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

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

Sustainability and process control: A survey and perspective

“…Improvement of biomass productivity through tight pH and temperature control has been the main theme for optimal operation of microalgae-based processes. Control for the corresponding photobioreactors has been targeted using PI control [180], input/output linearizing control [181,182], nonlinear output feedback control [183], passivity-based control [184], sliding mode control [185], adaptive control [186], linear MPC [187][188][189][190][191] and nonlinear MPC [192,193]. Lack of continuous online measurements has motivated the use of interval state estimation [194], moving horizon estimation [189] and extended Kalman filtering [182].…”

Hierarchical predictive control strategy of microalgae culture in a photobioreactor

“…The min-max optimization problem (3) is converted into a robust regularized least squares problem when applying (11)(12)(13) in the presence of uncertain data [8], as presented in [9]. Let us consider the following optimization problem:…”

“…The application of (18-21) provides the solution of (3-4) as follows [9]: step 1. λ o is computed from the following minimization problem:…”

“…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). The proposed control strategy is further improved by combining the rLRMPC with a PI control law, similarly to the control structure proposed in [10].…”