Switching and sweeping vibration absorbers: Theory and experimental validation

Abstract This paper investigates the principal properties of time varying operation modes for tuneable vibration absorbers mounted on distributed structures to reduce vibrations produced by stationary broad frequency band disturbances. The study considers a practical application where an electro-mechanical tuneable vibration absorber, comprising a seismic coil-magnet linear transducer, is fixed on a thin walled circular duct flexible structure. The absorber is commanded to either periodically switch or continuously vary the stiffness and damping of the elastic suspension holding the moving magnet. As a result, the tuneable vibration absorber fundamental natural frequency and damping ratio are respectively switched or swept to cyclically reduce the resonant response of multiple flexural natural modes of the duct structure. The study analytically shows, and confirms with simulations and experiments, that the vibration control produced by a simple “blind sweep” operation mode of the tuneable vibration absorber does not differ significantly from the (sub)optimal performance attainable via a switching operation mode.

[1]  Richard D. Braatz,et al.  Switched model predictive control of switched linear systems: Feasibility, stability and robustness , 2016, Autom..

[2]  J. Zhou,et al.  Spectral properties and their applications of frequency response operators in linear continuous-time periodic systems , 2009 .

[3]  Michael J. Brennan,et al.  Global Control of Vibration Using a Tunable Vibration Neutraliser , 2000 .

[4]  Simon J. Estève,et al.  Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators. , 2002, The Journal of the Acoustical Society of America.

[5]  Patrizio Colaneri,et al.  Stability and Stabilization of Continuous-Time Switched Linear Systems , 2006, SIAM J. Control. Optim..

[6]  Patrizio Colaneri,et al.  Dynamic Output Feedback Control of Switched Linear Systems , 2008, IEEE Transactions on Automatic Control.

[7]  P. Colaneri State-feedback problems in H2 and H for continuous-time periodic systems. Part I: theoretical aspects , 2000 .

[8]  Frank Fahy,et al.  High frequency structural vibration , 2004 .

[9]  Franco Blanchini,et al.  Constant and switching gains in semi-active damping of vibrating structures , 2012, Int. J. Control.

[10]  Pablo A. Iglesias,et al.  Continuous-time time-varying entropy , 1997, Math. Control. Signals Syst..

[11]  D. J. Mead Passive Vibration Control , 1999 .

[12]  Franco Blanchini,et al.  Convexity of the cost functional in an optimal control problem for a class of positive switched systems , 2014, Autom..

[13]  Paolo Gardonio,et al.  Integrated tuned vibration absorbers: a theoretical study. , 2013, The Journal of the Acoustical Society of America.

[14]  Franco Blanchini,et al.  Switched Positive Linear Systems , 2015, Found. Trends Syst. Control..

[15]  Patrizio Colaneri,et al.  Relations between stochastic stability of Markovian jump linear systems and stabilization of deterministic switched linear systems , 2008 .

[16]  Paolo Gardonio,et al.  Experimental implementation of switching and sweeping tuneable vibration absorbers for broadband vibration control , 2015 .

[17]  F. Fahy Sound and structural vibration , 1985 .

[18]  Jian-Qiao Sun,et al.  Passive, Adaptive and Active Tuned Vibration Absorbers—A Survey , 1995 .

[19]  Paolo Gardonio,et al.  Sweeping shunted electro-magnetic tuneable vibration absorber: Design and implementation , 2017 .

[20]  Deyu Li,et al.  Dynamic vibration absorbers for vibration control within a frequency band , 2011 .

[21]  Emiliano Rustighi,et al.  Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation , 2012 .

[22]  S. Bittanti,et al.  Periodic Systems: Filtering and Control , 2008 .

[23]  Michael Margaliot,et al.  Root-mean-square gains of switched linear systems: A variational approach , 2007, 2007 46th IEEE Conference on Decision and Control.

[24]  Robert Shorten,et al.  Dwell-time control of continuous-time switched linear systems , 2014, 53rd IEEE Conference on Decision and Control.

[25]  Franco Blanchini,et al.  A separation principle for linear switching systems and parametrization of all stabilizing controllers , 2008, 2008 47th IEEE Conference on Decision and Control.

[26]  Paolo Gardonio,et al.  TIME-VARYING SHUNTED PIEZOELECTRIC PATCH ABSORBERS FOR BROADBAND VIBRATION CONTROL , 2017 .

[27]  Patrizio Colaneri,et al.  Theoretical aspects of continuous-time periodic systems , 2005, Annu. Rev. Control..

[28]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.