Theoretical and experimental studies are conducted to control nonlinear vibration of a two-link flexible manipulator via internal resonance. A vibration control method is proposed and an effective vibration absorber is implemented based on a servomotor to establish a 2:1 internal resonance relationship with the flexible manipulator. By way of perturbation analysis, it is proven that internal resonance can be successfully established for the flexible manipulator undergoing rigid motion. In the presence of damping, the vibration energy of the flexible manipulator can be transferred to and dissipated by the vibration absorber via internal resonance. Numerical simulations and experimental investigation have verified the effectiveness and feasibility of the proposed method.
AbikoSYoshidaK (2010) Adaptive reaction control for space robotic applications with dynamic model uncertainty. Advanced Robotics24(8-9): 1099–1126.
2.
Ahmad MA, Suid MH, Ramli MS, et al. (2010) PD fuzzy logic with non-collocated PID approach for vibration control of flexible joint manipulator. In: 6th international colloquium on signal processing and its applications, Melaka, Malaysia, 21–23 May 2010. US: IEEE Computer Society.
3.
AshourONNayfehAH (2002) Adaptive control of flexible structures using a nonlinear vibration absorber. Nonlinear Dynamics28(3-4): 309–322.
4.
BianYGaoZYunC (2011) Study on vibration reduction and mobility improvement for the flexible manipulator via redundancy resolution. Nonlinear Dynamics65(4): 359–368.
5.
Cui LL and Xiao ZQ (2003) Optimum structure design of flexible manipulators based on GA. In: Proceedings of the IEEE international conference on intelligent transportation systems, vol.2, Shanghai, China, 12–15 October 2003, pp.1622–1626. Institute of Electrical and Electronics Engineers Inc.
6.
DixitUSKumarRDwivedySK (2006) Shape optimization of flexible robot manipulators. Journal of Mechanical Design, Transactions of ASME128(3): 559–565.
7.
DuquetteAPTuerKLGolnaraghiMF (1993) Vibration control of a flexible beam using a rotational internal resonance controller, Part II: Experiment. Journal of Sound and Vibration167(1): 63–75.
8.
GhazaviAGordaninejaddFChalhoubNG (1993) Dynamic analysis of a composite-material flexible robot arm. Computers and Structures49(2): 315–327.
9.
GolnaraghiMF (1991) Regulation of flexible structures via nonlinear coupling. Dynamics and Control1: 405–428.
10.
GolnaraghiMFTuerKLWangD (1994) Regulation of a lumped parameter cantilever beam via internal resonance using nonlinear coupling enhancement. Dynamics and Control4: 73–96.
11.
GordaninejaddFChalhoubNGGhazaviAet al. (1992) Nonlinear deformation of a shear-deformable laminated composite-material flexible robot arm. Journal of Mechanical Design114(1): 96–102.
12.
Heidari HR, Korayem MH, Haghpanahi M, et al. (2011) A new nonlinear finite element model for the dynamic modeling of flexible link manipulators undergoing large deflections. In: IEEE international conference on mechatronics, Istanbul, Turkey, 13–15 April 2011, pp.375–380. US: IEEE Computer Society.
13.
HeidariHRKorayemMHHaghpanahiM (2015) Maximum allowable load of very flexible manipulators by using absolute nodal coordinate. Aerospace Science and Technology45: 67–77.
14.
HuiCKLeeYYNgCF (2011) Use of internally resonant energy transfer from the symmetrical to anti-symmetrical modes of a curved beam isolator for enhancing the isolation performance and reducing the source mass translation vibration: Theory and experiment. Mechanical Systems and Signal Processing25: 1248–1259.
15.
KhajepourAGolnaraghiMFMorrisKA (1997) Application of center manifold theory to regulation of a flexible beam. ASME Journal of Vibration and Acoustics119: 158–165.
16.
KrishnamurthyKChandrashekharaKRoyS (1990) A study of single-link robots fabricated from orthotropic composite materials. Computers and Structures136(1): 139–146.
17.
Mahamood RM and Pedro JO (2011) Hybrid PD/PID controller design for two-link flexible manipulators. In: 8th Asian control conference, Kaohsiung, Taiwan, 15–18 May 2011, pp.1358–1363. US: IEEE Computer Society.
18.
Mojtaba RK, Faezeh F, Maysam ZP, et al. (2011) Variable structure control and anti-control of flexible joint manipulator with experimental validation. In: IEEE international conference on mechatronics, Istanbul, Turkey, 13–15 April 2011, pp.294–299. US: IEEE Computer Society.
19.
OrszulikRRShanJ (2011) Vibration control using input shaping and adaptive positive position feedback. Journal of Guidance, Control and Dynamics34(4): 1031–1044.
20.
OueiniSSGolnaraghiMF (1996) Experimental implementation of the internal resonance control strategy. Journal of Sound and Vibration191(3): 377–396.
21.
PaiPFRommelBSchulzMJet al. (2000) Non-linear vibration absorbers using higher order internal resonances. Journal of Sound and Vibration234(5): 799–817.
22.
Sasaki M, Asai A, Shimizu T, et al. (2009) Self-tuning control of a two-link flexible manipulator using neural networks. In: ICCAS–SICE 2009 – ICROS-SICE international joint conference, Fukuoka, Japan, 18–21 August 2009, pp.2468–2473. US: IEEE Computer Society.
23.
TheodoreRJGhosalA (2003) Robust control of multilink flexible manipulators. Mechanism and Machine Theory38(4): 367–377.
24.
TuerKLDuquetteAPGolnaraghiMF (1993) Vibration control of a flexible beam using a rotational internal resonance controller, Part I: Theoretical development and analysis. Journal of sound and Vibration167(1): 41–62.
25.
TuerKLGolnaraghiMFWangD (1994) Development of a generalised active vibration suppression strategy for a cantilever beam using internal resonance. Nonlinear Dynamics5: 131–151.
26.
YamanMSenS (2007) Determining the effect of detuning parameters on the absorption region for a coupled nonlinear system of varying orientation. Journal of Sound and Vibration300(1-2): 330–344.
