A novel nonlinear model predictive control strategy and its application to maglev ball system

Abstract

For processes with strong nonlinearity and fast response, a Nonlinear Model Predictive Control (NMPC) algorithm is proposed based on Laguerre functions and Radial Basis Function-based AutoRegressive model with eXogenous variable (RBF-ARX-LMPC), which is built to capture the nonlinear dynamics of such process. Firstly, the RBF-ARX model is transformed into an extended Non-Minimal State-Space (NMSS) model in which integral action and set-point information are naturally contained to decrease steady-state error. Then, to reduce computational burden, the control variables of the NMPC is parameterised by Laguerre polynomials for dimensionality reduction. The proposed control strategy is applied to a maglev ball system and is compared with Proportional–Integral–Derivative (PID) controller, the RBF-ARX model-based Linear Quadratic Regulator (RBF-ARX-LQR), and the RBF-ARX model-based Model Predictive Control (RBF-ARX-MPC). The experimental results show that the proposed control strategy improves transient performance and computational efficiency.

KEYWORDS:

• Nonlinear system
• model predictive control
• RBF-ARX model
• Laguerre functions
• maglev ball system

Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their very valuable comments and suggestions, which greatly improved the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Major Program from Xiangjiang Laboratory under [Grant 23XJ01010] and the National Natural Science Foundation of China under [Grant 52275105, 61773402, 51575167, 61540037, and 71271215].