  This paper presents a systematic method for the selection of the Model
Predictive Control (MPC) stage cost. We match the MPC feedback law to a
proportional-integral (PI) controller, which we efficiently tune by
high-performance Monte Carlo (MC) simulation. The PI tuning offers a wide range
of tuning possibilities that is then inherited by the MPC design. The MC
simulation tuning of the PI controller is based on the minimization of two
different objectives; 1) the 2-norm tracking error, and 2) a bi-objective
consisting of the 2-norm tracking error and a 2-norm input rate of movement
penalty. We apply the method to design MPC for an exothermic chemical reaction
conducted in an adiabatic continuous stirred tank reactor (CSTR). The process
is of interest as the nonlinear dynamics result in a desired operating point
very close to a constraint. Our MPC design includes stage costs automatically
designed to match the tuned PI controllers, hard input constraints, and a soft
output constraint. Stochastic simulation results show that both the PI
controller and the MPC can track the desired operating point. However, the MPC
shows reduced output constraint violation compared to the PI controller. As
such, the MPC design method successfully combines the efficient tuning of the
PI controller with the constraint handling properties of MPC.
