Model Predictive Control Tuning by Monte Carlo Simulation and Controller Matching

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.