The objective of this study is to design a Nonlinear Model Predictive Controller for a microalgae culture process to regulate the biomass concentration at a chosen setpoint. The optimization problem is discretized and transformed into a nonlinear programming problem, solved by Control Vector Parametrization technique. However, the performances of the NMPC usually decrease when the true plant evolution deviates significantly from that predicted by the model. Therefore, a control approach that considers model uncertainty is further considered by adding a system-model error signal which represents the gap between the system output and the model prediction. In order to reduce the influence of measurement noise introduced by sensors and to have a smooth control signal, a penalty term on the control variation is added in the objective function. Finally, the method is validated in simulation and numerical results are given to illustrate the efficiency of the control strategy for setpoint tracking in the presence of parameter uncertainties, measurement noise and light variation.

No abstract

International audienceThis 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

Summary This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameter uncertainties. First, this work focuses on the design of a robust nonlinear model predictive control (RNMPC) law subject to model parameter uncertainties implying solving a min‐max optimization problem. Secondly, a new approach is proposed, consisting in relating the min‐max problem to a more tractable optimization problem based on the use of linearization techniques to ensure a good trade‐off between tracking accuracy and computation time. The developed strategy is applied in simulation to a simplified macroscopic continuous photobioreactor model and is compared to the RNMPC and nonlinear model predictive controllers. Its efficiency and its robustness against parameter uncertainties and/or perturbations are illustrated through numerical results.