Skip to main content
SpringerLink
Log in

Algorithms in Active Vibration Control

  • Chapter
  • First Online:
Model Predictive Vibration Control

Abstract

With the advent of active vibration control (AVC) systems and their gradual transfer to commercial products, building a solid knowledge base on feedback systems and their components has become increasingly important for the vibration engineering community. In addition to the actuating elements that transfer the necessary dynamic changes to vibrating mechanical systems and sensors that provide feedback on vibration levels, the control strategy itself is also an essential component of the feedback system. This chapter introduces the reader to some control strategies that are routinely implemented in vibration attenuation systems. In addition to a brief theoretical primer on the control theory standing behind these strategies, examples of their use in AVC applications are given. The chapter is meant to provide a review of strategies alternative to the model predictive control (MPC) approach that is at the center of attention of this book. First, classical control strategies are introduced which are based on position or velocity feedback and use a fixed gain to compute control input. After a short discussion on the ever-so-popular proportional integral derivative (PID) controller, the focus is shifted to the essentials of optimization-based algorithms. The linear quadratic (LQ) controller is in close relationship with MPC and it is utilized both often and very effectively in vibration control. The underlying idea behind another optimization based strategy, the \({{\fancyscript{H}}}_{\infty}\) (H-infinity) controller is reviewed as well. The chapter is finished by a section on some of the more exotic control approaches, which due to their potential to tackle hysteresis and non-linearity can be very valuable for AVC. These soft computing approaches are genetic algorithms, neural networks and fuzzy control.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    See Chap. 6 in [13].

  2. 2.

    Matrix D is omitted when accelerometers are not used for measuring output.

  3. 3.

    Nodes are also referred to as neurons, processing elements or units.

  4. 4.

    Also referred to as phenotypes or creatures.

  5. 5.

    Also referred to as genomes, genotypes and strings.

References

  1. Agrawal BN, Bang H (1996) Adaptive structures for large precision antennas. Acta Astronaut 38(3):175–183. doi:10.1016/0094-5765(96)00062-8, http://www.sciencedirect.com/science/article/B6V1N-3VTW8Y7-3/ 2/a53f7c4acb3ee1541568e0db4062d985

    Google Scholar 

  2. Ahmed B, Pota H (2011) Dynamic compensation for control of a rotary wing UAV using positive position feedback. J Intell Rob Syst 61:43–56. doi: 10.1016/0094-5765(96)00062-8,10.1007/s10846-010-9487-7

  3. Al-Nassar YN, Siddiqui M, Al-Garni AZ (2000) Artificial neural networks in vibration control of rotor-bearing systems. Simul Pract Theory 7(8):729–740. doi:10.1016/S0928-4869(00)00004-5

  4. Alam M, Tokhi M (2008) Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator. Eng Appl Artif Intell 21(2):229–246. doi:10.1016/j.engappai.2007.04.008, http://www.sciencedirect.com/science/article/B6V2M-4P0N8W7-1/ 2/0151e11caeeaab40012fcffe7059861b

  5. Alam M, Tokhi M (2008) Hybrid fuzzy logic control with genetic optimisation for a single-link flexible manipulator. Eng Appl Artif Intell 21(6):858–873. doi:10.1016/j.engappai.2007.08.002, http://www.sciencedirect.com/science/article/B6V2M-4PPNM5K-1/2/e0cab5d17ae1330863c846be1692e6c8

  6. Allaire PE, Lewis DW, Knight JD (1983) Active vibration control of a single mass rotor on flexible supports. J Franklin Inst 315(3):211–222. doi:10.1016/0016-0032(83)90025-X, http://www.sciencedirect.com/science/article/B6V04-45D9SMR-M/2/62024de7918cc7b0b23d9703691ab67a

  7. Alli H, Ucar A, Demir Y (2003) The solutions of vibration control problems using artificial neural networks. J Franklin Inst 340(5):307–325. doi:10.1016/S0016-0032(03)00036-X, http://www.sciencedirect.com/science/article/B6V04-48XD30R-1/2/6aea0a5487a31fa2ed46dc803323b4f5

    Google Scholar 

  8. Amer Y, Bauomy H (2009) Vibration reduction in a 2DOF twin-tail system to parametric excitations. Commun Nonlinear Sci Numer Simul 14(2):560–573. doi:10.1016/j.cnsns.2007.10.005, http://www.sciencedirect.com/science/article/B6X3D-4PYP723-2/ 2/b9d5375168fadb0b4e67857e92948bfc

    Google Scholar 

  9. Antsaklis PJ, Michel AN (2005) Linear systems, 2nd edn. Birkhäuser, Boston (originally published by McGraw-Hill, Englewood Cliffs, 1997)

    Google Scholar 

  10. Antsaklis PJ, Michel AN (2007) A Linear systems Primer. Birkhäuser, Boston (originally published by McGraw-Hill, Englewood Cliffs, 1997)

    Google Scholar 

  11. Bandyopadhyay B, Janardhanan S (2004) Discrete-time sliding mode control: a multirate output feedback approach. In: Thoma M, Morari M (eds) Hybrid systems: computation and control, lecture notes in control and information sciences. Springer, Berlin

    Google Scholar 

  12. Belavý C (2009) Teória Automatického Riadenia II: Návody na cvičenia, 1st edn. Slovenská vysoká škola technická v Bratislave: Strojnícka Fakulta, Bratislava, (Theory of automatic control ii: seminar guide) in Slovak language

