A conventional vibration absorber is valid when the external excitation frequency falls into the neighborhood of a specific value. It is not feasible for vibration suppression applications subject to frequency-varying excitations. In this paper, an adaptive controller is proposed to learn the disturbance spectrum in real time so that output vibration suppression can be achieved regardless of the variations in the excitation frequency. The Lyapunov-like analysis is used to verify the closed-loop stability and ensure boundedness of internal signals. Simulation cases show that the proposed strategy can give satisfactory performance.
AbéMIgusaT (1996) Semi-active dynamic vibration absorbers for controlling transient response. Journal of Sound and Vibration198(5): 547–569.
2.
BarmishBRLeitmannG (1982) On ultimate boundedness control of uncertain systems in the absence of matching assumptions. IEEE Transactions on Automatic ControlAC-27(1): 153–158.
3.
BrennanMJDayouJ (2000) Global control of vibration using a tunable vibration neutralizer. Journal of Sound and Vibration232(3): 585–600.
4.
BuppRTBernsteinDSChellaboinaVS (2000) Resetting virtual absorbers for vibration control. Journal of Vibration and Control6(1): 61–83.
5.
BurdissoRAHeilmannJD (1998) A new dual-reaction mass dynamic vibration absorber actuator for active vibration control. Journal of Sound and Vibration214(5): 817–831.
6.
ChenPCHuangAC (2005) Adaptive sliding control of non-autonomous active suspension systems with time- vary loadings. Journal of Sound and Vibration282(3–5)1119–1135.
7.
ChenYDFuhCCTungPC (2005) Application of voice coil motors in active dynamic vibration absorbers. IEEE Transactions on Magnetics41(3): 1149–1154.
8.
ChenYFHuangAC (2012) Controller design for a class of underactuated mechanical systems. IET Control Theory and Applications6(1): 103–110.
9.
ChienMCHuangAC (2007) Adaptive control of flexible-joint electrically-driven robot with time-varying uncertainties. IEEE Transactions on Industrial Electronics54(2): 1032–1038.
10.
CohenKYaffeRWellerT (2002) Experimental studies on adaptive fuzzy control of a smart structure. Journal of Vibration and Control8(8): 1071–1083.
11.
DavisCLLesieutreGA (2000) An actively tuned solid-state vibration absorber using capacitive shunting of piezoelectric stiffness. Journal of Sound and Vibration232(3): 601–617.
12.
Den HartogJP (1956) Mechanical Vibrations, New York: McGraw-Hill.
13.
El-BadawyAAEl-DeenTNN (2007) Quadratic nonlinear control of a self-excited oscillator. Journal of Vibration and Control13(4): 403–414.
14.
FilipovićDSchröderD (1998) Bandpass vibration absorber. Journal of Sound and Vibration214(3): 553–566.
15.
FilipovicDSchroderD (1999) Vibration absorption with linear active resonators: Continuous and discrete time design and analysis. Journal of Vibration and Control5(5): 685–708.
16.
HollkampJStarchvilleT (1994) A self-tuning piezoelectric vibration absorber. Journal of Intelligent Material Systems and Structures5(4): 559–566.
17.
HosekMOlgacNElmaliH (1999) The centrifugal delayed resonator as a tunable torsional vibration absorber for multi-degree-of-freedom systems. Journal of Vibration and Control5(2): 299–322.
18.
HuangACChenYC (2004a) Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties. Automatica40(11): 1939–1945.
19.
HuangACChenYC (2004b) Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties. IEEE Transactions on Control Systems Technology12(5): 770–775.
20.
Huang AC and Chien MC (2010) Adaptive Control of Robot Manipulators – A Unified Regressor-free Approach. Singapore: World Scientific.
21.
HuangACKuoYS (2001) Sliding control of nonlinear systems containing time-varying uncertainties with unknown bounds. International Journal of Control74(3): 252–264.
22.
HuangSLianR (1994) A dynamic absorber with active vibration control. Journal of Sound and Vibration178(3): 323–335.
23.
HuyananSSimsND (2007) Vibration control strategies for proof-mass actuators. Journal of Vibration and Control13(12): 1785–1806.
