Self-stabilizing Economic Nonlinear Model Predictive Control of Modular Membrane Reactor Systems

In recent years, economic Nonlinear Model Predictive Control (eNMPC) has emerged as a viable alternative for distributed control systems. Because eNMPC involves the solution of a dynamic optimization problem, it provides the control actions that lead the system to the most economical transient operations, which may be periodic instead of converging to a steady state[1]. Since eNMPC has been typically used for standalone unit operations instead of plantwide control, an unsteady operation of a unit may lead to undesirable operations of downstream units. This work proposes a self-stabilizing eNMPC formulation, in which a pre-calculated steady-state condition is not required. Lyapunov functions with embedded steady-state optimal conditions are employed as additional constraints of the eNMPC formulation, so that the asymptotically stable behavior can be achieved. The performance of the proposed eNMPC is demonstrated with two case studies of a membrane reactor for natural gas utilization. In the first case study, the proposed eNMPC can effectively bring the system toward the feasible steady-state optimal operation. In the second case study, a cost-optimal steady-state does not exist due to the time-varying disturbance, and the closed-loop behavior is shown to be bounded if the disturbance is also bounded.