Fuzzy Modeling and Control for Conical Magnetic Bearings Using Linear Matrix Inequality

A general nonlinear model with six degree-of-freedom rotor dynamics and electromagnetic force equations for conical magnetic bearings is developed. For simplicity, a T–S (Takagi–Sugeno) fuzzy model for the nonlinear magnetic bearings assumed no rotor eccentricity is first derived, and a fuzzy control design based on the T–S fuzzy model is then proposed for the high speed and high accuracy control of the complex magnetic bearing systems. The suggested fuzzy control design approach for nonlinear magnetic bearings can be cast into a linear matrix inequality (LMI) problem via robust performance analysis, and the LMI problem can be solved efficiently using the convex optimization techniques. Computer simulations are presented for illustrating the performance of the control strategy considering simultaneous rotor rotation tracking and gap deviations regulation.