Gain Conditioning for Linear Model Predictive Control

Abstract

Linear model predictive control (MPC) is used in a wide variety of process industries. Linear MPCs calculate adjustments in multiple manipulated variables (MVs) to ensure that operating constraints are obeyed and that controlled variables (CVs) are maintained near their setpoints. Industrial practitioners who develop MPC applications are interested in preventing erratic behavior of MPCs, which can be caused by imperfect models with ill-conditioned gain matrices. Currently, control practitioners use time-consuming methods based on relative gain arrays and singular-value thresholding to condition their gain matrices to prevent degraded controller performance. These techniques tend to require many iterations to successfully condition a large gain matrix. In the proposed approach I extend an orthogonalization-based parameter-ranking algorithm, which was originally developed to aid parameter estimation in fundamental models, so it can be used to identify and address gain conditioning problems. The proposed method ranks MVs from most influential to least influential while accounting for correlated steady-state influences of MVs on CVs. Problematic MVs are identified, and a linear optimization algorithm is used to find optimal gain adjustments to condition the gain matrix. To test the effectiveness of the proposed methodology, I use industrial case studies based on fluidized catalytic cracking models.