    Google Scholar 

  13. Benaroya H, Nagurka ML (2010) Mechanical vibration: analysis, uncertainities and control, 3rd edn. CRC Press, Taylor & Francis Group, Boca Raton

    Google Scholar 

  14. Bittanti S, Cuzzola FA (2002) Periodic active control of vibrations in helicopters: a gain-scheduled multi-objective approach. Control Eng Pract 10(10):1043–1057. doi:10.1016/S0967-0661(02)00052-7,  http://www.sciencedirect.com/science/article/B6V2H-45KSPJJ-/2/9647861ce849d131c7d4b90cdb964751

  15. Blondel V, Tsitsiklis JN (1996) NP-hardness of some linear control design problems. SIAM J Control Optim 35:2118–2127

    Article  MathSciNet  Google Scholar 

  16. Blondel VD, Tsitsiklis JN (2000) A survey of computational complexity results in systems and control. Automatica 36(9):1249–1274. doi:10.1016/S0005-1098(00)00050-9, http://www.sciencedirect.com/science/article/pii/S0005109800000509

  17. Bohn C, Cortabarria A, Härtel V, Kowalczyk K (2004) Active control of engine-induced vibrations in automotive vehicles using disturbance observer gain scheduling. Control Eng Pract 12(8):1029–1039. doi:10.1016/j.conengprac.2003.09.008, http://www.sciencedirect.com/science/article/B6V2H-49Y3VWS-/2/dd7bcefd1618f3820896ddbd6dce7430, in special section on emerging technologies for active noise and vibration control systems

  18. Braghin F, Cinquemani S, Resta F (2010) A model of magnetostrictive actuators for active vibration control. Sens Actuators A (in press). Corrected proof. doi: 10.1016/j.sna.2010.10.019, http://www.sciencedirect.com/science/article/B6THG-51F25N5-/2/f5cf46980d38877c74a3c4d34fbd894d

  19. Bruant I, Gallimard L, Nikoukar S (2010) Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm. J Sound Vib 329(10):1615–1635. doi:10.1016/j.jsv.2009.12.001, http://www.sciencedirect.com/science/article/pii/S0022460X090

  20. Camino J, Arruda J (2009) \({\fancyscript{H}}_2\) and \({\fancyscript{H}}_\infty\) feedforward and feedback compensators for acoustic isolation. Mech Syst Sig Process 23(8):2538–2556. doi:10.1016/j.ymssp.2009.04.006, http://www.sciencedirect.com/science/article/B6WN1-4W7J0YN-2/ 2/918091cd3d7b23193d5b3637eb2342ce

  21. Carotti A, Lio G (1991) Experimental active control: bench tests on controller units. Eng Struct 13(3):242–252. doi:10.1016/0141-0296(91)90036-C, http://www.sciencedirect.com/science/article/B6V2Y-4829VWB-CG /2/4414a8cb4321f4e346ca04468e610264

  22. Chang CS, Liu TS (2007) LQG controller for active vibration absorber in optical disk drive. IEEE Trans Magn 43(2):799–801. doi:10.1109/TMAG.2006.888417

    Google Scholar 

  23. Chen K, Chou C, Chang S, Liu Y (2008) Intelligent active vibration control in an isolation platform. Appl Acoust 69(11):1063–1084. doi: 10.1016/j.apacoust.2007.06.008,  http://www.sciencedirect.com/science/article/B6V1S-4PMYXPB-1/ 2/55a19d9f917a53bef57682bb9d03dac2

    Google Scholar 

  24. Choi SB, Hong SR, Sung KG, Sohn JW (2008) Optimal control of structural vibrations using a mixed-mode magnetorheological fluid mount. Int J Mech Sci 50(3):559–568. doi:10.1016/j.ijmecsci.2007.08.001, http://www.sciencedirect.com/science/article/B6V49-4PD4XHC-1/

  25. Chu CL, Wu BS, Lin YH (2006) Active vibration control of a flexible beam mounted on an elastic base. Finite Elem Anal Des 43(1):59–67. doi:10.1016/j.finel.2006.07.001, http://www.sciencedirect.com/science/article/pii/S0168874X060

  26. Creasy M, Leo D, Farinholt K (2008) Adaptive positive position feedback for actively absorbing energy in acoustic cavities. J Sound Vib 311(1–2):461–472. doi: 10.1016/j.jsv.2007.09.013, http://www.sciencedirect.com/science/article/B6WM3-4R2HKR0-3/ 2/e9d3c9817e3b4c302a861a4a3bb6fcb1

    Google Scholar 

  27. Darus IM, Tokhi M (2005) Soft computing-based active vibration control of a flexible structure. Eng Appl Artif Intell 18(1):93–114. doi: 10.1016/j.engappai.2004.08.017 , http://www.sciencedirect.com/science/article/B6V2M-4DFT21W-2/2/0e01e702eebed40a2e2dbd2925feed5c

  28. Davari P, Hassanpour H (2009) Designing a new robust on-line secondary path modeling technique for feedforward active noise control systems. Signal Process 89(6):1195–1204. doi:10.1016/j.sigpro.2009.01.003, http://www.sciencedirect.com/science/article/pii/S01651684090

