Multilinear model decomposition and predictive control of MIMO two-block cascade systems

This paper presents a new multilinear model decomposition method for multiple-input multiple-output (MIMO) two-block cascade systems and a model predictive control (MPC) algorithm for the resulting representation. First, a normal vector included angle division method is developed to decompose the operating space and determine the minimum linear model bank through evaluating the nonlinearity of the steady-state I/O surfaces. For a prescribed angle threshold, the minimum linear model bank can be constructed to approximate the original two-block cascade system sufficiently closely. Next, a multilinear MPC algorithm is designed with the proposed trajectory scheduling technique, which can reduce output oscillations caused by hard switching and avoid the difficulty of calculating/tuning complex weighting functions/parameters used in soft switching. A benchmark chemical reactor process is studied to illustrate the effectiveness and advantages of the proposed decomposition method and the predictive control algorithm.