|Robust H∞ Control for Uncertain Nonlinear Active Magnetic Bearing Sys-tems via Takagi-Sugeno Fuzzy Models
Dong Hwan Lee, Jin Bae Park, Young Hoon Joo*, Kuo Chi Lin, and Chan Ho Ham
International Journal of Control, Automation, and Systems, vol. 8, no. 3, pp.636-646, 2010
Abstract : In this paper, a systematic procedure to design the robust fuzzy controller for a nonlinear active magnetic bearing (AMB) system affected by time-varying parametric uncertainties is presented. First, the continuous-time Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear AMB system. Next, based on the obtained fuzzy model, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for robust stability and performance of the control system. The main feature of this paper is that some drawbacks existing in the previous approaches such as truncation errors and nonconvex bilinear matrix inequality (BMI) problem are eliminated by utilizing the homogeneous fuzzy model which includes no bias terms in the local state space models rather than the affine one which includes bias terms. Hence, the design method presented here will prove to be more tractable and accessible than the previous ones. Finally, numerical simulations demonstrate the effectiveness of the proposed approach.
Keyword : Active magnetic bearing (AMB), fuzzy controller, linear matrix inequality (LMI), robust performance, Takagi-Sugeno (T-S) fuzzy models.