# Development of Piezoelectric Inertial Rotary Motor for Free-Space Optical Communication Systems
## 4 Experimental Investigation of Motor
Experimental measurements of the angular resolution of the motor were performed using a non-contact displacement sensor optoNCDT 1420 (Micro-Epsilon, Ortenburg, Germany). The burst-type sawtooth excitation signal consisting of 15 cycles at the resonance frequency of the motor during a 750 ms one-step time period was used. These excitation parameters were indicated experimentally, i.e., it was indicated that 15 cycles are the minimal number of cycles necessary to obtain angular motion at 40 V\({}_{\text{p-p}}\) excitation signal amplitude, while 750 ms is the shortest time range which is necessary for proper displacement capture by the optoNCDT 1420 (Micro-Epsilon, Ortenburg, Germany) sensor. Therefore, these parameters were used to drive the motor while this arrangement of the excitation signal ensures a stable stepping-motion mode of the motor. The results are depicted in Figure 18.  
In the first range (40-100 V\({}_{\text{p-p}}\)) in Figure 18a, the motor demonstrated a clear stepwise motion pattern, with the maximum angular displacement of 9.85\({}^{\circ}\) observed at 100 V\({}_{\text{p-p}}\). This corresponds to a displacement-voltage amplitude of 26.9\(\cdot\) 10\({}^{-3\circ}\)/V\({}_{\text{p-p}}\). At the lowest excitation voltage of 40 V\({}_{\text{p-p}}\), the motor's angular displacement was much lower, reaching 0.22\({}^{\circ}\), corresponding to a displacement of 5.5\(\cdot\)10\({}^{-3\circ}\)/V\({}_{\text{p-p}}\). This result confirms that the motor's displacement resolution is directly proportional to the excitation voltage, with higher voltages leading to greater angular displacements. The stepwise nature of the motor's angular motion, as depicted in the graph, shows that each step corresponds to a specific angular displacement achieved by the motor at each voltage level. This precise control over angular displacement is critical for applications requiring fine positioning adjustments, such as satellite orientation or free-space optical (FSO) communication systems. In the second range (120-180 V\({}_{\text{p-p}}\)) in Figure 18b, the motor performance continued to show a proportional increase in displacement with increasing excitation voltage. At 120 V\({}_{\text{p-p}}\), the angular displacement reached approximately 22\({}^{\circ}\), increasing incrementally with voltage, up to a maximum of around 34\({}^{\circ}\) at 180 V\({}_{\text{p-p}}\). The linear and consistent stepping behavior across this voltage range indicates that the motor maintains stable and predictable performance under higher excitation conditions. The resolution at higher voltages also confirms that the motor can be fine-tuned for tasks that require larger angular motions while still retaining precise control. These data suggest that the piezoelectric inertial motor is capable of delivering highly controlled angular displacements across a wide range of voltages. At lower excitation voltages, the motor is suitable for applications requiring very fine, precise movements, whereas at higher voltages, it can achieve larger angular displacements for tasks that require more significant motion. The consistency of the stepwise motion at different voltage levels is particularly important for space applications where accuracy and predictability in motion control are paramount. The next stage of the experimental investigation focused on determining the stall torque of the motor under different excitation voltages. Measurements were performed with PCE DFG N10 (PCE Instruments UK Ltd., Meschede, UK). The results of the measurements are given in Figure 19.  
Figure 15.0 Angular motion resolution under different excitation signal amplitudes: (**a**)—in range from 40 V\({}_{\text{p-p}}\) to 100 V\({}_{\text{p-p}}\); (**b**)—in range from 120 V\({}_{\text{p-p}}\) to 180 V\({}_{\text{p-p}}\). As shown in Figure 19, the stall torque increases proportionally with the excitation voltage.