*3.2.2. Implementation of velocity feedback controller*

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

**Table 1.** Mechanical properties of host structure and piezoelectric patch

**Figure 5.** Thin steel plate with piezoelectric patches

analog implementation of the controller is explained.

*3.2.1. Design of proportional feedback controller* 

**3.2. Controller architecture** 

Property Steel Piezoelectric Patch

This section presents design and implementation of the active vibration controller via piezoelectric actuators. At first, proportional feedback controller is presented and then

Proportional feedback control is a very simple and easily implementable controller methodology. Since only a sensor signal is passed through a negative amplifier and fed back to the system, the total computational and implementation cost is very low. Thus, it is possible to apply this control scheme using analog circuits since it does not need online

Length (mm) 1000 65 Width (mm) 1000 31 Depth (mm) 1.5 0.5 Elastic modulus (GPA) 190 70.2 Poisson's ratio 0.33 0.36 Density (kg/m3) 6305 7800 Piezoelectric Strain Constant d31 (10-10 m/V) - 1.74 Piezoelectric Strain Constant d33 (10-10 m/V) - 3.94 Piezoelectric Strain Constant d51 (10-10 m/V) - 5.35

> The designed proportional velocity feedback controller is implemented on a breadboard by using the circuit shown in Fig. 6. This analog circuit includes one inverting amplifier and low-pass filter.

> The measured sensor voltage signal (Vin) is passed through a low pass filter which is in the form of resistor-capacitor (RC) filter. The cut-off frequency of this filter equals to one divided by multiplication of resistor and capacitance value. The aim of this low-pass filter is the reduction of high-frequency components of the sensor signal. After passing through this filter, the filtered signal is fed to the inverting amplifier. This inverting amplifier includes an operational amplifier (op-amp) and two resistors as indicated in Fig. 6. The op-amp is powered by dual polarity. The filtered sensor voltage is connected through input resistor Rc to the positive input channel of the op-amp. Then, a jumper resistor Rf is included between positive input channel and the output channel, whereas negative input channel is connected to the ground. By passing through this inverting amplifier, the sign of filtered sensor signal is inverted and its voltage value is amplified. The amplifier ratio is equivalent the ratio of jumper resistor Rf and input resistor Rc. Finally, this amplified and inverted signal serves as the proportional controller output signal.

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

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

#### **3.3. Experimental setup**

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 the voltage amplifier and the input signal is amplified by factor of 50. By closing-thecontroller loop, an active damping system for vibration suppression is created. While the vibration suppression experiments are conducted, the output signal of a microphone properly located in one of the compartments is also recorded at the same time to demonstrate the suppression of noise.
