H∞ Robust Control for Chaotic Motion of the Fractional-Order D-PMSG via the PDC Approach

Abstract

The stability analysis and controller design problems for the fractional-order (FO) direct-drive permanent magnet synchronous generator (FOD-PMSG) wind turbine with parameter uncertainties and external disturbance are addressed. Takagi–Sugeno (T-S) model is used to approximate nonlinearities, and the parallel distributed compensation (PDC) technique is employed to construct the fuzzy state feedback controller. In order to suppress the external disturbance more effectively, the global Mittag-Leffler stability definition satisfying the H∞ performance index is proposed for the first time. Using the FO Lyapunov direct method, applying the Cauchy matrix inequality (CMI), and combining with the Schur complement lemma, the sufficient conditions of Mittag-Leffler stability meeting the H∞ performance index are given in the form of linear matrix inequalities (LMIs). Simulation results clearly show that the proposed control scheme can make the system get rid of the chaotic state quickly and have strong robustness under parameter uncertainties and external disturbance varying randomly.

Design and Implementation of a Novel Intelligent Strategy for the Permanent Magnet Synchronous Motor Emulation

“…Nowadays, combined fuzzy neural methods with sliding mode control [4,5], inverse control [6], robust control [7], H ∞ [8], adaptive estimator [9], etc. to control the speed and position of the permanent magnet synchronous motor are widely used.…”