## 6 Experiments  
Several tests were performed with the cantilevered flexible beam. The tests are divided into two cases of vibration reduction control: one for the baseline structure of the beam, and one for a beam with variable mass. The LMS and SM-LMS algorithms are applied to compare the vibration reduction performance. The control parameters were tuned to obtain the best results. Figure 19 shows the control results for the baseline beam structure. The plot on the left indicates the strain change of the aluminum beam in the time domain from the PZT sensor outputs. Note that the vibration stops in 0.2 to 0.3 s with LMS and SM-LMS, whereas it takes longer than 1 s to stop without a controller. The plot on the right compares the frequency response plots between open-loop and closed-loop cases, and some amplitude reductions can be seen for each peak frequency. Figure 17: Notch filter control result: (**a**) tracking error of impulse response; and (**b**) zoomed plot of (**a**). Figure 18: Notch filter control result: (**a**) tracking error of step response; and (**b**) zoomed plot of (**a**). After 0.3 s, the vibration amplitudes with both control algorithms are very similar, but LMS shows worse vibration isolation performance than SM-LMS. The frequency response shows a more obvious performance difference between the two methods, as shown in Table 4.  
There is excellent attenuation of mode 1 and slight attenuation of mode 2 with LMS, while higher frequencies show slight amplifications. SM-LMS shows excellent attenuation of modes 1 and 2 and slight attenuation of mode 4, while mode 3 shows slight amplification. At every peak, the difference in attenuated amplitude between the two methods is about 3 to 5 dBs. The amplitudes of 1 st, 2 nd, and 4 th modal frequencies are reduced, and the 3 rd modal frequency has some spill-over with SM-LMS. However, with LMS, the 3 rd and 4 th peaks have spillovers, and the amounts are higher than in the case with SM-LMS. When observing the vibration level in broadband, the SM-LMS shows better vibration isolation performance, thus reducing the overall RMS value. Next, to incorporate the fact that the plant will change and to highlight the efficacy of the controller, an additional mass is attached to the original system (increasing the total weight by about a 20%). A bracket is fastened near the tip of the beam, as shown in Figure 11. Since an added mass implies decreased resonance frequencies, a modified frequency response with reduced resonance frequencies for each peak is obtained to measure the performance of the controller in these cases. Note that the SM-LMS is not related to the original structural dynamics and can make the system have desired dynamics. Moreover, the parameters of the SM-LMS used for the baseline structures are maintained for this case of control in order to observe the robustness of the controller. Again, the time-domain responses caused by impulsive disturbances show significant reduction visible, as shown in Figure 20. Furthermore, the amplitudes of each resonance peak and other frequencies are decreased, regardless of the significant change in the plant dynamics. Similarly, the vibration stops in 0.4 to 0.5 s with LMS and SM-LMS, whereas it takes longer than 1 s without a controller. The plot on the right compares the frequency response between the open-loop and closed-loop cases, in which some amplitude reductions can be seen for each peak frequency.