Offset-free multi-model economic model predictive control for changing economic criterion

Abstract

Economic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant. However, throughout the operation of the plant, if the economic criterion changes – due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. – the optimal operation point also changes. In industrial applications, a nonlinear description of the plant may not be available, since identifying a nonlinear plant is a very difficult task. Thus, the models used for prediction are in general linear. The nonlinear behavior of the plant makes that the controller designed using a linear model (identified at certain operation point) may exhibit a poor closed-loop performance or even loss of feasibility and stability when the plant is operated at a different operation point. A way to avoid this issue is to consider a collection of linear models identified at each of the equilibrium points where the plant will be operated. This is called a multi-model description of the plant. In this work, a multi-model economic MPC is proposed, which takes into account the uncertainties that arise from the difference between nonlinear and linear models, by means of a multi-model approach: a finite family of linear models is considered (multi-model uncertainty), each of them operating appropriately in a certain region around a given operation point. Recursive feasibility, convergence to the economic setpoint and stability are ensured. The proposed controller is applied in two simulations for controlling an isothermal chemical reactor with consecutive-competitive reactions, and a continuous flow stirred-tank reactor with parallel reactions.