Advances in Nonlinear Model Predictive Control and Their Applications in Chemical Engineering

Model Predictive Control (MPC) has emerged as a promising optimization-based controller in various industrial applications because of its nature of coping with variable bounds and multiple-input-multiple-output (MIMO) dynamic processes. Non-linear MPC (NMPC) is the nonlinear branch of MPC that makes use of the nonlinear model and constraints to achieve higher accuracy for systems with complicated dynamics. However, the performance of NMPC is influenced by process uncertainty and computational delays. In addition, it faces stability challenges when considering economically oriented objectives. This thesis aims to enhance the performance of NMPC by developing advanced features that improve robustness, stability, and economic efficiency while maintaining reasonable online computation by leveraging both control and optimization theory. 

First, we consider the well pumping period in hydraulic fracturing and propose a robust control strategy aimed at addressing the constraint violations on operating pressure and terminal requirements resulted from the uncertainty in the rock layer. A comprehensive dynamic model that captures the process is constructed and incorporated into the predictive model of the robust multistage NMPC, which uses a scenario tree to depict the evolution of states with respect to uncertain parameters. The results demonstrate the promising robustness of the controller, as it satisfies all constraints in the face of the rock uncertainty that changes in time. 

Next, we develop a strategy to alleviate the online computational burden associated with solving Moving Horizon Estimation (MHE) problems, which is essential for NMPC when the process information is incomplete. We propose to solve an extended horizon MHE within a specified number of delayed sampling steps. This approach uses predicted future measurements in background and nonlinear programming (NLP) sensitivity to execute online corrections once the true measurements are available. The proposed algorithm is applied to a large-scale distillation column to show satisfactory estimation performance with negligible online computational effort. 

Finally, we propose two stable economic NMPC (eNMPC) formulations that achieve dual objectives of optimizing the economic goal and ensuring closed-loop stability. The proposed formulations track the optimality conditions of the real-time optimization problem instead of the exact setpoint, which eliminates the requirement of solving for the new setpoint when updating parameters related to the economic objective or system. We demonstrate the developed controllers on benchmark examples from the literature, including a continuous stirred-tank reactor and the aforementioned distillation column with improved economic results and guaranteed stability.