  29. de Abreu GLCM, Ribeiro JF (2002) A self-organizing fuzzy logic controller for the active control of flexible structures using piezoelectric actuators. Appl Soft Comput 1(4):271–283. doi:10.1016/S1568-4946(02)00020-0, http://www.sciencedirect.com/science/article/B6W86-454T5BG-1/ 2/a19272d9ab350a5ebca766ecab7b2192

  30. de Callafon R, Zeng J, Kinney C (2010) Active noise control in a forced-air cooling system. Control Eng Pract 18(9):1045–1052. doi:10.1016/j.conengprac.2010.05.007, http://www.sciencedirect.com/science/article/pii/S0967066110001243

    Google Scholar 

  31. De Cuyper J, Swevers J, Verhaegen M, Sas P (2000) \({\fancyscript{H}}_\infty\) feedback control for signal tracking on a 4 poster test rig in the automotive industry. In: 25th international conference on noise and vibration engineering, Leuven, pp 61–68

    Google Scholar 

  32. Doyle J, Francis B, Tannenbaum A (1992) Feedback control theory, 2nd edn. Macmillan Publishing, New York

    Google Scholar 

  33. Eissa M, Bauomy H, Amer Y (2007) Active control of an aircraft tail subject to harmonic excitation. Acta Mech Sin 23:451–462. doi:10.1007/s10409-007-0077-2

    Google Scholar 

  34. El-Badawy AA, Nayfeh AH (2001) Control of a directly excited structural dynamic model of an F-15 tail section. J Franklin Inst 338(2–3):133–147. doi:10.1016/S0016-0032(00)00075-2, http://www.sciencedirect.com/science/article/B6V04-42HNMDV-3/ 2/e3bf6f797834c8e8638324be88fb78f7

  35. Eski I, Yıldırım S (2009) Vibration control of vehicle active suspension system using a new robust neural network control system. Simul Modell Pract Theory 17(5):778–793. doi:10.1016/j.simpat.2009.01.004, http://www.sciencedirect.com/science/article/B6X3C-4VHSDJ4-1/ 2/d2fe946695b369279d2e1229f15a61bd

  36. Espinosa J, Vandewalle J, Wertz V (2005) Fuzzy logic, identification and predictive control. Advances in industrial control. Springer, London

    Google Scholar 

  37. Fanson JL, Caughey TK (1990) Positive position feedback control for large space structures. AIAA J 28(4):717–724. doi:10.2514/3.10451

    Article  Google Scholar 

  38. Feliu V, Pereira E, Diaz IM, Roncero P (2006) Feedforward control of multimode single-link flexible manipulators based on an optimal mechanical design. Rob Autom Syst 54(8):651–666. doi:10.1016/j.robot.2006.02.012, http://www.sciencedirect.com/science/article/pii/S09218890060, Morphology, Control and Passive Dynamics

  39. Fischer D, Isermann R (2004) Mechatronic semi-active and active vehicle suspensions. Control Eng Pract 12(11):1353–1367. doi:10.1016/j.conengprac.2003.08.003, http://www.sciencedirect.com/science/article/B6V2H-49V1CR4-2/2/0dd89d1b7760e7303a32b5bdd2cbbf9b, Mechatronic Systems

  40. Fu M (2004) Pole placement via static output feedback is np-hard. IEEE Trans Autom Control 49(5):855–857. doi:10.1109/TAC.2004.828311

    Article  Google Scholar 

  41. Fuller C (1990) Active control of sound transmission/radiation from elastic plates by vibration inputs: I. analysis. J Sound Vib 136(1):1–15. doi:10.1016/0022-460X(90)90933-Q, http://www.sciencedirect.com/science/article/pii/0022460X9090

    Google Scholar 

  42. Fuller CR, Elliott SJ, Nelson PA (1996) Active control of vibration, 1st edn. Academic Press, San Francisco

    Google Scholar 

  43. Fung RF, Liu YT, Wang CC (2005) Dynamic model of an electromagnetic actuator for vibration control of a cantilever beam with a tip mass. J Sound Vib 288(4–5):957–980. doi:10.1016/j.jsv.2005.01.046, http://www.sciencedirect.com/science/article/B6WM3-4G4N5VD-1/ 2/fc3710f0625ef69f19d16c8778a63e58

  44. Gao W, Chen JJ, Ma HB, Ma XS (2003) Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters. Comput Struct 81(1):53–60. doi:10.1016/S0045-7949(02)00331-0, http://www.sciencedirect.com/science/article/pii/S00457949020

  45. Goh CJ, Caughey TK (1985) On the stability problem caused by finite actuator dynamics in the collocated control of large space structures. Int J Control 41(3):787–802. doi:10.1080/0020718508961163, 10.1080/0020718508961163

  46. Green M, Limebeer D (1995) Linear robust control. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  47. Guclu R (2006) Sliding mode and PID control of a structural system against earthquake. Math Comput Modell 44(1–2):210–217. doi: 10.1016/j.mcm.2006.01.014, http://www.sciencedirect.com/science/article/B6V0V-4JP9FV5-1/ 2/0900f85ba6e764d746c054ac040aff77 (Advances in business modeling and decision technologies, pp 1–95)

