## 5 Results and Discussion
### Static Performance of Piezoelectric Actuator System  
The first discrete value of the piezoelectric actuator system stroke, \(x_{\text{pa}}\), is achieved by activating a single PE (Table 3 and Figure 10, Case 1--activation of PE1, PE2, or PE3). In all three scenarios, the average stroke is 29.3 microns (at steady state), with no significant effect under which PE is activated. Based on 10 tests for each PE, the standard deviation of the piezoelectric actuator stroke remains within 1%. Activating two PEs (Table 3 and Figure 10, Case 2) results in an average stroke of 52.7 microns, while activating all three PEs (Table 3 and Figure 10, Case 3) yields an average stroke of 71.2 microns. The actuator stroke is noticeably smaller than the free displacement of an individual PE (\(x_{\text{free}}=46.7~{}\upmu\)m). According to the variable load applied to the piezoelectric stack actuator and the operating principle presented in Figure 3 and Equation (8), these results are expected and align with the theoretical curve shown in Figure 5. The actuator system displacement (stroke) decreases linearly as preload increases. Additionally, the minor contraction of inactive PEs, caused by their stiffness (less than one micron per PE), contributes to the overall reduction. Inactive PEs act as elastic bodies with a high stiffness affected by the external load generated by the active PE. The piezo effect, used in sensor technology, is clearly demonstrated by analyzing the electrical voltage curves shown in Figure 11. Seven different combinations of active piezo stacks are analyzed in detail. Figure 9: Step response of a second-order system. The first three scenarios, presented in Figure 11a-c, show one active PE. The high electrical voltage overshoot observed on PE2 (Figure 11a, UPE2) can be attributed to its proximity to the active PE3, where it is influenced by the high axial force generated by the actuator system's response. Activating PE2 or PE3 results in a lower electrical voltage overshoot at the inactive PE1. This can be explained by the fact that PE2 affects both PE1 and PE3, distributing the generated force between them. The maximum electrical voltage measured at the inactive PEs remains consistent across all three scenarios, at around 80 \(\pm\) 5 V. Similar explanations apply to other scenarios where two or three PEs are activated. When two PEs are active, shown in Figure 11d-f, the measured electrical voltage is higher, around 100 \(\pm\) 5 V in the stationary state. This is because two active PEs provide a greater stroke of the piezoelectric actuator system (greater extension of PEs), resulting in a higher pretension in the disc spring unit and consequently, a higher axial force acting on the system. A detailed analysis of the three-active-PE scenario reveals two regions of electrical voltage increase. The first region shows an increase in voltage up to 100-120 V, followed by a decrease. The second region represents an additional voltage increase up to the maximum value of 200 V. We believe this intermediate phenomenon is due to the high generated piezo force (blocking force) observed at the beginning of piezo actuator activation before the extension begins. With the appropriate piezo electronics and a combination of pulse number modulation (PNM) and pulse width modulation (PWM), the number of discrete values for the piezoelectric actuator system stroke can be increased. Operating with a base signal width of 10 \(\upmu\)s allows us to create a 5 V control signal ranging from 10 \(\upmu\)s to 1000 \(\upmu\)s, with increments of 10 \(\upmu\)s. The PWM signal width directly affects the activation of high-response switches in the high-voltage electronics, thereby increasing the control voltage applied to the piezo stacks.