## 4 Experimental Results  
This section presents the experimental results obtained by operating the ultrasonic system at the estimated mechanical resonant frequency of the piezo element using the LSTM model. Figure 15 shows the experimental environment and configuration. The configuration consists of a control board, a power board, a piezo element, and a pressure press system for applying the user's desired pressure to the piezo element. The press system for applying pressure to the piezo element is designed to detect pressure in real time using a strain gauge and to apply pressure in the vertical direction to the piezo element. Through this, conditions for always applying a constant pressure to the piezo element can be created, and the variation in the procedure can be minimized for analysis. Figure 16 shows the actual system operation results on the relationship graph between the resonant frequency of the ultrasonic system and the mechanical resonant frequency of the piezo element. In the graph, the x-axis represents the entire system resonant frequency at the ultrasonic system output stage and the y-axis represents the mechanical resonant frequency of the piezo element. The red points within the graph indicate the mechanical resonant frequencies of the piezo element at different system resonant frequencies under various applied pressures, ranging from 0 g to 5000 g in 250 g increments. The waveform  
below corresponds to a pressure of 1000 g. The control algorithm is divided into three modes: Mode 1, the initial operation stage, applies PWM switching at the designed resonant frequency of the piezo element. Mode 2 detects the system resonant frequency using a frequency detection circuit and calculates the mechanical resonant frequency of the piezo element. Mode 3 operates at the calculated mechanical resonant frequency of the piezo element. The transitions between modes are confirmed using a trigger signal. The following presents the experimental waveforms at the input stage of the piezo element. The control algorithm's three stages were verified during the experiment. Figure 17 shows the initial 31.95 kHz PWM switching operation in Mode 1 and the operation transition to Mode 2, demonstrating the phase difference between the voltage and current of the piezo element in both modes. Figure 18 shows the transition from Mode 2 to Mode 3. Near the end of the system resonant frequency detection in Mode 2, the voltage and current phases of the piezo element appear almost aligned, indicating the transient state rather than the actual mechanical resonant frequency. Figure 19 illustrates the stable switching at the calculated frequency in Mode 3 based on the LSTM model's estimated mechanical resonant frequency of the piezo element and the detected system resonant frequency of 31.221 kHz from Mode 2. Comparing the LSTM model's estimated data in Figure 20, the mechanical resonant frequency of the piezo element was accurately estimated to be 30.618 kHz. Figure 16: Actual system operation results in the resonant frequency relationship graph. Figure 15: Ultrasonic system experimental environment and configuration. Figure 19: Operation waveform 3 (piezo element voltage, current waveform). Figure 17: Operation waveform 1 (piezo element voltage, current waveform). Figure 18: Operation waveform 2 (piezo element voltage, current waveform). The above experimental results show that the method using the LSTM model is more efficient than the existing frequency tracking method (the method using PLL). PLL is basically well suited to linear systems, and the accuracy may decrease when the system has strong nonlinearity. On the other hand, LSTM can learn complex temporal dependencies, including nonlinearity, so it can better model the complex response of the piezo element. In addition, as shown in the analysis results in Chapter 2 of this study, a piezo element can have multiple resonance modes in addition to one mechanical resonance frequency.