Improved gain conditioning for linear model predictive control

Abstract

Industrial practitioners who develop linear model predictive control (MPC) applications want to prevent undesirable controller behaviour caused by ill-conditioned gain matrices and model mismatch. In this work, we propose improvements to an existing orthogonalization-based method for gain conditioning. In this offline algorithm, manipulated variables (MVs) are ranked based on their influences on the controlled variables (CVs), so that problematic MVs with correlated effects can be identified. A constrained linear least-squares optimization problem is then solved to adjust columns in the gain matrix that correspond to problematic MVs. Our goal is to update this optimization problem to prevent the optimizer from switching the signs of some gains. The updated algorithm also permits control practitioners to hold key gains constant if their estimated values are trusted. Finally, we extend the methodology to condition gain submatrices, which arise when CVs are removed from the MPC problem. An industrial fluidized catalytic cracking case study is used to test the proposed method. The conditioned gains lead to improved controller performance and less aggressive movement of MVs when there is a plant-model mismatch.