Flexible dynamic behavior of ultra-precision motion stage significantly deteriorates control performance. To tackle this problem, this paper presents an norm based parameter optimization of multiple Tuned Mass Dampers (TMDs) for resonance suppression applied on linear flexible structures, assuming all parameters of multiple TMDs are independent, and considering locations of TMDs as variables. Linear flexible structures with multiple TMDs are modeled as a closed-loop control system through modeling in steps. Genetic algorithm is implemented employing norm as the optimization criterion. The effectiveness of the optimization is numerically verified on a free-free thin plate. The effects of uncertainties in TMDs parameters, linear flexible structure parameters, and TMDs failure on the vibration suppression effect are studied. The proposed modeling and optimization methods are promising for application to various flexible structures with provided modal frequencies and mode shape matrix.
ArazO (2021) Optimum passive tuned mass damper systems for main structures under harmonic excitation. Mühendislik Bilimleri ve Tasarım Dergisi9: 1062–1071.
2.
ArazOKahyaV (2018) Effects of manufacturing type on control performance of multiple tuned mass dampers under harmonic excitation. Journal of Structural Engineering & Applied Mechanics1: 117–127.
3.
Asami (2002) Analytical solutions to H∞ and H2 optimization of dynamic vibration absorbers attached to damped linear systems. Journal of Vibration and Acoustics124(002): 284.
4.
ButlerH (2011) Position Control in Lithographic Equipment [Applications of Control]. New York: IEEE, 28–47.
5.
CarpinetoNLacarbonaraWVestroniF (2010) Mitigation of pedestrian-induced vibrations in suspension footbridges via multiple tuned mass dampers. Journal of Vibration and Control16: 749–776.
6.
ChenGSunYZhangF, et al. (2018) Dynamic accuracy design method of ultra-precision machine tool. Chinese Journal of Mechanical Engineering31: 8.
7.
CheungYLWongWO (2009) H∞ and H2 optimizations of a dynamic vibration absorber for suppressing vibrations in plates. Journal of Sound and Vibration320: 29–42.
8.
CrandallSHMarkWD (1963) Random Vibration in Mechanical Systems.
9.
DayouJ (2006) Fixed-points theory for global vibration control using vibration neutralizer. Journal of Sound and Vibration292: 765–776.
10.
Den HartogJP (1956) Mechanical Vibrations. Somerset: McGraw-Hill.
11.
DingRDingCXuY, et al. (2020) An optimal actuator placement method for direct-drive stages to maximize control bandwidth. IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society556–561.
12.
DomaneschiMMartinelliLPoE (2015) Control of wind buffeting vibrations in a suspension bridge by TMD: hybridization and robustness issues. Computers & Structures155: 3–17.
13.
EleftheriouE (2011) Nanopositioning for storage applications. IFAC Proceedings Volumes44: 2003–2011.
14.
EliasSMatsagarVDattaTK (2019a) Dynamic response control of a wind-excited tall building with distributed multiple tuned mass dampers. International Journal of Structural Stability and Dynamics19: 1950059.
15.
EliasSMatsagarVDattaTK (2019b) Distributed tuned mass dampers for multi-mode control of benchmark building under seismic excitations. Journal of Earthquake Engineering23: 1137–1172.
16.
ErkorkmazKGorniakJMGordonDJ (2010) Precision machine tool X–Y stage utilizing a planar air bearing arrangement. CIRP Annals59: 425–428.
17.
FrahmH (1911) Device for Damping Vibrations of Bodies. In Google Patents.
18.
GongDZhouJSunW, et al. (2017) Method of multi-mode vibration control for the carbody of high-speed electric multiple unit trains. Journal of Sound and Vibration409: 94–111.
19.
GuMXiangH (1992) Optimization of TMD for suppressing buffeting response of long-span bridges. Journal of Wind Engineering and Industrial Aerodynamics42: 1383–1392.
20.
HuangQZhangG (2013) Precision design for machine tool based on error prediction. Chinese Journal of Mechanical Engineering26: 151–157.
21.
JacquotRG (1978) Optimal dynamic vibration absorbers for general beam systems. Journal of Sound and Vibration60: 535–542.
22.
JacquotRG (2001) Suppression of random vibration in plates using vibration absorbers. Journal of Sound and Vibration248: 585–596.
23.
JangidRSDattaTK (1997) Performance of multiple tuned mass dampers for torsionally coupled system. Earthquake Engineering & Structural Dynamics26: 307–317.
24.
KentonBJFlemingAJLeangKK (2011) Compact ultra-fast vertical nanopositioner for improving scanning probe microscope scan speed. Review of Scientific Instruments82: 123703.
25.
LanHDingYLiuH, et al. (2007) Review of the wafer stage for nanoimprint lithography. Microelectronic Engineering84: 684–688.
