Robust Nonlinear Model Predictive Control for Regulation of Microalgae Culture in a Continuous Photobioreactor

Abstract

This paper proposes the design of a robust predictive control strategy which guarantees robustness towards parameters mismatch for a simplified macroscopic continuous photobioreactor model, obtained from mass balance based modelling. Firstly, this work is focused on classical robust nonlinear model predictive control law under model parameters uncertainties implying solving min-max optimization problem for setpoint trajectory tracking. Secondly, a new approach is proposed, consisting in reducing the basic min-max problem into a regularized optimization problem based on the use of linearization techniques, to ensure a good trade-off between tracking accuracy and computation time. Finally, the developed control law is compared to classical and robust predictive controllers. Its effciency is illustrated through numerical results and robustness against parameter uncertainties is discussed for the worst case model mismatch.