On the Analytical Computation of Optimal Trajectories for Batch Reactors

Analytical solutions are found to an optimal control for fed-batch reactors with inhibition kinetics. The analytical solutions are found for rate expressions of the form R(c) = K(cf-c)^N where cf is the feed concentration. This type of rate model leads to nilpotent reactor models, and might be used to construct nilpotent approximations to more realistic rate models. The control law can used to implement a Model Predictive Control in which a parameter optimization, and possibly a rate law approximation, is performed at each time step.