Nonlinear model predictive control using parameter varying BP-ARX combination model

Abstract

A novel back-propagation AutoRegressive with eXternal input (BP-ARX) combination model is constructed for model predictive control (MPC) of MIMO nonlinear systems, whose steady-state relation between inputs and outputs can be obtained. The BP neural network represents the steady-state relation, and the ARX model represents the linear dynamic relation between inputs and outputs of the nonlinear systems. The BP-ARX model is a global model and is identified offline, while the parameters of the ARX model are rescaled online according to BP neural network and operating data. Sequential quadratic programming is employed to solve the quadratic objective function online, and a shift coefficient is defined to constrain the effect time of the recursive least-squares algorithm. Thus, a parameter varying nonlinear MPC (PVNMPC) algorithm that responds quickly to large changes in system set-points and shows good dynamic performance when system outputs approach set-points is proposed. Simulation results in a multivariable stirred tank and a multivariable pH neutralisation process illustrate the applicability of the proposed method and comparisons of the control effect between PVNMPC and multivariable recursive generalised predictive controller are also performed.

Keywords:

• model predictive control
• nonlinear systems
• neural networks
• ARX model
• least-squares methods

Acknowledgements

The authors thank the Editor, Associate Editor and anonymous reviewers for their constructive suggestions. The study is partially supported by ‘Qing Lan’ Talent Engineering Funds by Lanzhou Jiaotong University and National Science Foundation of China (nos. 60904058 and 61004079).