Abstract
An integral state feedback control method based on T-S fuzzy model is proposed for nonlinear and unstable magnetic levitation ball system in this paper. Firstly, the fuzzy model of the magnetic levitation ball is derived from the nonlinear dynamic model by using the sector nonlinearity, and the local controller is designed by using the integral state feedback control. The global controller is constructed by a parallel distributed compensation (PDC) method, and the feedback gain is obtained using a linear matrix inequality (LMI). Finally, the integrated state feedback controller is applied to the position control of the magnetic levitation ball system, and a dSPACE real-time control platform is established for experimental research. The simulation and experiment are performed to prove that the designed controller can levitate the ball stably, and has better control performance.
Highlights
Magnetic levitation technology applies magnetic force to overcome gravity to suspend a magnetic object
In the research of magnetic levitation technology, the single-degree-of-freedom magnetic levitation ball system is a simplification of other complex magnetic levitation systems
Based on the analysis of the structure and working principle of the magnetic levitation ball system, the T-S fuzzy model of the system is established for the nonlinear characteristics of system
Summary
Magnetic levitation technology applies magnetic force to overcome gravity to suspend a magnetic object. In [16], A fuzzy H∞ robust state feedback controller for magnetic levitation systems is designed based on parallel distribution compensation (PDC) design method and the proposed T-S model. In [17], a switched fuzzy controller is proposes and a magnetic levitation system is modeled by two self-organizing neural–fuzzy techniques to achieve linear and affine Takagi–Sugeno (T–S) fuzzy systems(more freedom than linear T-S model). Based on the T-S fuzzy model, a parallel distributed compensation (PDC) method is applied to design the integral state feedback controller, and the stability of the control algorithm was proved using Lyapunov’s theorem. The experimental device controls the movement or suspension of the ball in the vertical direction by adjusting the current in the coil of the electromagnet
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