## 3 Piezoelectric Actuator System Design  
The main idea of the piezoelectric actuator-sensor system presents the use of three piezoelectric stack actuators placed in series to achieve the desired maximum stroke, several discrete strokes, an improved stroke resolution, and the ability to sense the actuator behaviour. The idea is to combine the piezo and inverse piezo effect, thus achieving the functionality of the actuator-sensor system. As noted in [19], the partially failed piezoelectric stack actuators may have a major impact on actuator performance and can be detected during the operation by monitoring their static and dynamic behaviour. The concept, shown in Figure 4a, is employed as a piezoelectric actuator-sensor system in hydraulic on/off valves integrated into a four-way digital fluid control unit (4 WDFCU). The piezoelectric actuator system assembly, as shown in Figure 4b and its real picture in Figure 4c, consists of the following components: (1) a screw cap that provides a proper preload for the piezo stacks, (2) a spacer combined with a ball bearing to eliminate torsion, (3) an actuator housing, (4) a flange for installation in the hydraulic valve, (5) disc springs, and (6) a control piston and piezo element (PE). All the main steel parts of the actuator system (components 1, 2, 3, and 6) have been analyzed using the finite element method (FEM) to ensure the construction achieves a longitudinal deformation of less than one micron during operation. The actuator housing, combined with disc springs and a control piston, facilitates the proper installation of the piezo elements. Using three piezoelectric elements (PEs) within a single actuator system allows for at least three discrete actuator stroke values, which is crucial for managing production costs and ensuring a high response rate when charging individual PEs. As mentioned, the non-activated PEs serve as sensors to monitor the PEs and the actuator system by measuring the electric voltage, which results from the extension of the active PEs and the generated force acting as an external load on the non-activated PEs. Digital fluid control units typically consist of multiple on/off valves arranged in parallel, meaning several valves and actuators must be used to achieve multiple discrete output values (in the case of hydraulic actuators, the output value is the actuator stroke, which directly corresponds to the valve flow rate). The main characteristics of the piezoelectric stack actuator used in this investigation are presented in Table 1. It is made from SONOX P505 material and manufactured by CeramTec [14]. The key static performance characteristics include dimensions (cross  
Figure 4: Concept of piezoelectric actuator system (**a**), cross-section view of serial-connected piezo elements (PE) (**b**), and real picture of piezoelectric actuator system (**c**). section of 7 \(\times\) 7 mm and effective height of 32.4 mm), the maximum free displacement (approximately 0.15% of the effective height), blocking force (2 kN), and the maximum control voltage (200 V). The actuator's dynamic performance is defined by its electrical capacitance and resonant frequency. The preload for the piezoelectric stack actuator is achieved using the screw cap, as shown in Figure 4b, position 1. The second important component of the piezoelectric actuator system is the disc spring unit, which provides the necessary initial preload for the piezoelectric elements (PEs). The disc spring unit deflects when the PEs are activated, as shown in Figure 4b, position 5. Table 2 presents the theoretical characteristics of a single disc spring (Value 1) and the measured characteristics of the disc spring unit (Value 2) used in the piezoelectric actuator system [20]. Three single disc springs are arranged in series to achieve the appropriate stiffness for the disc spring unit. The assembly of the disc springs was conducted under dry conditions (cleaned and dried discs) with no lubrication added between the discs.