## 4 Semi-Active Vibration Control of the Thin Plate Using the ERF Embedded ATVA
### Semi-Active Vibration Control Using the Interval Type-2 Fuzzy  
The fuzzy rules of semi-active control are usually obtained by using the expert database or the relation between input and output from experimental results [17]. In this paper, to establish the fuzzy controller's rule base at the different frequencies, we measure the vibration response of the structure with the ERF ATVA with different applied electric field at different frequency; then, according to the experimental results, the optimal electric field at different frequency is recorded to establish the expert database of the fuzzy rules. In all experiments, a sinusoidal signal is input to the shaker's amplifier at follows. \[r(t)=A\sin(2\pi ft) \tag{6}\]  
where \(A\) is the amplitude of the input signal and \(f\) is the frequency of the sinusoidal signal. The signal is amplified to drive the electromagnetic vibration shaker and then the shaker provides the stimulating vibration to the structure. Consequently, the electric field of the ATVA is tuned at different levels of 0-2 (kV/mm) to perform the vibration experiments; the vibration displacement of the structure is measured by the eddy-current displacement sensors and recorded by the NI CRIO 9074 simultaneously. For an external vibration produced by the shaker with the sinusoidal signals of different amplitudes at 8-80 Hz, Tables 7 and 8 record the frequency responses of this smart structure with respect to the different external electric field applied to ERF, where the vibration displacement is computed by using the root mean square (RMS) value of the eddy-current sensor's output. In these tables, the smaller RMS value of displacement sensor implies that the ATVA has better ability of absorbing vibration. In the same column, the bold-face type number shows that the structure has the smaller vibration with suffering the same external vibration. For example, check the first column of Table 7, if A = 50 mV and f = 8 Hz, the best choice for the controller is E = 1.5 (kV/mm), because the vibration displacement of the structure is the smallest with this electric field of E = 1.5 kV/mm. For the first mode of vibration with the frequency range of 8-17 Hz, the experimental results show that the ATVA has the better performance with the larger external electric field. These experimental results imply that the ATVA has better ability of absorbing vibration if its viscous coefficient is larger for the frequencies at the first vibration mode. However, for the second mode of vibration, the optimal external electric field is different from the first mode. With the exception of the vibration at the frequency of 21 Hz, the ATVA has better ability of absorbing vibration with a smaller electric field at the frequencies  
Figure 12: Experimental schematic diagram of semi-active vibration control architecture for the ERF embedded ATVA. of 19, 23 and 25 Hz. With the vibration at the frequency of 21 Hz, the ATVA with the electric field of E = 1 kV/mm has better ability of absorbing vibration than the others. In addition, for the third vibration mode, the ability of absorbing vibration for the ATVA is changed again. According to the experimental results in Table 8, with the exception of the vibration at the frequency of 88 Hz, the ATVA has better ability of absorbing vibration with the electric field of E = 1.5 kV/mm for the vibration with the frequency of 74, 76, and 78 Hz. From the experimental results in Tables 7 and 8, it is obvious that the relation between the optimal electric field and the vibration frequency of the smart structure is nonlinear. In some cases, the amplitude of vibration is also influence the performance of the proposed ATVA. Therefore, we need to design a semi-active vibration controller to produce the optimal electric field with respect to the vibration. Because of the nonlinear relation between the optimal electric field and the ability of absorbing vibration, a type-2 fuzzy controller is proposed to establish the input-output mapping according to the experimental results.