<p>Using a integral terminal sliding surface for the first time and a new adaptive Reaching law (NARL), this paper focuses on the design of a new controller for the speed control of a permanent-magnet synchronous motor (PMSM) from the sliding mode family called adaptive integral terminal sliding mode contro (AITSMC), which improves the convergence speed, tracking accuracy, and chattering phenomenon. More specifically, the distance from the sliding surface determines how much of a series of gains in the NARL alter adaptively. In addition to their decreasing value, the adaptive parameters in this Reaching law are also adjusted to minimize the chattering phenomenon as they approach the sliding surface. The adaptive parameters in this Reaching law have a large value when the distance from the sliding surface is large in order to increase the convergence speed. In designing this controller using Lyapunov theory, the finite-time stability condition is satisfied, and another important feature of this controller is that this finite-time is computationally feasible. In this regard, by adjusting the controller parameters, this convergence time can also be predetermined and calculated. A number of real-world tests on a PMSM motor have been carried out in the laboratory to examine the performance of the suggested approach, and the results have been contrasted with those of the traditional sliding method. In this sense, the outcomes validate the efficacy and outstanding performance of the suggested approach in decreasing chattering and accelerating convergence.</p>