The paper presents a new nonlinear control design methodology for inducing modal, self-excited oscillation in a class of multi degrees-of-freedom mechanical systems. The system is assumed to be fully actuated and the controller operates in a centralized fashion based on the direct nonlinear velocity feedback. The linear part of the controller is designed to assign negative modal damping in the mode to be excited and positive modal damping in other modes. The nonlinear modal interaction is investigated using averaging analysis and different excitation regimes are delineated in the control parameter space. The nonlinear part of the controller is optimized to minimize the control cost. Numerical simulations of the control system are performed to substantiate the analytical results and validate the accuracy of the design. The control method is also shown to have some degree of robustness against parametric variations over the nominal values.
BabitskyVIKalashnikovANMolodtsovFV (2004) Autoresonant control of ultrasonically assisted cutting. Mechatronics14: 91–114.
3.
BatakoADBabitskyVIHalliwellNA (2003) A self-excited system of percussive-rotary drilling. Journal of Sound and Vibration259(1): 97–118.
4.
ChatterjeeS (2011) Self-excited oscillation under nonlinear feedback with time delay. Journal of Sound and Vibration330: 1860–1876.
5.
ChatterjeeSMalasA (2012) On the stiffness-switching methods for generating self-excited oscillations in simple mechanical systems. Journal of Sound and Vibration331: 1742–1758.
6.
EfimovDAlexanderFTetsuyaI (2013) Exciting multi-DOF systems by feedback resonance. Automatica49: 1782–1789.
7.
FriesenW (1994) Reciprocal inhibition: A mechanism underlying oscillatory animal movements. Neuroscience and Biobehavioral Reviews18(4): 547–553.
8.
FuHLiuCLiuY (2011) Selective photothermal self-excitation of mechanical modes of a micro-cantilever for force microscopy. Applied Physics Letters99: 173501.
9.
HatsopoulosN (1996) Coupling the neural and physical dynamics in rhythmic movements. Neural Computation8(3): 567–581.
10.
HatsopoulosNGWarrenWH Jr (1996) Resonance tuning in rhythmic arm movements. Journal of Motor Behaviour28(1): 3–14.
11.
HideomiMYutakaKYuichiM (2001) Generation and control of self-exited vibration by self-sensing actuator. Dynamics & Design Conference 20017: 1551–1556.
12.
Kobayashi T, Oyama S, Okada H, et al. (2012). An electrostatic field sensor driven by self-excited vibration of sensor/actuator integrated piezoelectric microcantilever. In: MEMS 2012, Paris, France, 29 January–2 February.
13.
KuritaYMuragishiY (1997) Self-excited driving of electromagnetic-type vibratory machine. Transactions of the Japan Society of Mechanical Engineers Series C63(605): 35–40.
14.
KuritaYMatsumuraYTanakaA (2003) Vibration transportation by cooperation of decentralized self-excited vibratory machines. Transactions of the Japan Society of Mechanical Engineers Series C69: 1191–1196.
15.
KuritaYMuragishiYYasudaH (1996a) Self-excited driving of resonance-type vibratory machine by vibration quantity feedback. Transactions of the Japan Society of Mechanical Engineers Series C62(597): 1691–1696.
16.
KuritaYMuragishiYYasudaH (1996b) Amplitude control using variable feedback gain in self-excited driving vibratory machine. Transactions of the Japan Society of Mechanical Engineers Series C62(598): 2140–2146.
17.
KurodaMYabunoHHayashiK (2008) Amplitude control in a van der Pol-type self-excited AFM micro cantilever. Journal of System Design and Dynamics2(3): 886–897.
18.
KwasniewskiJDominikILalikK (2012) Application of self-oscillating system for stress measurement in metal. Journal of Vibroengineering14(1): 1392–8716.
19.
Lee SS and White RM (1995) Self-excited piezoelectric cantilever oscillators. In: Proceedings of the eighth international conference on solid-state sensors and actuators and Eurosensors IX, Stockholm, Sweden, 25–29 June 1995.
20.
LeeYLimGMoonW (2007) A piezoelectric micro-cantilever bio-sensor using the mass-micro-balancing technique with self-excitation. Microsystem Technology13: 563–567.
21.
Li C and He X (2007) A bio-mimetic pipe crawling microrobot driven based on self-excited vibration. In: Proceedings of the IEEE international conference on robotics and biomimetics, Sanya, China, 15–18 December 2007.
22.
MatsuokaK (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biological Cybernetics52: 367–376.
23.
MatsuokaK (1987) Mechanisms of frequency and pattern control in the neural rhythm generators. Biological Cybernetics56: 345–353.
24.
MizunoTYaoitaJTakeuchiM (2009) Mass measurement using self-excited oscillations via two-relay controller. IEEE Transactions of Automatic Control54(2): 416–420.
25.
OkajimaTSekiguchiH (2003) Self-oscillation technique for AFM in liquids. Applied Surface Science210: 68–72.
26.
OnoKOkadaT (1998) Self-excited vibratory system for a flutter mechanism. Transactions of the Japan Society of Mechanical Engineers Series C41(3): 621–629.
27.
OnoKFuruichiTTakahashiR (2004) Self-excited walking of a biped mechanism with feet. International Journal of Robotics Research23(1): 55–68.
28.
OnoKTakahashiRImaduA (2001) Self-excited walking of a biped mechanism. International Journal of Robotics Research20(12): 953–966.
29.
RamosDMertensJCallejaM (2008) Photothermal self-excitation of nanomechanical resonators in liquids. Applied Physics Letters92: 173108.
30.
SergiGDanielFElenaP (2012) Pulsed digital oscillators for electrostatic MEMS. IEEE Transactions on Circuits and Systems I: Regular Papers59(12): 2835–2845.
31.
WilliamsonM (1998) Neural control of rhythmic arm movements. Neural Network11: 1379–1394.
32.
YabunoHKanekoHKurodaM (2008) Van der Pol type self-excited micro cantilever probe of atomic force microscopy. Nonlinear Dynamics54: 137–149.
33.
YabunoHSeoYKurodaM (2013) Self-excited coupled cantilevers for mass sensing in viscous measurement environments. Applied Physics Letters103: 063104.
