Analysis and correction of ill-conditioned model in multivariable model predictive control

Ill-conditioned model usually appears in modelling high purity and complicated production processes such as the high-purity distillation column. Model predictive control (MPC) via closed-loop feedback is a class of methods for which a plant model is used to forecast the outputs or states of controlled systems and to then solve a linear or nonlinear programming with multivariable and constraints by so-called receding horizon optimisation. Ill-conditions can cause many negative effects on the implementation of MPC including system instability and controller failure. In this paper, these phenomena such as output static error and stability decreasing of ill-conditioned model caused in MPC are found by simulating simple examples, and the close correlation between the movement direction of the controlled system output and the characteristics of ill-conditioned model is also observed. The geometry tools and singular value decomposition (SVD) in linear algebra are used to analyse the essential cause of ill-conditioned model generation. A new offline quantitative strategy is proposed to improve the ill-conditioned model. Based on modified model of reengineering and implementation of model predictive control, the closed-loop control performance and stability can be significantly enhanced.