  48. Guclu R, Yazici H (2008) Vibration control of a structure with ATMD against earthquake using fuzzy logic controllers. J Sound Vib 318(1–2):36–49. doi:10.1016/j.jsv.2008.03.058, http://www.sciencedirect.com/science/article/B6WM3-4SM0XJT-1/2/fe8f6a66297ad6e12f0791a83e4eed36

  49. Hatch MR (2000) Vibration simulation using MATLAB and ANSYS, 1st edn. Chapman and Hall/CRC, Boca Raton

    Google Scholar 

  50. Hellerstein JL, Diao Y, Parekh S, Tilbury DM (2004) Feedback control of computing systems. Wiley/IEEE Press, Hoboken

    Book  Google Scholar 

  51. Ho CC, Ma CK (2007) Active vibration control of structural systems by a combination of the linear quadratic Gaussian and input estimation approaches. J Sound Vib 301(3–5):429–449. doi:10.1016/j.jsv.2005.12.061, http://www.sciencedirect.com/science/article/B6WM3-4MV19X0-1/ 2/39db74e66a9494e834cdab9f0da4b886

  52. Hong SR, Choi SB, Han MS (2002) Vibration control of a frame structure using electro-rheological fluid mounts. Int J Mech Sci 44(10):2027–2045. doi:10.1016/S0020-7403(02)00172-8, http://www.sciencedirect.com/science/article/B6V49-47BX3RX-4/ 2/53a10ce8cbf8dfa679c34e04beb688e4

  53. Hu Q (2009) A composite control scheme for attitude maneuvering and elastic mode stabilization of flexible spacecraft with measurable output feedback. Aerosp Sci Technol 13(2–3):81–91. doi: 10.1016/j.ast.2007.06.007, http://www.sciencedirect.com/science/article/B6VK2-4P96269-2/ 2/5fbc47249fdd3f1963c5ba856f071c55

  54. Huang SJ, Man RJ (1996) Active vibration control of a dynamic absorber using fuzzy algorithms. Mechatronics 6(3):317–336. doi:10.1016/0957-4158(95)00081-X, http://www.sciencedirect.com/science/article/B6V43-3WRJ1S0-5/2/d0cec849f4495c8788cf58ae50bcd708

    Google Scholar 

  55. Inman DJ (2006) Vibration with control. Wiley, Chichester

    Book  Google Scholar 

  56. Inman DJ (2007) Engineering vibrations, 3rd edn. Pearson International Education (Prentice Hall), Upper Saddle River

    Google Scholar 

  57. Jakob A, Möser M (2003) Active control of double-glazed windows, Part I: feedforward control. Appl Acoust 64(2):163–182. doi:10.1016/S0003-682X(02)00070-1, http://www.sciencedirect.com/science/article/pii/S0003682X020

    Google Scholar 

  58. Jastrzebski RP, Hynynen KM, Smirnov A (2010) \({\fancyscript{H}}_\infty\) control of active magnetic suspension. Mech Syst Sig Process 24(4):995–1006. doi: 10.1016/j.ymssp.2009.10.008 , http://www.sciencedirect.com/science/article/B6WN1-4XJP3XR-2/2/51b0222180b2610516135c196f226b0e

  59. Jnifene A (2007) Active vibration control of flexible structures using delayed position feedback. Syst Control Lett 56(3):215–222. doi: 10.1016/j.sysconle.2006.10.005, http://www.sciencedirect.com/science/article/B6V4X-4MJC1V9-1/ 2/5fe33b4788d9ca97d9a9938bc7742194

    Google Scholar 

  60. Jung WJ, Jeong WB, Hong SR, Choi SB (2004) Vibration control of a flexible beam structure using squeeze-mode ER mount. J Sound Vib 273(1–2):185–199. doi:10.1016/S0022-460X(03)00478-4, http://www.sciencedirect.com/science/article/B6WM3-49DFFMM-1/ 2/1255ad59eca53b0c021632de61aef0b8

    Google Scholar 

  61. Kamman JW, Naghshineh K (1999) A comparison of open-loop feedforward and closed-loop methods for active noise control using volume velocity minimization. Appl Acoust 57(1):29–37. doi: 10.1016/S0003-682X(98)00043-7, http://www.sciencedirect.com/science/article/pii/S0003682X980

  62. Kang B, Mills JK (2005) Vibration control of a planar parallel manipulator using piezoelectric actuators. J Intell Rob Syst 42:51–70. doi:10.1007/s10846-004-3028-1

    Google Scholar 

  63. Karimi H, Zapateiro M, Luo N, Rossell J (2010) Feedback vibration control of a base-isolated building with delayed measurements using \(\fancyscript{H}_{\infty}\,\) techniques. In: American control conference (ACC), 2010, pp 750–55

    Google Scholar 

  64. Kawabe H, Tsukiyama N, Yoshida K (2006) Active vibration damping based on neural network theory. Mater Sci Eng A 442(1–2):547–550. doi:10.1016/j.msea.2006.02.234, http://www.sciencedirect.com/science/article/B6TXD-4KPFKNH-2/ 2/51634002bdd85fe7ee55df4b6b28e7e4, Proceedings of the 14th international conference on internal friction and mechanical spectroscopy

  65. Keane AJ (1995) Passive vibration control via unusual geometries: the application of genetic algorithm optimization to structural design. J Sound Vib 185(3):441–453. doi:10.1006/jsvi.1995.0391, http://www.sciencedirect.com/science/article/B6WM3-45R8DN4-16 /2/ef1e97179ca4c87ba2111dd2da839fd5

