A nonlinear optimal control method for bioreactors and biofuels production

Abstract

A nonlinear optimal H-infinity control approach is proposed for bioreactors aiming at improved biofuels production. The dynamic model of the bioprocess taking place in the bioreactor undergoes approximate linearization round temporary equilibria which are recomputed at each iteration of the control method. The linearization makes use of Taylor series expansion and of the computation of the system's Jacobian matrices. For the approximately linearized model of the bioprocess an H-infinity feedback controller is designed. The feedback gain of the controller is found from the repetitive solution of an algebraic Riccati equation, taking place at each iteration of the control method. The stability of the proposed control scheme is evaluated through Lyapunov analysis. First, it is demonstrated that the control system satisfies the H-infinity tracking performance criterion, which signifies robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop is globally asymptotically stable. The proposed control method solves finally the nonlinear optimal control problem for bioreactors in a computational efficient and of proven convergence manner.