24.
JaliliNKnowlesDW (2004) Structural vibration control using an active resonator absorber: modeling and control implementation. Smart Materials and Structures13(5): 998–1005.
25.
KhalilHK (2002) Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall.
26.
KooJ-HAhmadianMSetarehM (2004) In search of suitable control methods for semi-active tuned vibration absorbers. Journal of Vibration and Control10(2): 163–174.
27.
KrsticMKanellakopoulosIKokotovicPV (1995) Nonlinear and Adaptive Control Design, New York: Wiley.
28.
LeeTFHuangAC (2011) Vibration suppression in belt-driven servo systems containing uncertain nonlinear dynamics. Journal of Sound and Vibration330(1): 17–26.
29.
LiJHuaHXShenRY (2007) Saturation-based active absorber for a non-linear plant to a principal external excitation. Mechanical Systems and Signal Processing21(3): 1489–1498.
30.
MorganRAWangKW (2002) Active-passive piezoelectric absorbers for systems under multiple non-stationary harmonic excitations. Journal of Sound and Vibration255(4): 685–700.
31.
NagayaKKurusuAIkaiS (1999) Vibration control of a structure by using a tunable absorber and an optimal vibration absorber under auto-tuning control. Journal of Sound and Vibration228(4): 773–792.
32.
Olfati-SaberR (2002) Normal forms for underactuated mechanical systems with symmetry. IEEE Transactions on Automatic Control47(2): 305–308.
33.
OlgacNElmaliH (2000) Analysis and design of delayed resonator in discrete domain. Journal of Vibration and Control6(2): 273–289.
34.
OlgacNHolm-HansenB (1994) A novel active vibration absorption technique: Delayed resonator. Journal of Sound and Vibration176(1): 93–104.
35.
OlgacNJaliliN (1998) Modal analysis of flexible beams with delayed resonator vibration absorber: theory and experiments. Journal of Sound and Vibration218(2): 307–331.
36.
OrmondroydJDen HartogJP (1928) The theory of the dynamic vibration absorber. ASME Journal of Applied Mechanics50(7): 9–22.
37.
OueiniSSNayfehAH (2000) Analysis and application of a nonlinear vibration absorber. Journal of Vibration and Control6(7): 999–1016.
38.
OueiniSSNayfehAHPrattJR (1998) A nonlinear vibration absorber for flexible structures. Nonlinear Dynamics15(3): 259–282.
39.
RanaRSoongTT (1998) Parametric study and simplified design of tuned mass dampers. Engineering Structures20(3): 193–204.
40.
SemercigilSELammersDYingZ (1992) A new tuned vibration absorber for wide-band excitations. Journal of Sound and Vibration156(3): 445–459.
41.
SpongMW(1997) Underactuated mechanical systems. In: SicilianoBValavanisKP (eds) Control Problems in Robotics and Automation, London: Springer.
42.
SpoonerJTMaggioreMOrdonezR (2002) Stable Adaptive Control and Estimation for Nonlinear Systems—Neural and Fuzzy Approximator Techniques, New York: Wiley.
43.
SunHLZhangPQGongXL (2007) A novel kind of active resonator absorber and the simulation on its control effort. Journal of Sound and Vibration300(1–2): 117–125.
44.
SunJQJollyMRNorrisMA (1995) Passive, adaptive and active tuned vibration absorbers—a survey. Transactions of American Society of Mechanical Engineers117(B): 234–242.
45.
TsaiYCHuangAC (2008a) FAT based adaptive control for pneumatic servo system with mismatched uncertainties. Mechanical Systems and Signal Processing22(6): 1263–1273.
WalshPLLamancusaJS (1992) A variable stiffness vibration absorber for minimization of transient vibrations. Journal of Sound and Vibration158(2): 195–211.
48.
WilliamsKChiuGBernhardR (2002) Adaptive-passive absorbers using shape-memory alloys. Journal of Sound and Vibration249(5): 835–848.
49.
WrightRIKidnerMRF (2004) Vibration absorbers: A review of applications in interior noise control of propeller aircraft. Journal of Vibration and Control10(8): 1221–1237.
