Deterministic and stochastic optimal control of acid pre-treatment of bagasse

Abstract

Acid pre-treatment of bagasse is performed in a batch reactor, in which concentration of components evolve over time. This type of systems is usually studied using optimal control, which is concerned with dynamic systems and their optimization over time. This study applies the theory of optimal control for multi-objective optimization. The objectives include maximization of xylose and acid soluble lignin (ASL) fraction, which is obtained during acid pre-treatment. The Pontryagin's maximum principle in combination with the numerical method of steepest descent of Hamiltonian is used to solve multi-objective optimal control problem. The results showed that maximum xylose and acid soluble lignin (ASL) yield was obtained around 0.79 (g/g of xylan) and 0.3 (g/g of lignin), respectively, at final time (t f =300 min.). However, acid pre-treatment is influenced by various sources of uncertainties. Therefore, it is essential to optimize the acid pre-treatment process after considering these variabilities. In this work, variability in feedstock composition has been considered, and the stochastic maximum principle is used to perform stochastic multi-objective optimal control problem. Deterministic and stochastic control profiles were obtained for different weights. An open loop simulation of Ito model, using deterministic and stochastic control profile, was performed for 1000 samples and statistics were generated by assuming normal distribution with 95% confidence bound.