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To enhance system reliability and to reduce the cost and complexity, this paper presents an efficient wind-speed estimation method and a sensorless rotor-position/speed control method for a surface-mounted permanent-magnet synchronous generator (SPMSG)-based variable-speed direct-drive wind-energy conversion system (WECS). In this regard, sliding mode control (SMC) based on a linear matrix inequality (LMI) is proposed to estimate the rotor position of an SPMSG. This method depends on measured electrical quantities, such as stator voltages and estimated stator current error, to evaluate the back electromotive force components, which are used to estimate the rotor position. The rotor speed is assessed according to the rate of change of the estimated rotor position. The wind speed is estimated by estimating the backpropagation power flow according to the nonlinear dynamical power wind-speed characteristics of the wind turbine. In estimating the rotor position, the proposed LMI-based SMC design provides good steadystate and dynamic performances under all operating modes of the WECS. The proposed control schemes are validated by simulating a test system, i.e., a 250-kW SPMSG-based WECS, in MATLAB/Simulink. The results confirm the effectiveness and correctness of the designed control schemes in estimating and tracking the actual rotor position/speed and wind speed with trivial errors.INDEX TERMS Back electromotive force (BEMF), linear matrix inequality (LMI), sensorless control, sliding mode control (SMC), surface-mounted permanent-magnet synchronous generator (SPMSG), windenergy conversion system (WECS).

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