**3.4. Results**

688 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**Figure 6.** Implementation diagram for analog proportional velocity feedback controller

**Figure 7.** Experimental setup for active vibration and noise reduction

The experimental setup for active vibration control via analog velocity feedback controller is presented in Fig. 7 with the data acquisition system. The data acquisition system has the ability of generation and recording analog voltage signal while communicating with a PC through Ethernet connection. The system provides high frequency sampling with high measurement accuracy and also generates the disturbance signal to drive the shaker amplifier. The mechanical shaker is located in the left compartment in Fig.4, and attached to the thin-separation plate via a connecting rod and a force sensor. The vibration of this plate is measured by Polytech PDV100 laser Doppler vibrometer (LDV). The target location of the vibrometer is determined as the same point of the piezoelectric patch to obtain a collocated sensor and actuator pair. The voltage output of the LDV is connected to the analog controller as a sensor signal and sent to the data acquisition system for recording. By connecting the sensor signal to the analog circuit, the controller output signal is acquired. This controller signal is amplified by E-413 Dura-act Piezo Driver and sent to the PZT patches (Dura-act P876.A12). Control input voltage between -2V and +8V are accepted by

**3.3. Experimental setup** 

In this section, active vibration suppression of the thin separation plate and noise reduction inside the compartment via analog velocity feedback controller is presented. The experimental results are given in frequency and time domains for three different piezoelectric patch configurations. At first, the piezoelectric patch located at center and upper-left is used as an actuator independently, and then they are employed together as an actuator.

### *3.4.1. Suppression of vibration in time domain*

The performance of the analog velocity feedback control for the vibration suppression is evaluated in the time domain by disturbing the thin separation plate with the mechanical shaker. For this purpose, disturbance signal is applied to the mechanical shaker via data acquisition unit as a sine-wave at the first resonance frequency (approximately 13 Hz) and at the second-resonance frequency (approximately 26 Hz) of the plate. The vibration of the plate is monitored by targeting laser displacement to the center of the piezoelectric actuator patch. The experiments are conducted for each piezoelectric actuator configuration. Fig. 8 presents the results for forced vibration at the first resonance frequency. Fig. 8 (a) presents the open-loop vibration at the center of the plate. The open-loop response corresponds to the structural vibrations of the thin plate when the analog feedback controller is inactive. Fig. 8(b) shows the closed-loop vibration response of the plate when the active vibration suppression is obtained via piezoelectric patch located at center. In Fig. 8(c), the piezoelectric patch located at upper-left and is employed as actuator independently. The Fig. 8(d) shows the closed-response for the piezoelectric actuator in pair configuration where the center and upper-left patch are used as actuator jointly and laser displacement sensor is targeted to the center of the upper-left patch.

As can be seen from the subfigures of Fig. 8, the vibration of the plate at the first resonance frequency is attenuated for each piezoelectric actuator configuration. In fact, the best performance is acquired when the piezoelectric center patch is used as actuator independently. The performance of this configuration is better than the pair configuration because of phase mismatch of the piezoelectric patches in pair. Fig. 8 presents the open and closed vibration of the plate for the second resonance forced vibration. To measure the openloop vibrations of the plate, the LDV is targeted to the center of the upper-left patch. Fig. 9(a) presents the open-loop vibration measured at this location. Fig. 9(b) shows the performance of the active vibration control via piezoelectric actuator patch located at the upper-left of the plate. Besides, Fig. 9(c) presents the effectiveness of piezoelectric pair configuration for the vibration suppression of the plate.

**Figure 8.** Vibration response of the plate at the first resonance frequency (a) Open-loop (b) Closed-loop with piezoelectric patch located at center (c) Closed-loop with piezoelectric patch located at upper-left (d) Closed-loop with piezoelectric actuator patches in pair

**Figure 9.** Vibration response of the plate at the second resonance frequency (a) Open-loop (b) Closed-loop with piezoelectric patch located at upper-left (c) Closed-loop with piezoelectric actuator patches in pair


**Table 2.** Vibration suppression levels in time domain for different piezoelectric actuator configurations

To employ piezoelectric patches in pair for the second resonance mode of the plate, the LDV is targeted again to the center of the upper-left piezoelectric patch. It is obvious that the independent configuration of piezoelectric patch located at upper-left provides better vibration suppression when it is compared with the pair configuration. The reduction levels for each configuration are presented in Table 2.

