Cesar de Prada

Em. Prof. , Dpt. of Systems Engineering and Automatic Control, University of Valladolid

**Economic MPC with Modifier Adaptation using Transient Measurements**

Real-Time Optimization (RTO) is a family of techniques and algorithms that continuously evaluates and decides on process-operating conditions to improve industrial process performance and economy automatically. In general, the RTO layer solves an optimization problem using a nonlinear stationary model and passes the optimal set point values to a predictive control layer (MPC) that implements them in the field. The MPC layer uses a transient linear or nonlinear model to control the plant. However, the complexity of the industrial processes and the presence of disturbances cause a model-process mismatch and generally, the optimum calculated by the RTO does not correspond to the real process optimum. One way to approach this problem is to modify the cost and constraints functions in RTO layer, so the necessary conditions of optimality (NCO) of the problem are equal to those of the real plant. This strategy is known as the Modifier Adaptation methodology (MA) (Marchetti et al., 2009) and adds modifiers to the cost function and constraints using gradient information from the real process and RTO model. Most of MA methods use static information for gradient calculation so the next RTO iteration could only be computed after the real process reaches several steady states. Therefore, when dealing with slow dynamics processes, as often happens in practice, the time required for computing corrective actions with RTO-MA can be so large that the method becomes impractical. To avoid this, some new methods that use transient data to compute the process gradients were developed, François & Bonvin (François and Bonvin, 2014) applied a method that estimates gradient via neighbouring extremals using transient measurements. Afterwards, Rodríguez-Blanco (Rodríguez-Blanco et al., 2017) presented an algorithm to apply the Recursive Extended Least Squares algorithm (RELS) to estimate the plant gradients using transient data. This allows formulating the process-model mismatch problem in the context of eMPC, merging RTO economic aims and dynamics. This is the path followed by recent works that study the unification of the RTO+MA layer and MPC in an economic MPC (eMPC) with MA as in (Pannocchia, 2018) and (Faulwasser and Pannocchia, 2019) that uses different approaches to estimate process gradients. The present work describes the problem in a unique optimization economical problem integrating eMPC with MA and presents a different way to estimate on-line the process gradients using an on-line identification algorithm (TMA). The eMPC integrated with MA proposed is applied in a benchmark example of Williams-Otto reactor. The results show that eMPC+TMA can approach the plant real steady state optimum despite process-model mismatch without using steady state measurements in a sensible period of time.