Multilinear Model Decomposition and Predictive Control of MIMO Two-Block Cascade Systems

Abstract

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.

A systematic decomposition approach of nonlinear systems by combining gap metric and stability margin

“…In these processes, getting an acceptable performance in set-point tracking, disturbance rejection, and so on is not feasible using a single controller based on linearization of the nonlinear system around only one equilibrium point. The multi-model approach is a suitable candidate for dealing with those issues, and has received a great attention in different fields of studies such as modelling of complex systems (Prasad and Rao, 2019; Wang et al, 2020; Zhang et al, 2017), fault determination and diagnosis (Linlin and Steven, 2020; Madrigal-Espinosa et al, 2017; Rodrigues et al, 2013), and controller design (Ahmadi et al, 2019; Kersting and Buss, 2017; Song et al, 2018). In fact, the multi-model approach is a direct application from divide-and-conquer theory (Murray-Smith and Johansen, 1997) where a complex system could be broken down into two or more local models.…”