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To improve the performance of the conventional sliding mode speed observer at low-speed, a speed observer based on the techniques of modified exponent-approaching sliding mode control and extended Kalman filter is proposed. To simplify the algorithm of the voltage space vector modulation for three-level inverter, a simple modulation method with a minimum amount of harmonic distortion is studied in detail. Aimed at the nonlinear characteristics of a PMSM, a feasible nonlinear control scheme based on the fuzzy neural network technique is presented and the stability of the speed control system is proved. The simulation results confirm that the proposed cascade speed observer is a favorable state observer and can achieve the desired speed tracking objective under a wide-speed range. The output waveforms of the inverter voltages illustrate that the proposed modulation algorithm is effective and the neutral-point voltage is balanced. In contrast with the conventional backstepping controller, the developed nonlinear speed controller is robust to the uncertainties, which consists of a RFNN controller and an adaptation law controller.