## 5 Controller Implementation and Testing
This example shows that the effectiveness of adaptive feedback control increases with the increase in the accuracy of the model ( which was to be expected), moreover, it can be seen that adaptive feedback control is very effective even when the model order is not too high (nA = 6). Figure 5 shows the results of the frequency analysis for the 0.1 Vpp excitation amplitude. In the case of excitation with a frequency corresponding to the object resonant frequency 193 Hz, one can see the exact vibration reduction performance of the controllers in [dB]. As can be seen from Figure 5a, controller 1 reduces the plate response amplitude by 8 dB, and controler 2--by 15 dB (Figure 5b). To evaluate the adaptive properties of the controller, a signal with changing frequency, that is, a chirp signal, was used as plate excitation. The interfering signal was a signal with a linearly increasing frequency from 100 to 400 Hz in a 20 s cycle and an amplitude of 0.3 Vpp. In the presented graph (Figure 6), the controller was turned on after the first cycle of the disturbing signal (t = 20 s). As can be seen, at least two dominant resonance frequencies were suppressed, and the reduction in subsequent cycles remained at a similar level. In order to compare the obtained time waveforms more precisely, they were superimposed so that the amplitude values corresponded to the same frequencies of the disturbing signal (Figure 7), and also a FFT (Fast Fourier Transform) analysis was performed. The graph shows that two version of the considered controllers can suppress three resonant frequencies of the plate in the range from 100 Hz to 400 Hz. Figure 5: FFT analysis for two kinds of the adaptive controllers in case of the sinusoidal excitation. (a) Controller 1; (b) Controller 2. Figure 6: Time response of the system for a chirp excitation without control (0\(-\)20 s) and with the adaptive controller No.1 (20\(-\)40 s). (**a**) Plate response; (**b**) Control signal. Figure 7: Cont. Another test was performed for an analysis of the dynamics of the controller and their sensitivity to the chirp signal, with the frequency varying from 150-250 Hz, with a constant amplitude of 0.05 V and a frequency step of 2 Hz/s. The measured data were the subject of a frequency domain analysis using the FFT algorithm. The results are shown in Figure 8.  
The FFT plot of the plate response to the chirp signal shows that in the case of considering adaptive control, one can expect an average of 10 dB vibration reduction in close vicinity to the resonant frequency. Based on detailed frequency analyses, the levels of vibration reduction for individual resonance frequencies and their surroundings were determined and are summarized in Table 3.  
It can be seen that the vibration reduction level for the 193 Hz resonance frequency increased from 5.5 dB for controller 1 to 9.7 dB for controller 2. In addition, the noise level in the control system was reduced. During the tests, the possibility of increasing the level of vibration reduction was limited due to the saturation of the control signal, resulting from the need to work within the linear characteristics of the MFC actuator. Subsequent tests were performed for a sinusoidal disturbance with a frequency of 193 Hz and various amplitudes. Figure 5 shows the results of the frequency analysis for the 0.1 Vpp amplitude. In the case of excitation with a sinusoidal signal with a frequency corresponding to the resonant frequency of the object, the efficiency of the controllers is higher and amounts to 6.6 dB for controller 1 and 15.4 dB for controller 2, respectively. Figure 8: FFT plate responses to the chirp excitation of 150\(-\)200 Hz without control (blue plot) and with the adaptive controller (green and red plot). (**a**) Controller 1; (**b**) Controller 2.