An Approach to Fuzzy Modeling of Magnetic Levitation Systems
Radu‐Codruţ David, Claudia‐Adina Bojan‐Dragos, Raul-Gherasim Bulzan, Radu‐Emil Precup, Emil M. Petriu, Mircea‐Bogdan Rădac · 2012
This paper proposes an approach to fuzzy modeling of magnetic levitation systems. These unstable and nonlinear processes are first linearized around several operating points, and next stabilized by a State Feedback Control System (SFCS) structure. Discrete-time Takagi-Sugeno (T-S) fuzzy models of the stabilized processes are derived on the basis of the modal equivalence principle, and the rule consequents contain the state-space models of the local SFCS structures. Optimization problems are defined which aim the minimization of objective functions defined as the squared modeling error considered as the difference between the real-world process output and the fuzzy model output. The variables of the objective functions are represented by a part of the parameters of the input membership functions. Simulated Annealing algorithms are implemented to solve these optimization problems and to obtain optimal T-S fuzzy models. Real-time experimental results validate the fuzzy modeling approach and the new optimal T-S fuzzy models for a Magnetic Levitation System with Two Electromagnets (MLS2EM) laboratory equipment.