*Result*: FINITE-TIME NONLINEAR SPEED CONTROLLER OF PERMANENT MAGNET SYNCHRONOUS MOTOR USING C MEX S-FUNCTION.

*Permanent magnet synchronous motor (PMSM) has high torque and possesses a simple structure relative to its capacity. It has been popularly applied in numerous industrial applications. Nonetheless, PMSM is sensitive to both internal and external disturbances. It exhibits significant nonlinearity and functions as a multi-variable coupling system. Therefore, a control system capable of delivering superior performance must be nonlinear. Owing to its considerable robustness capability, the sliding-mode control (SMC) technique is extensively utilized in this research. This work also demonstrates the use of C Mex S-function, the most efficient code-oriented tool, to simulate the operation of nonlinear systems. The C-Mex S-function is an effective and practical approach for developing models within the SIMULINK/MATLAB user interface environment and utilizing its requisite capabilities. Consequently, the nonlinear controller established in this study is carried out via the C-Mex S-function. Let's manipulate the characteristics of the PMSM to converge to equilibrium within a finite time period. The tracking speed signal can be quickly followed with a high robustness against disturbances, uncertainties, and unmodeled variables. In addition, the Lyapunov function is employed to assess the stability of the developed SMC controllers, whereby the stable convergence property is demonstrated and proven. To illustrate the performance of the continuous fast-terminal sliding-mode control scheme, some simulation tests are performed on the speed regulation of the PMSM drive plant. The simulations are presented as code resembling the C programming language within SIMULINK/MATLAB. The findings show that the proposed controller achieves a speed overshoot of less than 3%, a settling time of approximately 0.15 seconds, and a steady-state error of less than 0.5 rad/s under a load torque of 1.5 Nm. These results highlight the high performance and robustness of the proposed speed controller. [ABSTRACT FROM AUTHOR]*