Real-time feasible multi-objective optimization based nonlinear model predictive control of particle size and shape in a batch crystallization process. (December 2017) - Cao, Yankai; Acevedo, David; Nagy, Zoltan K.; Laird, Carl D.
Abstract: This paper presents nonlinear model predictive control (NMPC) and nonlinear moving horizon estimation (MHE) formulations for controlling the crystal size and shape distribution in a batch crystallization process. MHE is used to estimate unknown states and parameters prior to solving the NMPC problem. Combining these two formulations for a batch process, we obtain an expanding horizon estimation problem and a shrinking horizon model predictive control problem. The batch process has been modeled as a system of differential algebraic equations (DAEs) derived using the population balance model (PBM) and the method of moments. Therefore, the MHE and NMPC formulations lead to DAE-constrained optimization problems that are solved by discretizing the system using Radau collocation on finite elements and optimizing the resulting algebraic nonlinear problem usingIpopt . The performance of the NMPC–MHE approach is analyzed in terms of setpoint change, system noise, and model/plant mismatch, and it is shown to provide better setpoint tracking than an open-loop optimal control strategy. Furthermore, the combined solution time for the MHE and the NMPC formulations is well within the sampling interval, allowing for real world application of the control strategy. Highlights: An NMHE–NMPC formulation is developed to control the crystal size and shape. Simultaneous method results in formulation that is real-time capable. NMHE–NMPC provides better setpoint tracking than open-loop optimal control. JModelica provides general modeling framework and optimization interface.