Multi-linear model set design based on the nonlinearity measure and H-gap metric

Design and Implementation of a Novel Self-adaptive Fuzzy Logic Controller for a pH Neutralization Process

“…The recent advancements in modern control systems and computer technology have led to the development of model predictive control techniques whereby a dynamic model of the controlled process is used directly online [23]. During the control action of the model predictive controller (MPC), the model computes predictions of the output/state variables which are then used during optimization of the control sequence [4].…”

“…Nevertheless, the ability of the pH dynamic model to replicate the actual nonlinear behavior of neutralization processes prevailed and this limited both the accuracy and ability of most of the pH controllers proposed up-to-date [3]. The fundamental step in developing a nonlinear MPC is to essentially designate an appropriate structure of a nonlinear model that accurately identifies the system dynamics [6,23]. However, the main disadvantage of the nonlinear modeling is that using a nonlinear model often leads to a complex dynamic model that is almost impossible to use in the nonlinear predictive control.…”

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

“…Then, Du et al generalized the method in ref to accommodate nonlinear systems with multiple scheduling variables, together with a gridding algorithm for reducing gridding points and decreasing computational burden. To accurately measure the distance between candidate linear models in all ranges of frequencies, Shaghaghi et al studied the H-gap metric based division method.…”

“…Such methods depend on the system dynamic information around operating points and are just effective in the case where a set of local linear models is available before dividing, such as the cases in refs and . Once local linear models are not available, system nonlinear models or a large number of local linear models would have to be identified from measured data, such as the cases in refs , , and . Because identifying an accurate nonlinear model or a large number of local linear models is generally time-consuming and costly, the gap metric based division methods are strictly restricted by the requirement of system dynamic information.…”

“…It initially partitions the system I/O surface into a certain number of polytopes and then employs the included angles between the normal vectors to these polytopes to evaluate system nonlinearity and decompose the system. It is usually more practical than the gap metric based methods, − because only static I/O mappings instead of system dynamic information are required for the system decomposition. The designed multilinear MPC algorithm with trajectory scheduling (MMPC-TS). At each sampling instant, by using a scheduling variable trajectory, the multilinear predictive model is transformed to be a certain local linear model within the prediction horizon.…”