Model predictive control using subspace model identification

Abstract

This paper addresses the problem of designing and implementing a data-driven model based model predictive controller (MPC). In particular, we consider the problem where a subspace identification approach is utilized to determine a state-space model, while applying first-principles based knowledge in the model identification (denoted as the constrained subspace model). The incorporation of the first-principles based constraints in the subspace matrix Patel et al. (2020) often leads to a feed-through matrix being present. Such a model then is the best representation of the system dynamics, but does not lend itself readily to existing linear MPC formulations where the feed-through matrix is assumed to be zero. Thus, an existing linear MPC formulation is adapted to handle the feed through matrix. The superior performance of this MPC design, which can utilize the constrained subspace model, over existing approaches is demonstrated using a two tank chemical stirred tank reactor process.