Robust H ∞ control for uncertain nonlinear active magnetic bearing systems via Takagi-Sugeno fuzzy models

Abstract

In this paper, a systematic procedure to design the robust ∞ H 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 ∞ H 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.

System Identification and Robust Control of Multi-Input Multi-Output Active Magnetic Bearing Systems

“…With the growing interest in the applications of fast and precise AMBs, there is a demand for developing advanced controllers that ensure robust performance of such systems in the presence of unmodeled dynamics and unknown external disturbances [9]- [12]. Although several works can be found on the analytical modeling and simulation of robust controllers on AMBs [13]- [16], system identification and real-time robust control of AMBs is a relatively recent development [17]- [26]. However, the results presented in the recent works have many shortcomings to consider this problem as solved.…”

Lokale Stabilitätsanalyse von Takagi-Sugeno Systemen unter Berücksichtigung ihres Gültigkeitsbereichs

“…Insbesondere dem LMI-basierten Stabilitätsnachweis wurde in den letzten Jahren viel Aufmerksamkeit gewidmet. Die Suche nach einer gemeinsamen quadratischen Lyapunov-Funktion stellt dabei einen sehr intuitiven Ansatz dar [2,8,12]. Erweiterungen dieser Methode beruhen auf stückweisen, polynomialen oder Fuzzy-LyapunovFunktionen (siehe [4,9] sowie deren Referenzen).…”

Stabilization of saturated discrete-time fuzzy systems

“…The nonlinear system can be represented by a Takagi-Sugeno (T-S) fuzzy model [20][21][22]. The control design is then carried out using known or recently developed methods from control theory [10,14,17,18,24].…”