4.2 Three-Axis Active Mount
4.2.5 Some Concluding Comments
T + − −1 T + =
A P PA PBR B P Q 0 (4.52)
Figure 4.31 shows the vibration control result in the z-axis. It is observed from the results that the amplitude level of the vibration is substantially reduced effectively by activating the LQR control algorithm associated with the inertial type of 3-axis piezoelectric mount. The corresponding input voltage of each actuator is shown in Figure 4.31. The vibration control results for the pitch and the roll motion are shown in Figures 4.32 and 4.33. From the results, it can be assured that the inertial type of 3-axis piezoelectric mount is very effective for vibration control of multi-degree-of- freedom motion of the structural system.
–0.8 –0.4 0.0 0.4 0.8
Roll angle (rad×10–3)
Time (s)
–200 –100 0 100 200
Input voltage (V)
Time (s) Actuator 1
–200 –100 0 100 200
Input voltage (V)
Time (s) Actuator 2
0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5
0.0 0.1 0.2 0.3 0.4 0.5 –2000.0 0.1 0.2 0.3 0.4 0.5 –100
0 100 200
Input voltage (V)
Time (s) Actuator 3
FIGURE 4.33 Control result in roll motion. (From Choi, S.B. et al., SAGE, 19, 1053, 2008.) –0.8
–0.4 0.0 0.4 0.8
Pitch angle (rad×10–3)
Time (s)
–200 –100 0 100 200
Input voltage (V)
Time (s) Actuator 1
–200 –100 0 100 200
Input voltage (V)
Time (s) Actuator 2
0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5
0.0 0.1 0.2 0.3 0.4 0.5 –2000.0 0.1 0.2 0.3 0.4 0.5 –100
0 100 200
Input voltage (V)
Time (s) Actuator 3
FIGURE 4.32 Control result in pitch motion. (From Choi, S.B. et al., SAGE, 19, 1053, 2008.)
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5 Control of Flexible Robotic Manipulators
5.1 TWO-LINK FLEXIBLE MANIPULATOR