The
Model Predictive Control (MPC) Toolbox is a collection of functions (commands) developed for the analysis and design of model predictive control (MPC) systems. Model predictive control was conceived in the 1970s primarily by
industry. Its popularity steadily increased throughout the 1980s. At present, there is little doubt that it is the most widely used multivariable control algorithm in the chemical
process industries and in other areas. Some of the popular names associated with model predictive control are DynamicMatrix Control (DMC), IDCOM, model
algorithmic control, etc.While these algorithms differ in certain details, the main ideas behind them are very similar. Indeed, in its basic unconstrained formMPC is closely related to linear quadratic
optimal control. In the constrained case, however, MPC leads to an optimization problem which is solved on-line in real time at each
sampling interval. MPC takes full advantage of the power available in today’s control computer hardware. This software and the accompanying manual are not intended to teach the user the basic ideas behind MPC. Background material is available in standard textbooks like those authored by Seborg, Edgar and Mellichamp (1989)1, Deshpande and Ash (1988)2 and the
monograph devoted solely to this topic authored byMorari and coworkers (Morari et al., 1994)3. This section provides a basic introduction to the main ideas behind MPC and the specific form of implementation chosen for this toolbox. The algorithms used here are consistent with those described in the monograph by Morari et al. Indeed, the software is meant to accompany the monograph and vice versa.