Robustification of Nonlinear Model Predictive Control - Application to sustainable development processes.

Abstract : The last few years have led to very rapid developments, both in the formulation and the application of Nonlinear Model Predictive Control (NMPC) algorithms, with a relatively wide range of industrial achievements. One of the most significant challenges encountered during the development of this control law is due to uncertainties in the model of the system. In this context, the thesis addresses the design of NMPC control laws robust towards model uncertainties. Usually, the above design can be achieved through solving a min-max optimization problem. In this case, the idea is to minimize the tracking error for the worst possible uncertainty realization. However, this robust approach tends to become too complex to be solved numerically online, especially in the case of multivariable systems with a large number of uncertain parameters. To address this shortfall, the proposed approach consists in simplifying the min-max optimization problem through a sensitivity analysis of the model with respect to its parameters, in order to reduce the calculation time. First, the criterion is linearized around the model parameters nominal values. The optimization variables are either the system control inputs or the control increments over the prediction horizon. The initial optimization problem is then converted either into a convex optimization problem, or a one-dimensional minimization problem, depending on the nature of the constraints on the states and commands. The stability analysis of the closed-loop system is also addressed. Finally, a hierarchical control strategy is developed, that combines a robust model predictive control law with an integral sliding mode controller, in order to cancel any tracking error. The proposed approaches are applied through two case studies to the control of microorganisms culture in bioreactors.
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Seif Eddine Benattia. Robustification of Nonlinear Model Predictive Control - Application to sustainable development processes.. Other. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLC066⟩. ⟨tel-01378666⟩

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