MPC of 2D channel flow via staggered grid

This paper discusses the performance of two different formulations of Model Predictive Control (MPC) over the problem of 2D incompressible channel flow control. The objectives are to compare performance index of both formulations in term of computational load on complex system, and be able to solve the problem of channel flow, which control inputs are applied at both top and bottom walls. The flow dynamics are represented using Navier-Stokes equations and linearized to the equilibrium Poiseuille flow profile. Discretization is then implemented using finite difference methods upon the setting of staggered grid. The simulation results show the performance of both formulations of MPC on stabilizing unstable flow into equilibrium flow profile, and the relationship between computational load and problem size for both formulations.