## 6 Experiments
This is expected to happen since the first two modes, corresponding to the first two pairs of dominant poles, are the ones that are mostly needed to be diminished. Moreover, it is also interesting to notice from Figure 19b that the three higher modes (the third, fourth and fifth peaks), excited by the impulse excitation of the EMV, also experience a small attenuation. Even though the corresponding poles have not been changed, this might be the influence of the first two pairs of poles that have been relocated. As the three higher vibration modes have fast convergence speed in the time domain, they are not dominant to affect the system response. The induced vibrations die down very quickly with the proposed controller as compared in Figure 15.2  
The amplitude of the controlled tip displacement reduces to 0.05 mm after a damping period of 13 s, while the damping period takes more than 60 s without the controller. Besides, it is necessary to notice as the peak value of the measured vibration response exceeds the range of the A/D board (\(\pm\)10 V) as plotted in Figure 19a; control saturation of actuators is inevitable. The control voltage applied on actuators is depicted in Figure 15.3  
Finally, experimental results of the poles placement controller with different locations of the closed loop poles are compared in Figure 22a-d. Significant attenuation of measured time responses measured by the strain sensors can be seen for the two cases, namely the further location of poles with damping ratio 0.85 (\(-\)48.37 \(\pm\) 56.9i, and \(-\)7.93 \(\pm\) 9.33i) and the optimal location of poles with damping ratio 0.707 (\(-\)40.23 \(\pm\) 56.9i, and \(-\)6.59 \(\pm\) 9.33i). Figure 15.4 Control voltage applied on actuators. Figure 15.5 Comparisons of measured tip displacement excited by the EMV. However, it is important to point out that the measured time responses with the further location of poles decays a little slower than that with the optimal location of poles in Figure 22a. The experimental results show the control effectiveness reduces with a further location of poles, which is different from simulations. In the case of further location of poles, it is observed that vibration responses of the first two modes are well suppressed, and a larger attenuation of the first mode is achieved in Figure 22b, compared with the optimal case. However, peaks corresponding to the other three higher modes (the third, fourth and fifth peaks) have larger amplitudes than that in the open loop case. All these can be attributed to the fact that the desired closed loop poles are placed too far from the imaginary axis; hence, the control voltage delivered by the controller severely exceeds the system limits, which leads to a severe control saturation phenomenon as demonstrated in Figure 22d. Furthermore, the spillover effect is caused by the control saturation, and vibrations of the higher modes are excited. Those results are further illustrated by the measured vibration response of the beam tip in Figure 22c. During the beginning period (0-1 s), vibrations of the higher modes are excited due to the severe spillover effect, thus the peak values of tip displacement with the further location of poles are slightly larger than that with the optimal case. As vibrations of the higher modes converge quickly in the time domain, the spillover effect disappears during the periods of 4-6 s, and the control force of the actuators is mainly used to deal with vibrations of the first two modes. Correspondingly, the control effectiveness with the further location of poles is better than that with the optimal case in the period of 4-6 s.  
In summary, locations of the closed loop poles must be carefully determined to implement the poles placement controller. The effectiveness of the optimal multi-poles placement method is validated by experiments. Multi-mode vibrations of the smart flexible manipulator are well suppressed with the proposed controller.