The Application Of RBF-ARX Model-based LQR Control In Magnetic Levitation System

At present, the magnetic levitation is a valuable topic, for it has a trait of "zero contact", and advantages of non-friction, non-noise, and non-lubrication, such as maglev train and magnetic bearing. However, the nonlinear and uncertainty of the magnetic levitation make it difficult to be controlled, and a better performance is urgently needed. The RBF-ARX model has provided a new way to cope with a complex nonlinear system. it is a offline identified global model which incorporates the high precision and fast convergence of RBF networks for nonlinear objects and the simple structure and easy application of ARX model. Therefore, by cooperating with some model based algorithm, the RBF-ARX model is perfectly fitting to solve the control problems of complex nonlinear systems. And LQR controller is a simple, easily realized, and model based controller, which requires a state space to compute the optimal control law. So the LQR controller based on RBF-ARX model must have better performance on magnetic levitation. In this paper, a exploration of LQR controller among the physic model, the ARX model, and the RBF-ARX model has been made on the magnetic levitation equipment. The design of RBF-ARX model based LQR controller on magnetic levitation is the focus of this paper, and we hope it can do some thing good for the industrial applications.This paper has several parts, the first is the background and the current development of magnetic system, and the introduction of the magnetic levitation equipment. According to its mechanics, an appropriately simplified linear model is established, then a preliminary analysis is done based on this model, and design a LQR controller based this model. The second is the establishment of the ARX model. The data for the identification is from the PID controlled system at some working point, and a detailed explanation for choosing the system orders, delay and constructing the state space is made as well. As the object is a nonlinear one, so a strategy of adopting a set of linear models at different working points is proposed to extend the region of the controller. At the last is the RBF-ARX model. As a global model, it is identified by a global data, and the SNPOM is used to optimize the model. The SNPOM, proposed by Peng, is a structured nonlinear parameter optimization method, which is an offline calculation using LMM method dealing with the nonlinear parameters and LSM dealing with the linear parameters. The experiment results of RBF-ARX based LQR controller shows a better performance than the former two.