Advances in Nonlinear Model Predictive Control for Large-Scale Chemical Process Systems

Model predictive control is an optimization based form of control that is commonly used in the chemical industry due to its natural handling of multiple-input-multiple-output systems and inequality constraints. Nonlinear model predictive control takes advantage of fully nonlinear process models in order to provide higher accuracy across a wider range of states. However, linear MPC is still much more common in the chemical industry than nonlinear MPC due to various additional complications in the implementation. This thesis seeks to ease the implementation and increase performance of NMPC for large-scale systems
via fundamental developments that leverage both control and optimization theory. First, we address the issues of NMPC applied with plant-model mismatch. Robust NMPC methods tend to be computationally expensive or lead to conservatism in performance. Therefore, we propose a framework by which NMPC may be given a straightforward
robust reformulation in order to ensure nonlinear programming properties that connect to the continuity properties of the Lyapunov function used to show robustness. These reformulations are shown to be easily extended to the more specialized NMPC formulations
shown later in the thesis. Also, we show a method by which robustness bounds may be calculated for processes under control by NMPC. Next, we consider the computation of terminal conditions (regions and costs). Terminal
conditions are a critical aspect of NMPC formulations that is closely intertwined with stability of the controller and feasibility of the optimization problem. We formulate terminal
conditions via the quasi-infinite horizon methodology, and propose an extension for bounding nonlinear system effects that allows application to large-scale nonlinear systems.
We demonstrate these calculations on examples of varying scales from the literature. Also, we consider the application of economic NMPC (eNMPC) to large-scale systems.
We propose an eNMPC scheme which enforces stability though a stabilizing constraint, a method which we deem eNMPC-sc. We show that eNMPC-sc is input-to-state practically stable (ISpS) with a robust reformulation, and we demonstrate on computational examples, including a large-scale distillation system, that eNMPC-ec can provide better
economic performance without burdensome offline calculations to ensure stability. Finally, we consider the selection of the predictive horizon length. In particular, we consider a method for updating horizon lengths online that we call adaptive horizon NMPC (AH-NMPC). We show an algorithm utilizing NLP sensitivity calculations from sIPOPT
that provides sufficient horizon lengths in real time, and we leverage the terminal conditions from the quasi-infinite horizon approach in order to show both nominal and robust
stability (ISpS) in the case of horizons changing from timepoint to timepoint. We then demonstrate this controller on benchmark examples from the literature, including
the large-scale distillation system analyzed earlier, and note significant decreases in the average solve time of the NLP solved online.