Optimal control of biodiesel production in a batch reactor: Part II: Stochastic control

The determination of time-varying profiles through dynamic optimization is an exclusive characteristic of optimal control problems; however, these types of problems become more challenging when variability and uncertainty in any parameter is included. In biodiesel production, there are inherent uncertainties arising due to variation in initial composition, operating parameters, and mechanical equipment design that can have a significant impact on the product quantity, quality and process economics. Thus, one of the most influential uncertainties in this process is the feed composition since the percentage and type of triglycerides in biodiesel composition varies considerable. In this work, the optimal control for biodiesel production in a batch reactor developed in Part 1 is extended to a problem when uncertainty in the feed composition is considerably. Under control of reactor temperature, we applied a numerical method, based on the Steepest Ascent of Hamiltonian to solve the stochastic optimal control problem that involved the application of Ito processes and the stochastic maximum principle. It has been found that the temperature profile obtained using deterministic optimal control is robust in the face of feed composition uncertainties also.