State-dependent ARX Model-based Predictive Control Applied To Magnetic Levitation System

Magnetic levitation technique has been widely applied into many engineering systems such as frictionless bearings and high-speed maglev trains, because of its contactless, low noise and low friction characteristics. For improving the control performance of maglev system, the maglev ball system is often used as one of important experimental platforms, which is a kind of typically nonlinear and open-loop unstable system. Its modeling and control strategies have received a great deal of attention around the world.In order to control the position of a steel ball in the maglev system, two model structures, which can be categorized into State-dependent ARX model, and predictive control strategies are presented in this paper.Firstly, an RBF-ARX model that is composed of Gaussian radial basis function (RBF) neural networks and the state-dependent AutoRegressive with eXogenous (ARX) model structure, is built to represent the dynamic behavior between the current of electromagnetic coil (input) and the position of ball (output). Furthermore, a predictive control method based RBF-ARX model has been applied into the maglev ball system, which exhibits a smaller overshoot, shorter adjustment time comparing with the predictive control based on ARX model (ARX-MPC) and classic PID control. The highlight is that the predictive control based on RBF-ARX model (RBF-ARX-MPC) has already successfully been applied into some slow-response systems, but not yet in a fast-response system, like maglev ball system (control period:5ms). This is the first time that a predictive controller based RBF-ARX model has been successfully applied into a real-time control of a fast-response system.Secondly, a newly proposed model structure, LLRBF-AR model, employs a set of local linear radial basis function networks (LLRBF) and SD-AR (State-Dependent AutoRegressive) model and has better prediction accuracy than the previous RBF-AR model. But still, no one has successfully apply it into a real-time control system. So I creatively develop it into a model structure with eXogenous input, namely LLRBF-ARX model-a new type of State-dependent ARX model. And it innovatively has been tentatively applied into the control of the magnetic levitation system.Thirdly, for capturing and quantifying the system’s nonlinearity, the position of ball is used as a state variable index to make the RBF-ARX model and LLRBF-ARX model parameters vary with system behavior. The model parameters are identified offline by applying the structured nonlinear parameter optimization method (SNPOM). Because a locally linear ARX model can be easily obtained from the off-line identified RBF-ARX model and LLRBF-ARX model, the locally linear model-based predictive controller with a computational burden that is small enough to allow for real-time implementation can be designed to control the underlying nonlinear and fast-response system. Effectiveness of the presented modeling and control methods are demonstrated by the simulation control and real-time control results on the maglev ball system.