Permanent-magnet synchronous motor drive (PMSMD) exhibit superior power density and efficiency, yet its highly coupled, parameter-sensitive, and non-linear dynamics challenge traditional linear controllers. This paper presents a complete Lyapunov-based Backstepping controller that are systematically exploits the nonlinear d-q model to obtain globally stable, disturbance-robust, and sensorless-capable current and speed regulators. Magnet Synchronous Motor Drive utilizing the Backstepping control technique, characterized by its recursive and systematic approach for synthesizing nonlinear control laws based on Lyapunov stability theory. The primary aim of this control scheme is to establish a virtual control at each synthesis step, thereby ensuring the convergence of the motor's speed to its desired setpoint and the direct-axis current to zero, which facilitates maximum torque operation. The methodology involves an initial definition of the PMSM's state model within the d-q reference frame, followed by the systematic synthesis of the Backstepping controller. A comparison between Backstepping and Neural Network controller is done in this study. The results obtained demonstrate the superiority of Backstepping approach in meeting the demanding requirements of PMSM drive systems. Simulation results, obtained using MATLAB/Simulink environment, effectively demonstrate the efficacy of the proposed speed control................. Keywords:.................. PMSM drive Model, Backstepping controller, Neural Network controller (NN), Speed control.