparison were obtained by adding 3M citric acid flow rate changes and a constant base flow rate, the desired ph simulation would not be achieved. Visual inspection of the ph profiles in Figure 5 indicates that the delayed ph changes are almost exactly opposite in about 6000s time domain. To gain insight into the patterns and mechanisms hidden in the bioprocess ph data with kefir yeast, it is shown how the simulation ph tends to underpredict the target profile by introducing 4M citric acid flow rate changes to the process without kefir yeast in the face of constant base flow. At similar operating conditions by using 7M citric acid flow rate changes, the ph profiles obtained with and without kefir yeast were in good agreement. 7M citric acid flow rate pattern was chosen as the simulator disturbance (see Figure 6). To determine the adequate concentration of sodium bicarbonate and citric acid for control purpose, 250ml medium of bioprocess without kefir yeast was tested by adding small amount of base or acid solution. The concentration of acid and base solutions was varied and the bioprocess ph values were measured for each case (see Table 1 and 2). A small amount of base flow rate with 0.5M concentration and 0.5M acid concentration were chosen as the controlled bioprocess constant inputs. The acid flow rate was chosen as variable input of the process. 164

4 ph set value for control purpose ph set value for control purpose Figure 3: The Simulation Of The Real Bioprocess By 1M Citric Acid Flow Rate Changes ph set value for control purpose Figure 6: The Simulation Of The Real Bioprocess By 7M Citric Acid Flow Rate Changes Table 1: Medium ph Changes Versus Volume And Concentration Of Base Volume of base solution, ml Figure 4: The Simulation Of The Real Bioprocess By 3M Citric Acid Flow Rate Changes Base concentration ph for sodium bicarbonate solution 0.01M M M M M ph set value for control purpose Table 2: Medium ph Changes Versus Volume And Concentration Of Acid Volume of acid solution, ml Figure 5: The Simulation Of The Real Bioprocess By 4M Citric Acid Flow Rate Changes Acid concentration ph for citric acid solution 0.01M M M M M

5 The performance criteria used in this work are given as follows: ISE = (y r) 2 (9) IAE = y r (10) (a) (b) Figure 7: The Control Of The ph Under The Effect Of 7M Citric Acid Flow Rate Changes. The Controller Tuning Factor Is W= Control of bioprocess medium ph was achieved by utilizing a predictive algorithm. The weighting factor (W) was varied in order to achieve appropriate performance. The integral square of the error (ISE) and the integral of absolute value of error (IAE) criteria are computed by comparing the performances of two time steps predictive controller with two different tuning weight factors in Table 3. From this table, it is clearly seen that the controller with tuning factor magnitude exhibited better results. This closed-loop ph changes versus time was shown in Figure 7a. The controller brings the medium ph back to set point after 2400 seconds but controlling flow rate continues oscillation until the end of the experiment (Figure 7b). An overshoot is observed at the beginning of the simulated bioprocess during the control in the simulator while acid flow rate is manipulating and base flow rate is held constant. Table 3: ISE And IAE Values Obtained For Two Time Steps Predictive Control Of The Bioprocess Simulator Medium ph Controller ISE IAE Controller tuning factor, W Two time steps predictive control CONCLUSION The proposed strategy was performed experimentally to control the ph at a constant desired value during the pre-determined ph condition created by 7M citric acid flow rate changes as disturbance in a batch bioprocess simulator. The performance comparison of the controller was compared by means of two different feasible small magnitudes of weighting factor. The results showed that the magnitude of was adequate for the bioprocess ph controller as the tuning factor, and that the batch process control optimization was effectively implemented for two future output values taking into account as an even number of time step range. In addition, it is noted that tolerable manipulation of coordinated acid and base flow rates can be used for more nonlinear batch bioprocesses to maintain process ph at desired constant value. ACKNOWLEDGMENTS Financial support from Ankara University Scientific Research Projects Coordination Unit is gratefully acknowledged. REFERENCES Altuntaş S., Ertunç S., Hapoglu H. and Alpbaz M., Discrete-time modelling of the cheese whey drink production and servo control of ph. Ordu University Journal of Science Technology, 1 (1): Altuntaş S., Ertunç S., Hapoglu H. and Alpbaz M., Servo Control Application of Predictive Algorithm to the Cheese Whey Drink Production. Journal of Engineering and Architecture Faculty of Eskişehir Osmangazi University, 25 (2): Bierman G.J., Measurement updating using the U-D factorization. Automatica, 12 (4): Bharathi N., Sivakurnar E. and Shanmugam, J., Control of ph in fed-batch neutralization processes. IEEE International Conference on Industrial Technology, 1 (6): Camcıoglu S., Özyurt B. and Hapoglu H., ph control of paper wastewater treatment with 166

6 electrocoagulation method. Anadolu University Journal of Science and Technology- A Applied Sciences and Engineering, 16 (2): Clarke D.W., Mohtadi C. and Tuffs P.S., Generalized predictive control-part I: the basic algoritm. Automatica, 23 (2), Ertunç S., Akay B., Bursali N., Hapoglu H. and Alpbaz M., Generalized minimum variance control of growth medium temperature of baker's yeast production. Food and Bioproducts Processing, 81: Hapoglu H., Nonlinear long range predictive control of an openloop unstable reactor. Computers and Chemical Engineering, 26: Hitit Z.Y., Boyacioglu H., Ozyurt B., Ertunc S., Hapoglu H. and Akay B., Self-tuning GMV cotrol of glucose concentration in fed-batch baker s yeast production. Applied Biochemistry and Biotechnology, 172: Kourkoutas Y., Psarianos C., Koutinas A.A., Kanellaki M., Banat I.M. and Marchant R., Continuous whey fermentation using kefir yeast immobilized on de-lignified cellulosic material. Journal of Agricultural and Food Chemistry, 50 (9): Meenakshipriya B., Saravanan K., Somasundaram S. and Kanthabhabha P., CDM-based PI-P control strategy in ph neutralization system. Instrumentation Sciences and Technology, 39: Paraskevopoulou A., Athanasiadis I., Blekas G., Koutinas A.A., Kanellaki M. and Kiosseoglov V., Influence of polysaccharide addition on stability of a cheese whey kefir-milk mixture. Food Hydrocolloids, 17 (5): Pekel L.C., Zeybek Z., Hapoglu H. and Alpbaz M., Textile wastewater treatment with coagulation and generalized predictive control. Chemical Engineering Transactions, 21 (21): AUTHORS BIOGRAPHY Semin Altuntaş is currently a senior expert of the Ministry of Environment and Urbanization. She holds a B. Sc., M. Sc., and Ph.D. from the Chemical Engineering Department of Ankara University, Turkey. She has written a number of articles on simulation and process control. Hale Hapoglu is a professor in the Chemical Engineering Department, Ankara University, Turkey. She holds the B.Sc. and M.Sc. from the same department and a Ph. D. from the Chemical Engineering Department of Wales University, U.K. She has written over hundred articles on modelling, simulation, and process control. 167