Hierarchical Control Strategy based on Robust MPC and Integral Sliding mode - Application to a Continuous Photobioreactor

Abstract

This paper proposes the design of a hierarchical control strategy formed by a two-level controller: a Linearized Robust MPC (LRMPC) and an Integral Sliding Mode (ISM) control laws. The proposed strategy guarantees robustness towards parameters mismatch for a macroscopic continuous photobioreactor model, obtained from mass balance based modelling. Firstly, as a starting point, this work focuses on classical robust nonlinear model predictive control law under model parameters uncertainties implying solving a basic min-max optimization problem for setpoint trajectory tracking. We reduce this 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. Secondly, in order to eliminate the static error due to the fact that the nonlinear model is approximated through linearization in the LRMPC law, an ISM controller is synthesized relying on the knowledge of the nonlinear model of the system. Finally, the efficiency of the developed hierarchical approach is illustrated through numerical results and robustness against parameter uncertainties is discussed for the worst case model mismatch.