A new multi-input single-output delay feedback controller is presented to reduce free vibrations of a cantilever beam. A linear model using the first mode is derived and used to analyze and characterize the damping produced by different delay-feedback controllers as a function of the controller's gains and delay. The stability regions and amount of damping produced by three different single delay feedback and the new combined delayed feedback are investigated. A three-dimensional figure for the new controller showing the stability regions as a function of the controller gains and delay is presented. The characteristic damping of the controller as predicted by the linear model is compared with that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controllers gains and delay are obtained, simulated, and compared. To validate the single mode approximation, numerical simulations are performed using three-mode full nonlinear model. The results obtained using multi-input delay-feedback controllers demonstrate an excellent improvement in mitigating the first-mode vibration.
AbreuGLRibeiroJFSteffenVJr (2003) Experiments on optimal vibration control of a flexible beam containing piezoelectric sensors and actuators. Shock and Vibration10: 283–300.
2.
AlhazzaKAAlhazzaAA (2004) A review of the vibrations of plates and shells. The Shock and Vibration Digest36: 377–395. DOI: 10.1177/0583102404045575.
3.
AlhazzaKADaqaqMFNayfehAHInmanDJ (2008a) Nonlinear vibrations of parametrically-excited cantilever beams subjected to nonlinear delayed-feedback control. International Journal of Non-Linear Mechanics43: 801–812. DOI: 10.1016/j.ijnonlinmec.2008.04.010.
4.
AlhazzaKAMasoudZNAlajmiMA (2008b) Nonlinear free vibration control of beams using acceleration delayed-feedback control. Smart Materials and Structures7: 015002–015002. DOI: 10.1088/0964-1726/17/01/015002.
5.
AlhazzaKANayfehAHDaqaqMF (2009) On utilizing delayed feedback for active-multimode vibration control of cantilever beams. Journal of Sound and Vibration319: 735–752. DOI: 10.1016/j.jsv.2008.06.052.
6.
ChatterjeeS (2008) Vibration control by recursive time-delayed acceleration feedback. Journal of Sound and Vibration317: 67–90.
7.
CrawleyEFde LuisJ (1987) Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal10: 1373–1385.
8.
Crespo da SilvaMRMGlynnCC (1978a) Nonlinear flexural–flexural–torsional dynamics of inextensional beams, I. Equations of motion. Journal of Structural Mechanics6: 437–448.
9.
Crespo da SilvaMRMGlynnCC (1978b) Nonlinear flexural–flexural–torsional dynamics of inextensional beams, II. Forced motions. Journal of Structural Mechanics6: 449–461.
10.
DaqaqMFAlhazzaKAArafatH (2008) Nonlinear vibrations of cantilever beams with feedback delays. International Journal of Non-Linear Mechanics43: 962–978.
11.
FilipovicDOlgacN (2002) Delayed resonator with speed feedback-design and performance analysis. Mechatronics12: 393–413.
12.
GhoneimHKarkoubMA (2001) Active, shunted, and passive constrained layer damping for the vibration suppression of a flexible four-bar Mechanism. Journal of Vibration and Control7: 551–563.
13.
HagoodAvon FlotowA (1991) Damping of structural vibrations with piezoelectric materials and passive electrical networks. Journal of Sound and Vibration146: 243–268.
14.
HosekMElmaliHOlgacN (1997) Tunable torsional vibration absorber: the centrifugal delayed resonator. Journal of Sound and Vibration205: 151–165.
15.
IrschikH (2002) A review on static and dynamic shape control of structures by piezoelectric actuation. Engineering Structures24: 5–11.
16.
JohnsonCDKeinholzDA (1982) Finite element prediction of damping in structures with constrained viscoelastic layers. AIAA Journal20: 1284–1290.
17.
KirbyGCMaticP (1994) Optimal actuator size and location using genetic algorithms for multivariable control. ASME Adaptive Structures and Composite Materials: Analysis and Application45: 325–335.
18.
LesieutreG (1998) Vibration damping and control using shunted piezoelectric materials. Shock and Vibration Digest30: 187–195.
19.
MalatkarPNayfehA (2003a) On the transfer of energy between widely spaced modes in structures. Nonlinear Dynamics31: 225–242.
20.
MalatkarPNayfehA (2003b) A parametric identification technique for single-degree-of-freedom weakly nonlinear systems with cubic nonlinearities. Journal of Vibration and Control9: 317–336.
MasoudZNNayfehAHNayfehNA (2005) Sway reduction on container cranes using delayed feedback controller. Journal of Vibration and Control11: 1103–1122.
23.
MeadDJMarkusS (1969) The forced vibration of a three-layered damped sandwich beam with arbitrary boundary conditions. Journal of Sound and Vibration10: 163–175.
24.
OlgacNHoim-HansenB (1994) A novel active vibration absorption technique: delayed resonator. Journal of Sound and Vibration176: 93–104.
25.
OlgacNElmaliHHosekMRenzulliM (1997) Active vibration control of distributed systems using delayed resonator with acceleration feedback. Journal of Dynamic Systems, Measurement, and Control119: 380–389.
26.
OueiniSSNayfehAHPrattJR (1998) A nonlinear vibration absorber for flexible structures. Nonlinear Dynamics15: 259–282.
27.
PereiraCESteffenVJr (2002) Discrete-continuous optimization techniques applied to smart structure vibration control. A Conference and Exposition on Structural DynamicsLos Angeles, CA.
28.
RaoDK (1978) Frequency and loss factors of sandwich beams under various boundary conditions. Journal of Mechanical Engineering Sciences20: 271–282.
29.
ShenYHomaifarABikdashMChenD (1998) Genetic algorithms and fuzzy based vibration control of plate using PZT actuators. Proceedings of the 37th IEEE Conference on Decision and ControlTampa, FL, pp. 2930–2933.
30.
ShenYHomaifarABikdashMChenD (1999) Active control of flexible structures using genetic algorithms and LQG/LTR approaches. Proceedings of the American Control ConferenceSan Diego, CA, pp. 4398–4402.
31.
SkeltonREYousuffA (1983) Component cost analysis of large scale system. International Journal of Control37: 285–304.
32.
TzouHSTsengCI (1990) Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach. Journal of Sound and Vibration138: 17–34.
33.
WangZChenSHanW (1999) Integrated structural and control optimization of intelligent structures. Engineering Structures21: 183–191.