  66. Kim I, Kim YS (2009) Active vibration control of trim panel using a hybrid controller to regulate sound transmission. Int J Precis Eng Manuf 10:41–47. doi:10.1007/s12541-009-0007-2

    Google Scholar 

  67. Krishnaswamy K, Rajamani R, Woo J, Cho Y (2005) Structural vibration control for broadband noise attenuation in enclosures. J Mech Sci Technol 19:1414–1423. doi:10.1007/BF03023900

    Google Scholar 

  68. Kumar R, Singh S, Chandrawat H (2007) MIMO adaptive vibration control of smart structures with quickly varying parameters: neural networks vs classical control approach. J Sound Vib 307(3–5):639–661. doi:10.1016/j.jsv.2007.06.028, http://www.sciencedirect.com/science/article/B6WM3-4PJ6BP9-1/ 2/69b80beb8f5338317e59823d40598c23

  69. Kvasnica M, Herceg M, Čirka L’, Fikar M (2009) Time-optimal control of Takagi-Sugeno fuzzy systems. In: Proceedings of the 10th European control conference, Budapest, pp 916–921

    Google Scholar 

  70. Kvasnica M, Herceg M, Čirka L’, Fikar M (2011) Explicit minimum-time controllers for fuzzy systems. In: Selected topics on constrained and nonlinear control. Preprints, STU Bratislava-NTNU Trondheim, pp 287–292

    Google Scholar 

  71. Kwak MK, Heo S (2007) Active vibration control of smart grid structure by multiinput and multioutput positive position feedback controller. J Sound Vib 304(1–2):230–245. doi:10.1016/j.jsv.2007.02.021, http://www.sciencedirect.com/science/article/B6WM3-4NH6N96-2/ 2/ca7b43602b9d052e388f4b2a28f1ebae

    Google Scholar 

  72. Kwakernaak H (1993) Robust control and \({\fancyscript{H}}_\infty\)-optimization-tutorial paper. Automatica 29(2):255–273. http://doc.utwente.nl/29962//

  73. Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley-Interscience/Wiley, New York

    MATH  Google Scholar 

  74. Landau ID, Zito G (2006) Digital control systems: design, identification and implementation. Communications and control engineering. Springer, London

    Google Scholar 

  75. Landau ID, Constantinescu A, Rey D (2005) Adaptive narrow band disturbance rejection applied to an active suspension–an internal model principle approach. Automatica 41(4):563–574. doi:10.1016/j.automatica.2004.08.022, http://www.sciencedirect.com/science/article/B6V21-4FB3X55-3/ 2/28887440b73dcde4fdbaefe4d507e857

    Google Scholar 

  76. Landis T, NASA Dryden Flight Research Center (NASA-DFRC) (2001) Full scale dynamic model of the EOS-AM1 satellite. Image ID: EC01-0288-2

    Google Scholar 

  77. Lee J, Kim J, Cheong C (1999) Piezoelectric smart structures for noise reduction in a cabin. J Mech Sci Technol 13:451–458. doi:10.1007/BF02947714, 10.1007/BF02947714

    Google Scholar 

  78. Lim CW (2008) Active vibration control of the linear structure with an active mass damper applying robust saturation controller. Mechatronics 18(8):391–399. doi:10.1016/j.mechatronics.2008.06.006, http://www.sciencedirect.com/science/article/pii/S09574158080

  79. Lin J, Liu WZ (2006) Experimental evaluation of a piezoelectric vibration absorber using a simplified fuzzy controller in a cantilever beam. J Sound Vib 296(3):567–582. doi:10.1016/j.jsv.2006.01.066, http://www.sciencedirect.com/science/article/B6WM3-4K0FG0H-2/ 2/e4fad7e52e98cf46123aa869cf780b65

  80. Lin LC, Lee TE (1997) Integrated PID-type learning and fuzzy control for flexible-joint manipulators. J Intell Rob Syst 18:47–66. doi:10.1023/A:1007942528058

    Google Scholar 

  81. Lin Q, Ermanni P (2004) Semi-active damping of a clamped plate using PZT. Int J Solids Struct 41:1741–1752

    Article  MATH  Google Scholar 

  82. Liu SJ, Huang ZH, Chen YZ (2004) Automobile active suspension system with fuzzy control. J Central South Univ Technol 11:206–209. doi:10.1007/s11771-004-0042-1

    Google Scholar 

  83. Luo T, Hu Y (2002) Vibration suppression techniques for optical inter-satellite communications. In: IEEE 2002 international conference on communications, circuits and systems and west sino expositions, vol 1, pp 585–589. doi:10.1109/ICCCAS.2002.1180687

  84. Mahmoodi SN, Craft MJ, Southward SC, Ahmadian M (2011) Active vibration control using optimized modified acceleration feedback with adaptive line enhancer for frequency tracking. J Sound Vib 330(7):1300–1311. doi:10.1016/j.jsv.2010.10.013, http://www.sciencedirect.com/science/article/B6WM3-51D894K-1/ 2/25e8ef1bcadb5fd2aa078de4d678c7f4

  85. Marzbanrad J, Ahmadi G, Jha R (2004) Optimal preview active control of structures during earthquakes. Eng Struct 26(10):1463–1471. doi:10.1016/j.engstruct.2004.05.010,http://www.sciencedirect.com/science/article/B6V2Y-4CYNR00-1/ 2/271b4c49fa053fb1a95d5df632c701c8

