I. Introduction
The permanent magnet synchronous machine (PMSM) is used in many applications [1] [2] because it has a high degree of efficiency, can be designed with a high power-to-mass ratio and is low-maintenance. For the controled operation of the PMSM, an inverter as well as a current and angle sensor are required. The inverter has the task of switching the nominal voltages into the respective phase. The current sensors are required to enable both torque-controlled operation and protection of the overall system. The angle sensors are required to convert the stator-oriented currents into a rotor-oriented coordinate system or to determine the phases to be controlled [3]. In addition, the angular velocity can be calculated by differentiating the position with respect to time. The angle sensor can be completely omitted with the help of angle estimation methods [4] [5]. However, an angle sensor is often used because the system can be put into operation easily and a shorter rise time can be achieved. Various measuring principles have been established for angle sensors. Optical angle sensors or Hall effect sensors are most frequently used. The main difference between the two types of sensor is the different resolution that can be achieved, which results in torque ripple when regulating the drive [6] [7]. The torque ripple is derived analytically in the article. Torque-controlled PMSM can do without the optical angle sensor for reasons of cost or space. Instead, they will then be operated with Hall sensors in the stator. With the Hall effect sensors it is possible to operate the PMSM with a conventional field-oriented control or with block commutation. Both types of control have their advantages and disadvantages, which are explained in more detail in the following. Section II describes analytically how the torque of the PMSM can be calculated. The test rigs used are then explained in section III. The results are presented in section IV. At the end follows a small summary of the findings in section V.