A MULTI-SCALE APPROACH TO FED-BATCH BIOREACTOR CONTROL by

A MULTI-SCALE APPROACH TO FED-BATCH BIOREACTOR CONTROL Abhishek Soni , M.S. University of Pittsburgh The rising energy costs, increased global competition in terms of both price and quality, and the need to make products in an environmentally benign manner have paved the way for the biological route towards manufacturing. Many of the products obtained by the biological route either cannot be produced, or are very difficult to obtain, by conventional manufacturing methods. Most of these products fall in the low volume/high value bracket, and it is estimated that the production of therapeutic proteins alone generated sales exceeding $25 billion in 2001 [1]∗. By increasing our understanding of these systems it may be possible to avoid some of the empiricism associated with the operation of (fed-)batch bioreactors. Considerable benefit, in terms of reduced product variability and optimal resource utilization could be achieved, and this work is a step in that direction. Biological reactors typically are governed by highly nonlinear behavior occuring on both a macroscopic reactor scale and a microscopic cellular scale. Reactions taking place at these scales also occur at different rates so that the bioreactor system is multi-scale both spatially and temporally. Since achievable controller performance in a model-based control scheme is dependent on the quality of the process model [2], a controller based on a model that captures events occuring at both the ∗Bracketed references placed superior to the line of text refer to the bibliography. iii reactor and cellular scales should provide superior performance when compared to a controller that employs a uniscale model. In the model considered for this work [3], μ, the specific growth rate is used as a coupling parameter integrating the behavior of both scales. On the cellular level, flux distributions are used to describe cellular growth and product formation whereas a lumpedparameter reactor model provides the macroscopic process representation. The control scheme for the fed-batch bioreactor is implemented in two stages, and the substrate feed rate serves as the manipulated variable. Initially, a constrained optimal control problem is solved off-line, in order to determine the manipulated variable profile that maximizes the end of batch product concentration for the product of interest, while maintaining a pre-specified, fixed final volume. The next step involves tracking of the optimal control trajectory, in closed-loop operation. The Shrinking Horizon Model Predictive Control (SHMPC)[4] framework is used to minimize the projected deviations of the controlled variable from the specified trajectories. At every time step, the original nonlinear model is linearized and the optimization problem is formulated as a quadratic program [5], that includes constraints on the manipulated input and the final volume. Finally, the performance of the controller is evaluated, and strategies for disturbance compensation are presented. The results of this approach are presented for ethanol production in a baker’s yeast fermentation case study [3]. DESCRIPTORS Fed-Batch Bioreactors Model Predictive Control Multi-scale Models Optimal Control