The Electric Dynamic Load Simulator plays a substantial role in testing electromechanical systems. But the torque control remains challenging due to nonlinear dynamics and disturbances. Conventional methods inherently face dimensional limitations, resulting in challenges such as slow response times, steady-state errors, and difficulty in tuning. Furthermore, the performance of other traditional algorithms heavily relies on the parameters of the weight function, often necessitating repetitive processes for convergence. These methods also demand large volumes of data for effective training, further complicating their application in dynamic environments. To overcome these challenges, we first developed a Super-Twisting Terminal Sliding Mode Control approach, then enhanced it to the Modified Super-Twisting Terminal Sliding Mode Control. This enhanced approach features following advancements: fractional-power terminal sliding surface for finite-time convergence, exponential gain scaling to reduce chattering, thereby being much faster and more robust than conventional STA. The suggested controllers (ST-TSMC and MST-TSMC) show better performance than traditional methods at both step response and sinusoidal tracking. In step response, the rise time of ST-TSMC (0.066 s) is 75 % faster than that of PID (0.27 s) and 53 % faster than Super-Twisting Integral Sliding Mode Control (0.14 s). MST-TSMC (0.029 s) further improves this to 89 % and 79 % faster, respectively. For sinusoidal tracking, ST-TSMC reduces error by almost 99.6 % compared to PID and by 90.5 % compared to STISMC. The improved MST-TSMC achieves even better performance, further reducing errors compared to ST-TSMC and minimising chattering to enhance stability.