RBF-ARX Modeling and Predictive Control Strategy Applied to a Liquid Level System

The main objective of this paper is to show in the first place that the RBF-ARX modeling technique can be used to model a dynamic nonlinear SISO liquid level system with higher precision and then to demonstrate that when the model obtained is taken as predictor of a model predictive controller (MPC) one may obtain an enhanced control performance. The RBF-ARX model is in fact a locally expanded Taylor ARX model with Gaussian radial basis function (RBF) network-style coefficients depending of the working point; it can be estimated offline to avoid any online uncertainty. It is built to globally describe the behavior of nonlinear dynamic system and exhibit an easy and advantageous means of obtaining a local linearization of any working point. The RBF-ARX model based MPC (RBF-ARX-MPC) is a predictive control strategy based on RBF-ARX model. It doesn't require online but offline parameters optimization in which the nonlinear parameters estimation depends on the Levenberg-Marquardt Method (LMM) and the linear one on the least-square method using singular value decomposition (SVD).