3.3 Vibration Control Using Piezostack Mount
3.3.6 Some Concluding Comments
controller associated to the hybrid mount. Control responses similar to those in Figure 3.28 are obtained in time domain for the 4th modal frequency (298 Hz).
mechanical model of the hybrid mount and the governing equation of the beam structure supported by the rubber and hybrid mounts, a sliding mode controller was formulated on the basis of the sliding mode condition. It has been shown through experimental realization of the controller that the imposed vibrations such as acceleration of the beam structure are substantially reduced at target reso- nances without performance deterioration in the non-resonant region. In addition, the forces transmitted to the base were remarkably attenuated by activating the
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Frequency (Hz)
Frequency (Hz) 160
0.0 0.5 1.0 1.5 2.0 2.5 3.0
f1/fexf2/fexf3/fex
Frequency (Hz)
Uncontrolled Controlled
320 300 280 260 240 220 200 180
160 180 200 220 240 260 280 300 320
160 180 200 220 240 260 280 300 320
FIGURE 3.27 Force transmissibility of the beam structure with SMC. (From Kim, S.H.
et al., Int. J. Mech. Sci., 46, 143, 2004. With permission.)
controller. The control results are quite self-explanatory, justifying that the hybrid mount associated with the rubber element and the piezoactuator can be effec- tively employed for vibration isolation of fl exible structures subjected to small- magnitude and high-frequency excitations.
REFERENCES
1. Bailey, T. and Hubbard, J.E. Jr. 1985. Distributed piezoelectric-polymer active vibra- tion control of a cantilever beam. Journal of Guidance, Control, and Dynamics 8:
605–611.
2. Crawley, E.F. and de Luis, J. 1987. Use of piezoelectric actuators as elements of intel- ligent structures. AIAA Journal 25: 1373–1385.
–50 –25 0 25
0 1 2 3 0 1 2 3
0 1 2 3
0 1 2 3
0 1 2 3 0 1 2 3
50
a1 (m/s2) a2 (m/s2)
Time (s)
–50 –25 0 25 50
Time (s)
–3 –2 –1 0 1 2 3
fT1 (N) fT2 (N)
Time (s)
–3 –2 –1 0 1 2 3
Time (s)
–30 –20 –10 0 10 20 30
Time (s)
–30 –20 –10 0 10 20 30
d2 (μm) d1 (μm)
Time (s)
FIGURE 3.28 Time responses of the beam structure with SMC at the excitation frequency of 180 Hz. (From Kim, S.H. et al., Int. J. Mech. Sci., 46, 143, 2004. With permission.)
3. Baz, A. and Poh, S. 1988. Performance of an active control system with piezoelectric actuators. Journal of Sound and Vibration 126: 327–343.
4. Tzou, H.S. 1991. Distributed modal identifi cation and vibration control of continua:
Theory and applications. ASME Journal of Dynamic Systems, Measurement, and Control 113: 494–499.
5. Choi, S.B., Cheong, C.C., Thompson, B.S., and Gandhi, M.V. 1995. Elastodynamic analysis and control of industrial robotic manipulators with piezoelectric-material-based elastic members. ASME Journal of Mechanical Design 117: 640–643.
6. Choi, S.B. and Shin, H.C. 1996. A hybrid actuator scheme for robust position control of a fl exible single-link manipulator. Journal of Robotic Systems 13: 359–370.
7. Jiang, Z.W., Chonan, S., and Tani, J. 1992. Tracking control of a miniature fl exible arm using piezoelectric bimorph cells. The International Journal of Robotic Research 11: 260–267.
8. Ge, P. and Jouaneh, M. 1996. Tracking control of a piezoceramic actuator. IEEE Transactions on Control Systems Technology 4: 209–216.
9. Okazaki, Y. 1990. A micro-positioning tool post using a piezoelectric actuator for dia- mond turning machines. Precision Engineering 12: 151–156.
10. Choi, S.B., Cho, S.S., and Park, Y.P. 1999. Vibration and position tracking control of piezoceramic-based smart structures via QFT. ASME Journal of Dynamic Systems, Measurement and Control 121: 27–33.
11. Chen, P. and Montgomery, S. 1980. A macroscopic theory for the existence of the hys- teresis and butterfl y loops in ferroelectricity. Ferroelectricities 23: 199–207.
12. Horowitz, I.M. 1991. Survey of the quantitative feedback theory. International Journal of Control 53: 255–291.
13. D’Azzo, J.J. and Houpis, C.H. 1988. Linear Control System Analysis and Design Conventional and Modern. New York: McGraw-Hill.
14. Sating, R.R. and Houpis, C.H. 1993. MIMO/QFT CAD Program. User’s Manual.
Wright-Patterson AFB, OH: Air Force Institute of Technology.
15. Franklin, G., Powell, J., and Workman, M. 1990. Digital Control of Dynamic Systems.
Reading, MA: Addison-Wesley.
16. Chopra, I. 2002. Review of state-of-art of smart structures and integrated systems. AIAA Journal 40: 2145–2187.
17. Tzou, H.S., Zhong, J.P., and Hollkamp, J.J. 1994. Spatially distributed orthogonal piezo- electric shell actuators: Theory and applications. Journal of Sound and Vibration 177:
363–378.
