Modeling, Analysis and Control of Nonlinear Switching Systems

Abstract

The first part of this two-part thesis examines the reverse-flow operation of auto-thermal methane reforming in a microreactor. A theoretical study is undertaken to explain the physical origins of the experimentally observed improvements in the performance of the reverse-flow operation compared to the unidirectional operation. First, a scaling analysis is presented to understand the effect of various time scales existing within the microreactor, and to obtain guidelines for the optimal reverse-flow operation. Then, the effect of kinetic parameters, transport properties, reactor design and operating conditions on the reactor operation is parametrically studied through numerical simulations. The reverse-flow operation is shown to be more robust than the unidirectional operation with respect to both optimal operating conditions as well as variations in hydrogen throughput requirements. A rational scheme for improved catalyst placement in the microreactor, which exploits the spatial temperature profiles in the reactor, is also presented. Finally, a design modification of the microreactor called "opposed-flow" reactor, which retains the performance benefits of the reverse-flow operation without requiring the input / output port switching, is suggested.

In the second part of this thesis, a novel simulation-based Approximate Dynamic Programming (ADP) framework is presented for optimal control of switching between multiple metabolic states in a microbial bioreactor. The cybernetic modeling framework is used to capture these cellular metabolic switches. Model Predictive Control, one of the most popular advanced control methods, is able to drive the reactor to the desired steady state. However, the nonlinearity and switching nature of the system cause computational and performance problems with MPC. The proposed ADP has an advantage over MPC, as the closed-loop optimal policy is computed offline in the form of so-called value or cost-to-go function. Through the use of an approximation of the value function, the infinite horizon problem is converted into an equivalent single-stage problem, which can be solved online. Various issues in implementation of ADP are also addressed.