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

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.