## 1 Introduction  
Machine condition monitoring currently arouses great interest among researchers and a widely defined industry. In modern industrial applications, the aim is to ensure the highest possible level of safety. Control structures are equipped with automatic diagnostics systems. The elements whose failure can lead to a catastrophe include electric motors. Currently, the most popular in this group are permanent magnet synchronous motors (PMSM). The control system, in the case of PMSM, requires stator currents and rotor speed sensors. Those sensors allow for the stable operation of the drive system in a wide range of speed changes. Particularly important is the position/speed sensor. Determining the position of the shaft is necessary to control the PMSM. For this reason, the diagnostics of measuring sensors are as important as the diagnostics of other motor components [1]. In the PMSM drive system for speed measurement resolvers, encoders and tachometric sensors are mostly used. Damage to these types of elements may be divided into four main categories [2]:* Intermittent or total loss of signal;
* Constant fault, where the measured signal takes a constant value, despite the motor rotation (the error may result from malfunctioning electronics or data acquisition system);
* Gain fault, where the measured signal is reduced or amplified in relation to the real value (error due to inappropriate scaling);
* Signal interference (in the case of the resolver and tachometer sensor, these are measurement noises appearing in analog signals, while in the encoder, such disturbances may arise during the cyclic loss of pulses). In the subject of damage to the speed sensor in the drive system with an electric motor, mainly one approach is described. State variable observers and comparative diagnostics are used. The estimated signal is compared with the measured value. When the difference between the estimated and measured value exceeds a certain constant, the detector indicates a failure, and the system is switched to a sensorless operation based on the estimated value [3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. Most of the works describe only simulation results. This is due to the fact that even a short loss of the correct measurement of the shaft position can lead the system out of stability. An example of such work is [2]. The authors proposed the detection of speed sensor damage using the high-order sliding mode observer. Simulation results are shown for several speed values, with the system under load, for two types of failures--constant fault and measurement noise. In the case of constant fault, detection with a significant increase in speed is shown; the reaction of the detection system to small changes in speed is unknown. During measurement noise, the detector pulses, which can be difficult to interpret in a practical application. Paper [3] also presents the simulation results for a detection mechanism of the same type, but only the constant fault failure was considered, and the Unknown input observer was used to estimate the speed. A slight modification of this approach is presented in [4]. Comparing the measured and estimated values was also applied for damage detection. In this case, the extended Kalman filter (KF) was used. The modification is switching the controller after a failure occurrence to a fuzzy logic controller. The simulation results show that during a small discrepancy between the measured and estimated speeds caused by a failure, the system can operate with a robust controller and does not require switching to sensorless mode. In the literature, it is also possible to find works using other types of estimators, such as model reference adaptive system (MRAS) [12] and the Luenberger observer (LO) [9]. The main disadvantage of the described solutions is the lack of experimental research. The use of other types of methods is shown in single articles. In [13], detection is based on the park current vector (PCV). This solution allows to detect the loss of the measurement signal.