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.

To research the chaotic motion problem of the direct-drive permanent magnet synchronous generator (D-PMSG) for a wind turbine with uncertain parameters and fractional order characteristics, a control strategy established upon fuzzy state feedback is proposed. Firstly, according to the working mechanism of D-PMSG, the Lorenz nonlinear mathematical model is established by affine transformation and time transformation. Secondly, fractional order nonlinear systems (FONSs) are transformed into linear sub-model by Takagi–Sugeno (T-S) fuzzy model. Then, the fuzzy state feedback controller is designed through Parallel Distributed Compensation (PDC) control principle to suppress the chaotic motion. By applying the fractional Lyapunov stability theory (FLST), the sufficient conditions for Mittag–Leffler stability are formulated in the format of linear matrix inequalities (LMIs). Finally, the control performance and effectiveness of the proposed controller are demonstrated through numerical simulations, and the chaotic motions in D-PMSG can be eliminated quickly.