A modelling and predictive control approach to linear two-stage inverted pendulum based on RBF-ARX model

Abstract

The Underactuated, Fast-responding, Nonlinear and Unstable (UFNU) system is a typical hard-to-control plant, such as multi-stage inverted pendulum (IP). This paper considers the modelling and stabilisation control of a Linear Two-Stage IP (LTSIP). To avoid the problems resulted from using first principle model this paper uses a data-driven approach to building a State-Dependent AutoRegressive eXogenous (SD-ARX) model without offset term, whose coefficients are approximated by Radial Basis Function (RBF) neural networks, to describe the LTSIP. Based on the RBF-ARX model, an infinite horizon Model Predictive Control (MPC) strategy is proposed to control the LTSIP plant, which is designed by using the locally linearised model obtained from the RBF-ARX model, and obtaining the locally optimal state feedback control law at each control period. Stability of the close loop system is proved. Real-time control experimental results demonstrate that the proposed modelling and control method is effective in modelling and controlling the UFNU system.

KEYWORDS:

• RBF-ARX model
• predictive control
• underactuated fast nonlinear system
• linear two-stage inverted pendulum
• close loop system stability

Acknowledgements

The authors would like to thank the editors and referees for their valuable comments and suggestions, which substantially improved the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 61773402, 51575167, 61540037], the Fundamental Research Funds for the Central Universities of Central South University [grant number 2017zzts132].