0960–3085/03/$23.50+0.00 # Institution of Chemical Engineers www.ingentaselect.com =titles =09603085.htm Trans IChemE, Vol 81, Part C, December 2003 GENERALIZED MINIMUM VARIANCE CONTROL OF GROWTH MEDIUM TEMPERATURE OF BAKERÂS YEAST PRODUCTION S. ERTUNC ¸ 1 , B. AKAY 1 , N. BURSALI 2 , H. HAPOG LU 1 and M. ALPBAZ 1 1 Ankara University, Faculty of Engineering, Department of Chemical Engineering, Tandog an, Ankara, Turkey 2 Yenimahalle Municipality, Department of Health, Yenimahalle, Ankara, Turkey T he control of optimum growth medium temperature of a batch bioreactor in which S.cerevisiae was grown under aerobic conditions has been studied. The generalized minimum variance (GMV) algorithm was applied for on-line computer control. A controlled autoregressive moving average model relating the bioreactor temperature and heat input was used to show the dynamic behaviour of the system. The heat input to the bioreactor was chosen as a manipulated variable. A pseudo-random binary sequence signal was applied to the system and the model parameters were determined using the Bierman algorithm. More suitable values of the GMV controller parameters were determined using a total simulation program. These control parameters were used in experimental and theoretical work under several disturbances. Keywords: bioreactor; parameter estimation; modelling; generalized minimum variance. INTRODUCTION In process operation, whether chemical or biochemical, the production of high-quality product, maximum prot and safe operation are desired. All of these purposes generally require control of the operation parameters. However, bioprocesses require extra control because of the number of complex reactions which take place simultaneously and which cannot be dened with simple mathematical models; in addition, there are no suitable state sensors. In recent years, there has been a great deal of interest in the application of bioprocesses in food, agriculture and pharmaceutical industries and the solution of the problems in these processes. As a result, modern control techniques have been developed to control the growth medium tempera- ture, pH, gas ow rate and substrate feed rate (Sargantanis et al. , 1998; Dochain and Bastin, 1984). Saccharomyces cerevisiae , known as Baker’s yeast, was used and the production of this microorganism in the batch culture was desired. Until now in the production of Baker’s yeast, whether continuous, batch or fed-batch bioreactors, different operating parameters have been controlled using modern control techniques so that maximum yeast produc- tion and economical prot can be achieved. One of the most popularcontrol techniquesis the self-tuning method. Genera- lized minimum variance, pole-placement self-tuning and generalized predictive control are known as self-tuning control techniques. The generalized minimum variance (GMV) controller (Clarke and Gawhrop, 1975) was formed basically as a modication of the minimum variance (MV) technique of Astro ¨m and Wittenmark (1973). This controller is obtained by minimizing a cost function for a provided linear input– output model. It is well known that MV controllers (Astro ¨m et al. , 1977) attempt to cancel explicitly the forward path zeros, some of which may lie outside the unit circle. In MV control it is critical that the time delay should be correctly chosen (Hang et al. , 1991). Wrong values of time delay can destabilize the control or at least result in deviations of the controlled variable. The GMV algorithm involves a feed- forward element represented by the polynomial Q. The presence of this usually avoids the problems which destabi- lize the system. The GMV control law (Clarke and Gawhrop, 1975) employs a one-step-ahead optimal control strategy. The evaluated parameters are employed precisely in the implicit GMV algorithm. However, due to the implicit character of this algorithm it can be shown that the design parameters of the controller cannot be varied on-line without degrading the parameter estimates (Clarke and Gawhrop, 1975). An additional modication to this design (Clarke and Gawtthrop, 1979) permits the control weighting to be altered on-line without inuencing the parameter estimates. In the latter case, the control law is not completely implicit (Pamuk et al. , 2000). The purpose of this study is to control the culture medium temperature at which the concentration of the microorgan- ism can be held at a maximum. In the rst part of the work, a mathematical model of the bioreactor was developed to observe and calculate the transient behaviour of the system and then a CARMA model was used to achieve the GMV control. The related model was solved by digital computer and was used in a total simulation program. In the second part of the work, some theoretical work was realized to obtain the temperature control and to track the 327