#### *3.4.2. Supression of vibration in frequency domain*

690 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

(d) Closed-loop with piezoelectric actuator patches in pair

**Figure 8.** Vibration response of the plate at the first resonance frequency (a) Open-loop (b) Closed-loop with piezoelectric patch located at center (c) Closed-loop with piezoelectric patch located at upper-left

**Figure 9.** Vibration response of the plate at the second resonance frequency (a) Open-loop (b) Closed-loop with piezoelectric patch located at upper-left (c) Closed-loop with piezoelectric actuator patches in pair

The aim of this section is to present the performance of the active vibration suppression in the frequency domain. The experiments are conducted for the same piezoelectric actuator configurations. In contrast to time-domain results, the disturbance signal applied to the mechanical shaker is changed to sine-sweep in the bandwidth of 2 Hz to 100 Hz. By monitoring the open-loop and closed-loop response of the plate, frequency responses are gathered using the data acquisition system. Fig. 10 presents the frequency responses for different piezoelectric configurations between vibrometer and the force transducer at the tip of the mechanical shaker. In Fig. 10(a), the performance of the active vibration suppression system via piezoelectric patch located at center is presented. It is noticeable that the vibration is attenuated very well in the first resonance mode of the plate; however the other resonance frequencies of the plate are not affected. This is due to the fact that the position of piezoelectric patch located at center corresponds to the anti-mode of the higher order modes. So, the higher structural modes are not affected. Fig. 10(b) presents the closed-loop performance of the piezoelectric patch located at upper-left. As can be seen this figure, the closed-loop system reduces the vibration of the plate in a broad frequency range for this configuration. Fig. 10(c) shows the effectiveness of the closed-loop system via piezoelectric actuator pair. It is noticeable that the performance of the closed-loop is improved considerably when piezoelectric pair configuration is adopted instead of using upper-left patch independently. Indeed, the closed-loop system reduces the vibration levels as compared to open-loop in all piezoelectric actuator configurations. Table 3 lists the vibration reduction levels in the frequency domain.

**Figure 10.** Frequency responses for different piezoelectric actuator configurations (a) Closed-loop with piezoelectric patch located at center(LDV at center) (b) Closed-loop with piezoelectric patch located at upper-left(LDV at upper-left) (c) Closed-loop with piezoelectric actuator patches in pair(LDV at upperleft)


**Table 3.** Vibration suppression levels in time domain for different piezoelectric actuator configurations

#### *3.4.3. Suppression of noise in frequency domain*

This section presents the noise reduction in one of the compartments for controller-inactive and active cases while disturbing the thin plate via shaker. The noise inside the compartment is measured with a microphone. The frequency responses between the microphone and the force transducer are gathered using the data acquisition system. Fig. 11 presents the results for noise in the frequency domain. As in the same manner with vibration suppression experiments, open-loop response shows the noise radiation in the compartment when the controller is inactive, whereas closed-loop response is monitored when the controller is active. In Fig. 11(a), the performance of noise reduction via piezoelectric patch located at center is given. It is noticeable that the low-frequency acoustic mode in the compartment coincides with the vibration mode of the plate. Since the vibration of plate at the first resonance mode is considerably attenuated, the noise radiation is also reduced for this mode. At the higher-acoustics modes, the closed-loop system does not improve and deteriorate the noise radiation in the compartment. Fig. 11(b) presents the effectiveness of the piezoelectric patch located at upper-left. Similar to the previous results, noise radiation is reduced by suppressing the vibration of the plate. However, it is obvious that the performance of the piezoelectric patch located at center is fairly better than the performance of the piezoelectric patch located at upper-left.

**Figure 11.** Noise levels in the one of the compartments for different piezoelectric patch configurations (a) Open and closed-response for the piezoelectric patch located at center (b) Open and closed-loop response for the piezoelectric patch located at upper-left

#### **4. Conclusion**

692 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**Figure 10.** Frequency responses for different piezoelectric actuator configurations (a) Closed-loop with piezoelectric patch located at center(LDV at center) (b) Closed-loop with piezoelectric patch located at upper-left(LDV at upper-left) (c) Closed-loop with piezoelectric actuator patches in pair(LDV at upper-

Configuration LDV Target Location First Mode Second Mode Center Center 63.7 % (8.8 dB) - Upper-left Center 34.1 % (4.4 dB) 52.8 % (6.5 dB)

(Pair Configuration) Upper-left 50.6 % (6.1 dB) 54.0 % (6.7 dB)

**Table 3.** Vibration suppression levels in time domain for different piezoelectric actuator configurations

This section presents the noise reduction in one of the compartments for controller-inactive and active cases while disturbing the thin plate via shaker. The noise inside the compartment is measured with a microphone. The frequency responses between the microphone and the force transducer are gathered using the data acquisition system. Fig. 11

left)

Piezoelectric Patch

Center and Upper-left

*3.4.3. Suppression of noise in frequency domain* 

In the first part of this chapter, a short review of literature about active vibration control is presented. The general controller design approach and the differences between various controller algorithms are discussed.

In the second part of this chapter, an application using an analog velocity feedback controller for vibration suppression of a flexible plate is presented. Experiments for vibration suppression of the flexible plate are conducted and by measured the vibration of the plate; the time-responses and frequency-responses are presented. Finally, the acoustic response in one of the compartments is also obtained for different piezoelectric actuator configurations. The results revealed that vibration reduction of the separation plate improves the noise radiation and the sound pressure level is decreased due to the reduction of the vibration. However, for an effective and powerful noise reduction, robust controller algorithms with multiple piezoelectric actuator patches can be preferred.
