A multi-rate Model Predictive Control algorithm for systems with fast-slow dynamics

This paper proposes a novel multi-rate model predictive control (MPC) scheme for linear discrete-time systems subject to input constraints. The proposed scheme is composed by two control layers, acting at two different time scales. At a slow time scale, the outputs associated with the slow dynamics are steered to their reference values while, at a fast timescale, a shrinking horizon MPC regulator is designed to refine the control action computed at the slow timescale. The proposed control scheme shows to be particularly useful, not only to control systems with different open-loop dynamics, but also in cases when the controlled variables are required to have different responsiveness in closed-loop. Simulation results on a Fire Tube Boiler example are reported, which indeed show that different dynamics can be efficiently imposed to the controlled variables, i.e. the boiler pressure and the water level, in presence of variations of the disturbance represented by the steam output flow rate.