18. Kim, H.S., Chattopadhyay, A., and Nam, C. 2002. Implementation of a coupled thermo- piezoelectric-mechanical model in the LQG controller design for smart composite shell.
Journal of Intelligent Material Systems and Structures 13: 713–724.
19. Kim, J.H., Choi, S.B., Cheong, C.C., Han, S.S., and Lee, J.K. 1999. H∞ control of structure-borne noise of a plate featuring piezoceramic actuators. Smart Materials and Structures 8: 1–12.
20. Tu, Y. and Fuller, C.R. 2000. Multiple reference feedforward active noise control part II:
Reference preprocessing and experimental results. Journal of Sound and Vibration 233:
761–774.
21. Sun, D. and Tong, L. 2001. Modal control of smart shells by optimized discretely distributed piezoelectric transducers. International Journal of Solids and Structures 38: 3281–3299.
22. Marcotte, P., Fuller, C.R., and Cambou, P. 1999. Control of the noise radiated by a plate using a distributed active vibration absorber (DAVA). Proceedings of ACTIVE 99, Fort Lauderdale, FL, pp. 447–456.
23. Marcotte, P., Fuller, C.R., and Johnson, M.E. 2002. Numerical modeling of distributed active vibration absorbers (DAVA) for control of noise radiated by a plate. Proceedings of ACTIVE 2002, ISRV, Southampton, U.K., pp. 535–546.
24. Maillard, J.P. and Fuller, C.R. 1999. Active control of sound radiation from cylinders with piezoelectric actuators and structural acoustic sensing. Journal of Sound and Vibration 222: 363–388.
25. Li, D.S., Cheng, L., and Gosselin, C.M. 2004. Optimal design of PZT actuators in active structural acoustic control of a cylinder shell with a fl oor partition. Journal of Sound and Vibration 269: 569–588.
26. Zhou, S.W., Liang, C., and Rogers, C.A. 1994. Modeling of distributed piezoelectric actuators integrated with thin cylindrical shells. Journal of Acoustical Society of America 96: 1605–1612.
27. Lester, H.C. and Lefebvre, S. 1993. Piezoelectric actuator models for active sound and vibration control of cylinders. Journal of Intelligent Material Systems and Structures 4: 295–306.
28. Sohn, J.W., Kim, H.S., and Choi, S.B. 2006. Active vibration control of smart hull struc- tures using piezoelectric actuators. Journal of Mechanical Engineering Science 220:
1329–1337.
29. Ansys Inc. 1999. ANSYS Theory Manual Ver. 5.5. Canonsburg, PA: SAS IP.
30. Nam, C., Chen, P.C., Liu, D., Kim, J., and Chattopadhyay, A. 2000. Neural net-based controller for fl utter suppression using ASTROS* with smart structures. Proceedings of SPIE’s 7th International Symposium on Smart Structures and Materials, vol. 3985, Newport Beach, CA, pp. 98–109.
31. Yu, Y., Peelamedu, S.M., Nagathan, N.G., and Dukkipati, R.V. 2001. Automotive vehicle engine mounting systems: A survey. ASME Journal of Dynamic Systems, Measurement and Control 123: 186–194.
32. Kim, G. and Singh, R. 1993. Nonlinear analysis of automotive hydraulic engine mount.
ASME Journal of Dynamic Systems, Measurement and Control 115: 482–487.
33. Gennesseaus, A. 1992. Research for new vibration isolation techniques. Hydro-mounts to active mounts. SAE Technical Paper Series 931324.
34. Choi, S.B., Park, Y.K., and Cheong, C.C. 1996. Active vibration control of intelligent composite laminate structures incorporating an electro-rheological fl uid. Journal of Intelligent Material Systems and Structure 7: 441–419.
35. Choi, S.B. 1999. Vibration control of a fl exible structure using ER dampers. ASME Journal of Dynamic Systems, Measurement and Control 121: 134–138.
36. Choi, S.B. and Cheong, C.C. 1996. Vibration control of a fl exible beam using SMA actuators. Journal of Guidance, Control, and Dynamics 19: 1178–1180.
37. Ushijima, T. and Kumakawa, S. 1993. Active engine mount with piezo-actuator for vibration control. SAE Technical Paper Series 930201.
38. Kamada, T., Fujita, T., Hatayama, T., Arikabe, T., Murai, N., Aizawa, S., and Tohyama, K.
1997. Active vibration control of frame structures with smart structures rising piezo- electric actuators (vibration control by control of bending moments of columns). Smart Materials and Structure 6: 448–456.
39. Choi, S.H., Choi, Y.T., Choi, S.B., and Cheong, C.C. 1996. Performance analysis of an engine mount featuring ER fl uids and piezoactuators. International Journal of Modern 10: 3143–3157.
40. Kim, S.H., Choi, S.B. Hong, S.R., and Han, M.S. 2004. Vibration control of a fl ex- ible structure using a hybrid mount. International Journal of Mechanical Sciences 46: 143–157.
41. Schwartz, M. 2002. Encyclopedia of Smart Materials. New York: Wiley-Interscience.
42. Kim, S.H. 2003. Vibration control of a beam structure using a hybrid mount. MS thesis, Inha University, Incheon, South Korea.
43. Chen, C.T. 1999. Linear System Theory and Design. New York: Oxford University Press.
65
4 Vibration Control Using Active Mount
4.1 ONE-AXIS ACTIVE MOUNT