A modeling and control approach to magnetic levitation system based on state-dependent ARX model

• Data-driven modeling technique is used to model a Maglev ball system.
• State-dependent ARX(SD-ARX) model can globally characterize the nonlinear, unstable and fast-response Maglev system.
• SD-ARX model-based predictive controller can realize real-time control of the Maglev ball.
• SD-ARX-MPC may attain better control performance in a wide range than other methods.
• For the first time, this method is successfully applied to a fast response system.

Magnetic levitation (Maglev) systems are usually strongly nonlinear, open-loop unstable and fast responding. In order to control the position of the steel ball in a Maglev system, a data-driven modeling approach and control strategy is presented in this paper. A state-dependent AutoRegressive with eXogenous input (SD-ARX) model is built to represent the dynamic behavior between the current of electromagnetic coil and the position of the ball. State-dependent functional coefficients of the SD-ARX model are approximated by Gaussian radial basis function (RBF) neural networks. The model parameters are identified offline by applying the structured nonlinear parameter optimization method (SNPOM). Based on the model, a predictive controller is designed to stabilize the magnetic levitation ball to a given position or to make it track a desired trajectory. The real-time control results of the proposed approach and the comparisons with other two approaches are given, which demonstrate that the modeling and control method presented in this paper are very effective and superior in controlling the fast-responding, strongly nonlinear and open-loop unstable system. This paper gives the real experimental evidence that the RBF-ARX model is capable of not only globally, but also locally capturing and quantifying a nonlinear and fast-response system's behavior, and the model-based predictive control strategy is able to work quite well in a wide working-range of the nonlinear system.