    Google Scholar 

  86. Mehrabian AR, Yousefi-Koma A (2011) A novel technique for optimal placement of piezoelectric actuators on smart structures. J Franklin Inst 348(1):12–23. doi:10.1016/j.jfranklin.2009.02.006, http://www.sciencedirect.com/science/article/B6V04-4VTCM9T-1/ 2/1d68ecf523d642a7246481a506f3edab, International symposium on mechatronics and its applications 2007

    Google Scholar 

  87. Michels K, Klawonn F, Kruse R, Nurnberger A (2006) Fuzzy control: fundamentals, stability and design of fuzzy controllers, studies in fuzziness and soft computing, vol 200. Springer, Berlin

    Google Scholar 

  88. Moon SJ, Lim CW, Kim BH, Park Y (2007) Structural vibration control using linear magnetostrictive actuators. J Sound Vib 302(4–5):875–891. doi:10.1016/j.jsv.2006.12.023, http://www.sciencedirect.com/science/article/B6WM3-4N2M6HH-5/2/417522adfca8640acfa76e890ae0533c

    Google Scholar 

  89. Moshrefi-Torbati M, Keane AJ, Elliott SJ, Brennan MJ, Rogers E (2003) Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm. J Sound Vib 267(4):879–892. doi:10.1016/S0022-460X(03)00192-5, http://www.sciencedirect.com/science/article/B6WM3-48NJ208-4/ 2/d00d9d286c87c83da9f2a01bba7d9209

  90. Moshrefi-Torbati M, Keane A, Elliott S, Brennan M, Anthony D, Rogers E (2006) Active vibration control (AVC) of a satellite boom structure using optimally positioned stacked piezoelectric actuators. J Sound Vib 292(1–2):203–220. doi:10.1016/j.jsv.2005.07.040, http://www.sciencedirect.com/science/article/pii/S0022460X050

  91. Ok SY, Kim DS, Park KS, Koh HM (2007) Semi-active fuzzy control of cable-stayed bridges using magneto-rheological dampers. Eng Struct 29(5):776–788. doi:10.1016/j.engstruct.2006.06.020, http://www.sciencedirect.com/science/article/B6V2Y-4KM46VD-4/ 2/1c85c3a0d12e30e2d5afddaa590f7059

    Google Scholar 

  92. Park HW, Yang HS, Park YP, Kim SH (1999) Position and vibration control of a flexible robot manipulator using hybrid controller. Rob Autom Syst 28(1):31–41. doi:10.1016/S0921-8890(99)00027-5, http://www.sciencedirect.com/science/article/B6V16-3X9YY2M-4/ 2/991e70955258e7604c6775467c5eea35, Robotics applications at FLINS’98

  93. Pasco Y, Robin O, Bélanger P, Berry A, Rajan S (2011) Multi-input multi-output feedforward control of multi-harmonic gearbox vibrations using parallel adaptive notch filters in the principal component space. J Sound Vib (in press). Corrected proof. doi:10.1016/j.jsv.2011.06.008, http://www.sciencedirect.com/science/article/pii/S0022460X110

  94. Passino KM, Yurkovich S (1998) Fuzzy control. Addison-Wesley, Berkley

    Google Scholar 

  95. Pradhan S (2005) Vibration suppression of FGM shells using embedded magnetostrictive layers. Int J Solids Struct 42(9–10):2465–2488. doi:10.1016/j.ijsolstr.2004.09.049, http://www.sciencedirect.com/science/article/B6VJS-4F6SSGN-1/2/b6f9e2e6ffc65bfc0c4af5083e37df0b

    Google Scholar 

  96. Preumont A (2002) Vibration control of active structures, 2nd edn. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  97. Preumont A, Seto K (2008) Active control of structures, 3rd edn. Wiley, Chichester

    Google Scholar 

  98. Rashidi M (1990) A computational strategy for active control of dynamic systems via minimizing the displacement magnitudes of dominant harmonics of vibration. Math Comput Modell 14:410–412. doi:10.1016/0895-7177(90)90217-B, http://www.sciencedirect.com/science/article/pii/089571779090

  99. Rios-Gutiérrez M, Silva-Navarro G (2010) Suppression of mechanical vibrations in a building like structure by means of a piezoelectric patch actuator and positive acceleration feedback. In: 2010 7th international conference on electrical engineering computing science and automatic control (CCE), pp 452–457. doi:10.1109/ICEEE.2010.5608581

  100. Roy T, Chakraborty D (2009) Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm. J Sound Vib 319(1–2): 15–40. doi:10.1016/j.jsv.2008.05.037, http://www.sciencedirect.com/science/article/B6WM3-4T0X2NT-1/2/6e02883f5e6352192210eb9b36700538

  101. Seba B, Nedeljkovic N, Paschedag J, Lohmann B (2005) \({\fancyscript{H}}_{\infty}\) feedback control and Fx-LMS feedforward control for car engine vibration attenuation. Appl Acoust 66(3):277–296. doi:10.1016/j.apacoust.2004.07.015, http://www.sciencedirect.com/science/article/B6V1S-4DTKD2W-1/2/d413b004e2a2e14e9df7fcf75f2df02f

