Smart Structures and Systems

  • 제3권2호
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  • Pages.147-172
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  • 2007
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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Sensor and actuator design for displacement control of continuous systems

  • Krommer, Michael (Institute for Technical Mechanics, Johannes Kepler University Linz) ;
  • Irschik, Hans (Institute for Technical Mechanics, Johannes Kepler University Linz)
  • 투고 : 2005.10.31
  • 심사 : 2006.11.27
  • 발행 : 2007.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present paper is concerned with the design of distributed sensors and actuators. Strain type sensors and actuators are considered with their intensity continuously distributed throughout a continuous structure. The sensors measure a weighted average of the strain tensor. As a starting point for their design we introduce the concept of collocated sensors and actuators as well as the so-called natural output. Then we utilize the principle of virtual work for an auxiliary quasi-static problem to assign a mechanical interpretation to the natural output of the sensors to be designed. Therefore, we take the virtual displacements in the principle of virtual work as that part of the displacement in the original problem, which characterizes the deviation from a desired one. We introduce different kinds of distributed sensors, each of them with a mechanical interpretation other than a weighted average of the strain tensor. Additionally, we assign a mechanical interpretation to the collocated actuators as well; for that purpose we use an extended body force analogy. The sensors and actuators are applied to solve the displacement tracking problem for continuous structures; i.e., the problem of enforcing a desired displacement field. We discuss feed forward and feed back control. In the case of feed back control we show that a PD controller can stabilize the continuous system. Finally, a numerical example is presented. A desired deflection of a clamped-clamped beam is tracked by means of feed forward control, feed back control and a combination of the two.

