In this paper, a novel methodology of nonlinear control is used, and a passivity-based control of contractive port-controlled Hamiltonian (PCH) systems is applied to a permanent magnet synchronous motor (PMSM). This methodology, also called “tIDA-PBC” (Trajectory Injection and Damping Assignment—Passivity-Based Control), uses passivity-based control of PCH systems “IDA-PBC” and exploits the properties of contractive Hamiltonian systems, resulting in a closed loop with its contractive system desired dynamics, thus obtaining an exponential trajectory tracking without relying on the error coordinates. In this system, a few steps are proposed in order to divide and modularize the methodology so it can be redesigned or reapplied in other systems by the reader. First, we define the model and set the way to solve the “matching equation.” Then the feasible and reference trajectories are obtained. After that, the desired Dirac structure and energy function are set in order to meet the methodology requirements. Finally, the control law is obtained, and simulations were performed. The desired trajectories (which can be time varying) are arbitrarily set, and the exponential convergence to the desired trajectories is archived. The results obtained from the simulations are an initial approach to the improvement of propulsion algorithms in electrified vehicles, where linear controls are still used and have poor performance compared to the visited methodology.