  102. Shan J, Liu HT, Sun D (2005) Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF). Mechatronics 15(4): 487–503. doi:10.1016/j.mechatronics.2004.10.003, http://www.sciencedirect.com/science/article/B6V43-4DR87K7-4/ 2/2dd311fdd61308e1415cd45c1edc3076

    Google Scholar 

  103. Simões-Moita JM, Correia VMF, Martins PG, Soares CMM, Soares CAM (2006) Optimal design in vibration control of adaptive structures using a simulated annealing algorithm. Compos Struct 75(1–4):79–87. doi:10.1016/j.compstruct.2006.04.062, http://www.sciencedirect.com/science/article/pii/S02638223060, thirteenth international conference on composite structures-ICCS/13

  104. Skogestad S, Postlethwaite I (2005) Multivariable feedback control: analysis and design, 2nd edn. Wiley, Chichester

    Google Scholar 

  105. Snyder SD (2000) Active noise control primer. Modern acoustics and signal processing. Springer/AIP Press, New York

    Book  Google Scholar 

  106. Song G, Qiao PZ, Bibienda WK, Zhou GP (2002) Active vibration damping of composite beam using smart sensors and actuators. J Aerosp Eng 15(3):97–103

    Article  Google Scholar 

  107. Sun D, Mills JK, Shan J, Tso SK (2004) A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement. Mechatronics 14(4):381–401. doi:10.1016/S0957-4158(03)00066-7, http://www.sciencedirect.com/science/article/B6V43-49DN5K4-1/2/fa21df547f182ad568cefb2ddf3a6352

    Google Scholar 

  108. Sun J, Yang Q (2007) Automotive suspension system with an analytic fuzzy control strategy. In: IEEE international conference on vehicular electronics and safety, 2007. ICVES, pp 1–4. doi:10.1109/ICVES.2007.4456375

  109. Sun W, Li J, Zhao Y, Gao H (2010) Vibration control for active seat suspension systems via dynamic output feedback with limited frequency characteristic. Mechatronics (in press). Corrected proof. doi:10.1016/j.mechatronics.2010.11.001, http://www.sciencedirect.com/science/article/B6V43-51KH6DW-1/ 2/9f06f9d31ca4a47bf3b8e034ba8c6150

  110. Sung KG, Han YM, Cho JW, Choi SB (2008) Vibration control of vehicle ER suspension system using fuzzy moving sliding mode controller. J Sound Vib 311(3–5):1004–1019. doi:10.1016/j.jsv.2007.09.049, http://www.sciencedirect.com/science/article/B6WM3-4R2H1TN-4/ 2/b3a297765c3ac7767b2d64fda7a6a3d7

    Google Scholar 

  111. Tso SK, Yang TW, Xu WL, Sun ZQ (2003) Vibration control for a flexible-link robot arm with deflection feedback. Int J Non Linear Mech 38(1):51–62. doi:10.1016/S0020-7462(01)00040-3, http://www.sciencedirect.com/science/article/B6TJ2-46BSCBF-5/2/db9a6ea06f0106fae187a067a96b1888

    Google Scholar 

  112. Tzou H, Chai W (2007) Design and testing of a hybrid polymeric electrostrictive/piezoelectric beam with bang-bang control. Mech Syst Sig Process 21(1):417–429. doi:10.1016/j.ymssp.2005.10.008, http://www.sciencedirect.com/science/article/B6WN1-4HR75KY-1/2/73701e5908a2ea598fa7bec1ce093563

  113. Vasques C, Rodrigues JD (2006) Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies. Comput Struct 84(22–23):1402–1414. doi:10.1016/j.compstruc.2006.01.026, http://www.sciencedirect.com/science/article/B6V28-4K4219V-1/ 2/fc83fdc87b19e200d95c2b596f8f0201, Composite adaptive structures: modelling and simulation

    Google Scholar 

  114. Šolek P (2009) Numerical analyses of piezoelectric elements, 1st edn. Slovenská technická univerzita v Bratislave, Nakladatel’stvo STU, Bratislava

    Google Scholar 

  115. Wang Z, Chen S, Han W (1999) Integrated structural and control optimization of intelligent structures. Eng Struct 21(2):183–191. doi:10.1016/S0141-0296(97)90158-9, http://www.sciencedirect.com/science/article/pii/S01410296979

  116. Wei JJ, Qiu ZC, Han JD, Wang YC (2010) Experimental comparison research on active vibration control for flexible piezoelectric manipulator using fuzzy controller. J Intell Rob Syst 59:31–56. doi:10.1007/s10846-009-9390-2, http://dx.doi.org/10.1007/s10846-009-9390-2

    Google Scholar 

  117. Wenzhong Q, Jincai S, Yang Q (2004) Active control of vibration using a fuzzy control method. J Sound Vib 275(3-5):917–930. doi:10.1016/S0022-460X(03)00795-8, http://www.sciencedirect.com/science/article/B6WM3-49P82Y8-3/2/4041c663559fb530f34deadda058c82d

    Google Scholar 

  118. Williams RL II, Lawrence DA (2007) Linear state-space control systems. Wiley, Hoboken

    Book  Google Scholar 

  119. Yaman M, Sen S (2007) Vibration control of a cantilever beam of varying orientation. Int J Solids Struct 44(3–4):1210–1220. doi:10.1016/j.ijsolstr.2006.06.015, http://www.sciencedirect.com/science/article/B6VJS-4K6KB0P-6/2/ec9c328d3a430cb47cf393bb4917a950