26.
LantzMARothuizenHEDrechslerU, et al. (2007) A vibration resistant nanopositioner for mobile parallel-probe storage applications. Journal of Microelectromechanical Systems16: 130–139.
27.
LeiZ (2005) Optimization of the individual stiffness and damping parameters in multiple-tuned- mass-damper systems. Journal of Vibration and Acoustics127: 77.
28.
LiHNiX (2007) Optimization of non-uniformly distributed multiple tuned mass damper. Journal of Sound and Vibration308: 80–97.
29.
LiHWuSChenQ, et al. (2021) Design of dynamic absorbers to control the flexural resonant vibration of structures characterized by multiple natural modes. Journal of Sound and Vibration513: 116415.
30.
MaroufiMBazaeiAReza MoheimaniSO (2015) A high-bandwidth MEMS nanopositioner for on-chip AFM: design, characterization, and control. IEEE Transactions on Control Systems Technology23: 504–512.
31.
Murat (2014) H2 optimization of damped-vibration absorbers for suppressing vibrations in beams with constrained minimization. Journal of Vibration and Acoustics136: 021012.
32.
Ontiveros-PérezSPMiguelLFF (2022) Reliability-based optimum design of multiple tuned mass dampers for minimization of the probability of failure of buildings under earthquakes. Structures42: 144–159.
33.
PantaziASebastianACherubiniG, et al. (2007) Control of MEMS-based scanning-probe data-storage devices. IEEE Transactions on Control Systems Technology15: 824–841.
34.
PellizzariFMaranoGCPalmeriA, et al. (2022) Robust optimization of MTMD systems for the control of vibrations. Probabilistic Engineering Mechanics70: 103347.
35.
RajanaKWangZGiaralisA (2023) Optimal design and assessment of tuned mass damper inerter with nonlinear viscous damper in seismically excited multi-storey buildings. Bulletin of Earthquake Engineering21: 1509–1539.
36.
RashidANicolescuCM (2008) Design and implementation of tuned viscoelastic dampers for vibration control in milling. International Journal of Machine Tools and Manufacture48: 1036–1053.
37.
RivinEIKangH (1992) Enhancement of dynamic stability of cantilever tooling structures. International Journal of Machine Tools and Manufacture32: 539–561.
38.
SchmidtRHM (2012) Ultra-precision engineering in lithographic exposure equipment for the semiconductor industry. Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences370: 3950–3972.
39.
ShenYPengHLiX, et al. (2017) Analytically optimal parameters of dynamic vibration absorber with negative stiffness. Mechanical Systems and Signal Processing85: 193–203.
40.
ShiXCaiCS (2008) Suppression of vehicle-induced bridge vibration using tuned mass damper. Journal of Vibration and Control14: 1037–1054.
41.
ShiHLuoRWuP, et al. (2014) Application of DVA theory in vibration reduction of carbody with suspended equipment for high-speed EMU. Science China Technological Sciences57: 1425–1438.
42.
SkogestadSPostlethwaiteI (2005) Multivariable Feedback Control: Analysis and Design. Hoboken, NJ: John Wiley & Sons.
43.
VellarLSOntiveros-PérezSPMiguelLFF, et al. (2019) Robust optimum design of multiple tuned mass dampers for vibration control in buildings subjected to seismic excitation. Shock and Vibration2019: 9273714.
44.
VerbaanKvan der MeulenSSteinbuchM (2017) Broadband damping of high-precision motion stages. Mechatronics41: 1–16.
WuJChenG (2000) Optimization of multiple tuned mass dampers for seismic response reduction. Proceedings of the American Control Conference1(6): 519–523.
47.
XuKIgusaT (1992) Dynamic characteristics of multiple substructures with closely spaced frequencies. Earthquake Engineering & Structural Dynamics21: 1059–1070.
48.
YamaguchiHHarnpornchaiN (1993) Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations. Earthquake Engineering & Structural Dynamics22: 51–62.
49.
YangYMuñoaJAltintasY (2010) Optimization of multiple tuned mass dampers to suppress machine tool chatter. International Journal of Machine Tools and Manufacture50: 834–842.
50.
YangFSedaghatiREsmailzadehE (2022) Vibration suppression of structures using tuned mass damper technology: a state-of-the-art review. Journal of Vibration and Control28: 812–836.
51.
ZhuXChenZJiaoY (2018) Optimizations of distributed dynamic vibration absorbers for suppressing vibrations in plates. Journal of Low Frequency Noise, Vibration and Active Control37: 1188–1200.
52.
ZuoLNayfehSA (2005) Optimization of the individual stiffness and damping parameters in multiple-tuned-mass-damper systems. Journal of Vibration and Acoustics127: 77–83.
