RBF-ARX model-based MPC strategies with application to a water tank system

A hybrid pseudo-linear RBF-ARX model that combines Gaussian radial basis function (RBF) networks and linear ARX model structure is utilized for representing the dynamic behavior of a class of smooth nonlinear and non-stationary systems. This model is locally linear at each working point and globally nonlinear within whole working range. Based on the structural characteristics of the RBF-ARX model, three receding horizon predictive control (RBF-ARX-MPC) strategies are designed: (1) the RBF-ARX-MPC algorithm based on single-point linearization (MPC-SPL); (2) the RBF-ARX-MPC algorithm based on multi-point linearization (MPC-MPL); and (3) the RBF-ARX-MPC algorithm based on globally nonlinear optimization (MPC-GNO). In the MPC-SPL, the future multi-step-ahead predictive output of the system is obtained based on the local linearization of the RBF-ARX model at only current working-point, while in the MPC-MPL the future long-term output prediction is obtained according to the future local characteristics from previous online optimization results of the RBF-ARX model based MPC. In the MPC-GNO, the globally nonlinear characteristics of the RBF-ARX model are fully used for online getting control variables of the MPC. Real-time control experiments for the three type MPCs are carried out on a water tank system, which are also compared with a classical AID control and a traditional linear ARX model-based MPC. The results verify that the modeling method and the model-based predictive control strategies are realizable and effective for the nonlinear and unstable system. Moreover, it is also shown that the MPC-GNO can obtain better control performance but need more computation time compared to the other MPCs, which makes it possible to be applied into some slowly varying processes. (C) 2015 Elsevier Ltd. All rights reserved.