Application Cases

Experiment Name: Spatial Vibration Suppression Experiment Based on Piezoelectric Ceramic Actuators

Experimental Principle:
Taking the z-axis rotational degree of freedom of the vibration suppression system prototype as an example, as shown in Figure a, when the upper movable plate is subjected to a torque $M_{33z}$ around the z-axis, it generates a tilt angle ${\theta }_{33z}$. The magnitude and direction of this tilt angle depend on the magnitude and direction of $M_{33z}$. When $M_{33z}$ is positive, ${\theta }_{33z}$ is positive. Since piezoelectric ceramics can only output thrust, a voltage should be applied to piezoelectric ceramic actuator No. 1 (PZT1) to compensate for this tilt angle and restore the upper movable plate to its horizontal position. Conversely, when $M_{33z}$ is negative, ${\theta }_{33z}$ is also negative, and a voltage should be applied to piezoelectric ceramic actuator No. 3 (PZT3) to compensate for the tilt angle and restore the upper movable plate to its horizontal position. Therefore, although only a single degree of freedom is controlled, it is a two-input, two-output system. The inputs are $M_{33z}$ and ${\theta }_{33}$ (measured as linear displacement in actual experiments), and the outputs are the voltages applied to PZT1 and PZT3. Only one of these two piezoelectric ceramic actuators can be powered at any given time.

Figure a: Schematic Diagram of System Vibration Suppression Principle (Example of z-axis rotational degree of freedom)

The experimental block diagram of the vibration suppression system is shown in Figure b. The host computer uses LabVIEW for data acquisition program development and fuzzy self-tuning PI control algorithm programming. The lower computer uses NI cRIO 9038 (with built-in analog voltage input modules NI 9205 and NI 9215) to read and collect data from four displacement sensors and a six-axis force sensor. Communication between the host computer and the lower computer is established via Ethernet. The DC servo motor generates an external torque acting on the vibration suppression system prototype, causing a deflection of a certain amplitude. The six-axis force sensor collects the magnitude and direction of this external torque in real time, while the four displacement sensors detect the displacement corresponding to the deflection angle. The data is collected in real time by the NI cRIO 9038, processed appropriately, and subjected to the corresponding control algorithm to determine the voltage value that the piezoelectric ceramic actuator at the corresponding position should output. This voltage value is transmitted to the host computer program via Ethernet. The host computer program then sends the voltage value to the ATA-2161 voltage amplifier via USB communication. The voltage is ultimately applied to the piezoelectric ceramic actuator of the vibration suppression system prototype to correct the deflection, thereby achieving the goal of active vibration suppression.

Figure b: Experimental Block Diagram of the Vibration Suppression System

Testing Equipment:
Host computer, ATA-2161 voltage amplifier, NI cRIO 9038, displacement sensors, force sensors, actuation system prototype

Experimental Procedure:

(1) 10 N·m Dynamic External Torque Vibration Suppression Experiment
Dynamic torque loading device applies dynamic torques with an amplitude of approximately 10 N·m (peak-to-peak value about 20 N·m) and frequencies of 0.5 Hz, 1 Hz, and 2 Hz to the mechanism. The resulting system vibration suppression performance is shown in Figure c. It should be noted that due to the limited performance of the DC servo motor used, the generated dynamic torque is not an ideal sinusoidal torque over time and exhibits some distortion and bias. However, since this experiment focuses on vibration suppression, this does not significantly affect the results.

Figure c: 10 N·m Dynamic External Torque Vibration Suppression Experiment
(a) 0.5 Hz external torque
(b) 1 Hz external torque
(c) 2 Hz external torque

(2) 20 N·m Dynamic External Torque Vibration Suppression Experiment
Similarly, dynamic torques with an amplitude of approximately 20 N·m (peak-to-peak value about 20 N·m) and frequencies of 0.5 Hz, 1 Hz, and 2 Hz are applied to the mechanism using the dynamic torque loading device. The experimental results for system vibration suppression performance are shown in Figure d.

Figure d: 20 N·m Dynamic External Torque Vibration Suppression Experiment
(a) 0.5 Hz external torque
(b) 1 Hz external torque
(c) 2 Hz external torque

Experimental Results:
Comprehensive analysis indicates that the maximum frequency of external torque that the vibration suppression system designed in this study can suppress does not exceed 2 Hz. To achieve better vibration suppression, the ideal operating condition is when the external torque amplitude is less than 20 N·m and the frequency is less than 1 Hz. Under these conditions, a vibration suppression rate higher than 64% can be achieved. Additionally, at the same frequency below 2 Hz, the vibration suppression effect is better when the external torque amplitude is 10 N·m compared to 20 N·m. This suggests that the vibration suppression effect is relatively better when the external torque amplitude is smaller.

The experimental results also show that the vibration suppression effect is poorer when the external torque switches between positive and negative values. This is likely related to the control strategy used. Since the actuation of the two piezoelectric ceramic actuators controlling a single degree of freedom depends on the direction of the external torque, the torque changes rapidly during this phase. Moreover, due to the limited accuracy of the sensors used, the system requires a certain amount of time to switch when the direction of the external torque changes and cannot achieve optimal performance quickly. This becomes particularly evident as the frequency of the external torque increases.

Figure: Specifications of the ATA-2161 High-Voltage Amplifier