    Google Scholar 

  120. Yang Y, Jin Z, Soh CK (2005) Integrated optimal design of vibration control system for smart beams using genetic algorithms. J Sound Vib 282 (3–5):1293–1307. doi:10.1016/j.jsv.2004.03.048, http://www.sciencedirect.com/science/article/B6WM3-4DJBPM1-6/ 2/944b2e30a1b99c969b56adbf527d9b1c

  121. Yau J (2009) Vibration control of maglev vehicles traveling over a flexible guideway. J Sound Vib 321(1–2):184–200. doi:10.1016/j.jsv.2008.09.030, http://www.sciencedirect.com/science/article/B6WM3-4TWSWP3-1/ 2/c2ef06bef3677e1ed29b82857a322d58

    Google Scholar 

  122. Yildirim S (2004) Vibration control of suspension systems using a proposed neural network. J Sound Vib 277(4–5):1059–1069. doi:10.1016/j.jsv.2003.09.057, http://www.sciencedirect.com/science/article/B6WM3-4BM6CCP-4/2/0db857f0580d634772e8d782485e76bf

    Google Scholar 

  123. Yousefi H, Hirvonen M, Handroos H, Soleymani A (2008) Application of neural network in suppressing mechanical vibration of a permanent magnet linear motor. Control Eng Pract 16(7):787–797. doi:10.1016/j.conengprac.2007.08.003, http://www.sciencedirect.com/science/article/B6V2H-4R003K1-1/2/42098496ccc03cdc28602bd04bc4858e

  124. Zames G (1979) Optimal sensitivity and feedback; weighted seminorms, approximate inverses, and plant invariant schemes. In: Proceedings 17th of the Allerton conference, pp 744–752

    Google Scholar 

  125. Zames G (1981) Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans Autom Control 26(2):301–320. doi:doi:10.1109/TAC.1981.1102603

    Article  MathSciNet  MATH  Google Scholar 

  126. Zapateiro M, Luo N, Karimi H, Vehi J (2009) Vibration control of a class of semiactive suspension system using neural network and backstepping techniques. Mech Syst Sig Process 23(6):1946–1953. doi:10.1016/j.ymssp.2008.10.003, http://www.sciencedirect.com/science/article/B6WN1-4TTMJRM-1/2/b6b45074716201902e0b01b664ebbeb9, special issue: Inverse Problems

  127. Zhang CL, Mei DQ, Chen ZC (2002) Active vibration isolation of a micro-manufacturing platform based on a neural network. J Mater Process Technol 129 (1–3):634–639. doi:10.1016/S0924-0136(02)00671-4, http://www.sciencedirect.com/science/article/B6TGJ-46V46C0-4P /2/8e8228760a4ac6759cef159e6fcb7606

    Google Scholar 

  128. Zhang H, Liu D (2006) Fuzzy modeling and fuzzy control. Control engineering. Birkhäuser, Boston

    Google Scholar 

  129. Zheng K, Zhang Y, Yang Y, Yan S, Dou L, Chen J (2008) Active vibration control of adaptive truss structure using fuzzy neural network. In: Control and decision conference. CCDC 2008. Chinese, pp 4872–4875. doi:10.1109/CCDC.2008.4598254

  130. Zhu C (2005) A disk-type magneto-rheological fluid damper for rotor system vibration control. J Sound Vib 283(3–5):1051–1069. doi:10.1016/j.jsv.2004.06.031, http://www.sciencedirect.com/science/article/B6WM3-4F4H9R2-1/ 2/48abebbf8d1230fcd80eee7d19fe52fa

    Google Scholar 

  131. Zhu H, Rajamani R, Dudney J, Stelson K (2003) Active noise control using a distributed mode flat panel loudspeaker. ISA Trans 42(3):475–484. doi:10.1016/S0019-0578(07)60148-7, http://www.sciencedirect.com/science/article/pii/S00190578076

  132. Zilletti M, Elliott SJ, Gardonio P (2010) Self-tuning control systems of decentralised velocity feedback. J Sound Vib 329(14):2738–2750. doi:10.1016/j.jsv.2010.01.024, http://www.sciencedirect.com/science/article/B6WM3-4YCGKVX-1/ 2/81a53368279e8e5c8664ee835d4b4985

    Google Scholar 

  133. Zmeu K, Shipitko E (2005) Predictive controller design with offline model learning for flexible beam control. In: Proceedings of the 2005 international conference on physics and control, pp 345–350. doi:10.1109/PHYCON.2005.1514005

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Institute of Automation, Measurement and Applied Informatics, Slovak University of Technology in Bratislava, Námestie slobody 17, 812 31, Bratislava 1, Slovakia

    Gergely Takács & Boris Rohal’-Ilkiv

Authors
  1. Gergely Takács
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Boris Rohal’-Ilkiv
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag London Limited

About this chapter

Cite this chapter

Takács, G., Rohal’-Ilkiv, B. (2012). Algorithms in Active Vibration Control. In: Model Predictive Vibration Control. Springer, London. https://doi.org/10.1007/978-1-4471-2333-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-2333-0_4

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2332-3

  • Online ISBN: 978-1-4471-2333-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation