A finite time parameter identification method for nonlinear systems is analyzed and applied to identify system parameters of a permanent magnet synchronous motor (PMSM). The identification is done in closed loop and a tracking controller is designed that stabilizes the system and that allows the tracking of a position reference signal. Both, identification and control system, are implemented as a continuous time as well as a discrete time system. State saturation effects that are not covered by the nominal mathematical model of the PMSM pose a major problem on the parameter estimation routine, and different approaches are introduced to tackle this problem. Various test cases are conducted with numerical simulation and the performance of both, parameter estimation and tracking control, is verified.