Robust Nonlinear Model Predictive Controller based on sensitivity analysis — Application to a continuous photobioreactor

Hierarchical predictive control strategy of microalgae culture in a photobioreactor

“…From the analysis of the sensitivity functions temporal evolution, and according to their magnitude order, one can select the parameters which are significantly the most influential on the model [7]. These parameters will be denoted κ.…”

“…The main objective of the control is to regulate the biomass concentration X to a reference value X r , while the dilution rate D is constrained to track the reference D r . The latter is computed from the knowledge of the targeted setpoint at each time instant as detailed in [7]. According to results obtained in [7], the substrate half saturation constant K s and the minimal cell quota K Q are the most influential parameters on the biomass concentration evolution (κ = [K s , K Q ]).…”

“…The latter is computed from the knowledge of the targeted setpoint at each time instant as detailed in [7]. According to results obtained in [7], the substrate half saturation constant K s and the minimal cell quota K Q are the most influential parameters on the biomass concentration evolution (κ = [K s , K Q ]). Now, the efficiency of the proposed control strategy is validated in simulation.…”

“…The performances of the above mentioned algorithms are compared in a worst uncertain parameters case. The parameters values of the system are chosen on the parameter subspace border ( [7], where the uncertain parameters subspace [θ − , θ + ] is given by [0.8θ nom , 1.2θ nom ]. The maximal admissible dilution rate D max equals 1.6d −1 .…”

“…The first idea of this study consists in proposing a robust formulation of the NMPC law implying a min-max optimization problem by taking into account only the most influential parameters. The considered parameters are determined on the basis of a sensitivity analysis as proposed in [7]. In addition, in order to reduce as much as possible the computation load, we propose an alternative procedure that transforms the min-max problem into a robust regularized least squares problem [8], through a model linearization technique (first order Taylor series expansion) at each sampling time, along the nominal trajectory [9] (called hereafter reduced Linearized Robust NMPC, rLRMPC).…”