키워드

참고문헌

  1. Alkhatib, R. and Golnaraghi, M. F. (2003), "Active structural vibration control: a review", The Shock Vib. Digest, 35(5), 367-383. https://doi.org/10.1177/05831024030355002
  2. Chadwick, P. (1999), Continuum Mechanics: Concise Theory and Problems (2nd exp. Ed.), Dover, New York.
  3. Chandrasekharaiah, D. S. and Debnath, L. (1994), Continuum Mechanics, Academic Press, Boston.
  4. Crawley, E. F. (1994), "Intelligent structures for aerospace: a technology overview and assessment", AIAA J., 32(8), 1689-1699. https://doi.org/10.2514/3.12161
  5. Dosch, J. J. and Inman, D. J. (1992), "A self-sensing piezoelectric actuator for collocated control", Int. J. Intelligent Mater. Sys. Struct., 3, 166-185. https://doi.org/10.1177/1045389X9200300109
  6. Gabbert, U. and Tzou, H. S. (2001), Preface: Proceedings of IUTAM-Symposium on Smart Structures and Structronic Systems, Magdeburg, Germany, September 2000.
  7. Gattringer, H., Nader, M., Krommer, M. and Irschik, H. (2003), "Collocative PD control of circular plates with shaped piezoelectric actuators / sensors", J. Vib. Control, 9, 965-982. https://doi.org/10.1177/10775463030098004
  8. Glaser, S. D., Shoureshi, R. A. and Pescovitz, D. (2005), "Frontiers in Sensors and Sensing Systems", Smart Structures and Systems, 1(1), 103-120. https://doi.org/10.12989/sss.2005.1.1.103
  9. Gopinathan, S. V., Varadan, V. V. and Varadan, V. K. (2001), "Active noise control studies using the rayleigh-ritz method", Proceedings of IUTAM-Symposium on Smart Structures and Structronic Systems, Magdeburg, Germany, September 2000.
  10. Gurtin, M. E. (1972), "The linear theory of elasticity", Handbuch der Physik, Vol. VIa/2, Springer, New York.
  11. Haftka, R. T. and Adelman, H. M. (1985), "An analytical investigation of static shape control of large space structures by applied temperature", AIAA-J., 23, 450-457. https://doi.org/10.2514/3.8934
  12. Irschik, H. (2002), "A review on static and dynamic shape control of structures by piezoelectric actuation", J. Eng. Struct., 24, 5-11. https://doi.org/10.1016/S0141-0296(01)00081-5
  13. Irschik, H. and Krommer, M. (2005), "Dynamic displacement tracking of force-loaded linear elastic or viscoelastic bodies by eigenstrain-induced actuation stresses", CD-Rom Proceedings of IDETC/CIE 2005, ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, CA, September 2005.
  14. Irschik, H. and Pichler, U. (2001), "Dynamic shape control of solids and structures by thermal expansion strains", J. Thermal Stresses, 24, 565-578. https://doi.org/10.1080/014957301300158102
  15. Irschik, H. and Pichler, U. (2004), "An extension of Neumann's method for shape control of force-induced elastic vibrations by eigenstrains", Int. J. Solids Struct., 41, 871-884. https://doi.org/10.1016/j.ijsolstr.2003.09.023
  16. Irschik, H. and Pichler, U. (2005), "Distributed strain sensors for measuring structural entities such as displacements or slopes: 3D-formulations and applications for piezoelectric beam sensing", Proceedings of 3rd European Conference on Structural Control, Vienna, Austria, July 2004.
  17. Irschik, H. and Ziegler, F. (1988), "Dynamics of linear elastic structures with selfstress: A unified treatment for linear and nonlinear problems", ZAMM, 68, 199-205. https://doi.org/10.1002/zamm.19880680602
  18. Irschik, H., Krommer, M., Belyaev, A. K. and Schlacher, K. (1999a), "Shaping of piezoelectric sensors/actuators for vibrations of slender beams: coupled theory and inappropriate shape functions", J. Intelligent Mater. Sys. Struct., 9, 546-554.
  19. Irschik, H., Krommer, M. and Pichler, U. (1999b), "Shaping of distributed piezoelectric sensors for flexural vibrations of smart beams", Proceedings of SPIE's 6th Annual International Symposium on Smart Structures and Materials, Newport Beach, CA, March 1999.
  20. Irschik, H., Krommer, M. and Pichler, U. (2000), "Shaping distributed piezoelectric self-sensing layers for static shape control of smart structures", J. Struct. Control, 7(2), 173-190. https://doi.org/10.1002/stc.4300070204
  21. Irschik, H., Krommer, M., Nader, M. and Pichler U. (2003), "Dynamic piezoelectric shape control applied of shells of revolution with translatory support excitation", Proceedings of US - Europe Workshop on Sensors and Smart Structures Technology, Como, Italy, April 2002.
  22. Irschik, H., Krommer, M. and Pichler, U. (2005), "A body-force analogy for dynamics of elastic bodies with eigenstrains", Proceedings of SPIE's 12th Annual International Symposium on Smart Materials and Structures, San Diego, CA, March 2005.
  23. Krommer, M. (2005), "Dynamic shape control of sub - sections of moderately thick beams", Computers & Structures (Special Issue on Modelling of Smart Structures), 83(15-16), 1330-1339.
  24. Krommer, M. and Varadan V. V. (2005), "Control of bending vibrations within sub - domains of thin plates - Part I: theory and exact solution", J. Appl. Mech., 72(3), 432-444. https://doi.org/10.1115/1.1839185
  25. Krommer, M., Irschik, H. and Pichler, U. (2005), "Design of sensors/actuators for structural control of continuous CMA systems", Proceedings of SPIE's 12th Annual International Symposium on Smart Materials and Structures, San Diego, CA, March 2005.
  26. Kugi, A. (2001), Non - linear Control Based on Physical Models, Springer, London.
  27. Lee, C.-K. and Moon, F.-C. (1990), "Modal sensors/actuators", J. Appl. Mech., 57, 434-441. https://doi.org/10.1115/1.2892008
  28. Liu, S.-C., Tomizuka, M. and Ulsoy, G. (2005a), "Challenges and opportunities in the engineering of intelligent structures", Smart Struct. Sys., 1(1), 1-12. https://doi.org/10.12989/sss.2005.1.1.001
  29. Liu, S.-C., Tomizuka, M. and Ulsoy, G. (2005b), "Strategic issues in sensors and smart structures", Proceedings of Third European Conference on Structural Control, Vienna, Austria, July 2004.
  30. Luo, Z.-H., Guo, B.-Z. and Morgul, O. (1999), Stability and Stabilization of Infinite Dimensional Systems with Applications, Springer, London.
  31. Malvern, L. E. (1969), Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs.
  32. Miu, D. K. (1992), Mechatronics: Electromechanics and Contromechanics, Springer, New York.
  33. Mura, T. (1991), Micromechanics of Defects in Solids (2nd ed.), Kluwer, Dordrecht.
  34. Nemenyi, P. (1931), "Eigenspannungen und Eigenspannungsquellen", ZAMM, 11, 1-8. https://doi.org/10.1002/zamm.19310110101
  35. Nijmeijer, H. and van der Schaft, A. J. (1991), Nonlinear Dynamical Control Systems, Springer, New York.
  36. Noda, N., Hetnarski, R. B. and Tanigawa, Y. (2000), Thermal Stresses, (2nd ed.), Lastran, New York.
  37. Preumont, A. (2002), Vibration Control of Active Structures (2nd Ed.), Springer, New York.
  38. Reissner, H. (1931), "Selbstspannungen elastischer Gebilde, ZAMM, 11, 59-70. https://doi.org/10.1002/zamm.19310110108
  39. Tani, J., Takagi, T. and Qiu, J. (1998), "Intelligent material systems: application of functional materials", Applied Mechanics Review, 51, 505-521. https://doi.org/10.1115/1.3099019
  40. Tzou, H. S. and Hollkamp, J. J. (1994), "Collocated independent modal control with self-sensing orthogonal piezoelectric actuators (theory and experiment)", J. Smart Mater. Struct., 3, 277-284. https://doi.org/10.1088/0964-1726/3/3/003
  41. Tzou, H. S. (1998), "Multifield transducers, devices, mechatronic systems and structronic systems with smart materials", The Shock Vib. Digest, 30, 282-294. https://doi.org/10.1177/058310249803000402
  42. Ziegler, F. (1998), Mechanics of Solids and Fluids (2nd corr. ed.), Springer, New York.

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