[en] The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam.
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Bibliography
Berardengo M Manzoni S Thomas O, et al. (2018) Piezoelectric resonant shunt enhancement by negative capacitances: Optimisation, performance and resonance cancellation. Journal of Intelligent Material Systems and Structures 29(12): 2581–2606.
Cardoso JM Coutinho JGF Diniz PC (2017) Embedded Computing for High Performance. Cambridge, MA: Elsevier.
Dal Bo L Gardonio P Casagrande DE, et al. (2019) Smart panel with sweeping and switching piezoelectric patch vibration absorbers: Experimental results. Mechanical Systems and Signal Processing 120: 308–325.
Fleming AJ (2004) Synthesis and implementation of sensor-less shunt controllers for piezoelectric and electromagnetic vibration control. PhD Thesis, University of Newcastle, Callaghan, NSW.
Fleming AJ Behrens S Moheimani SO (2000) Synthetic impedance for implementation of piezoelectric shunt-damping circuits. Electronics Letters 36(18): 1525.
Fleming AJ Moheimani SO (2002) Power harvesting piezoelectric shunt damping 1. IFAC Proceedings Volumes 35(2): 173–178.
Forward RL (1979) Electronic damping of vibrations in optical structures. Applied Optics 18(5): 690–697.
Franklin GF Powell JD Emami-Naeini A (2015) Feedback Control of Dynamic Systems. London: Pearson.
Franklin GF Powell JD Workman ML (1998) Digital Control of Dynamic Systems, 3rd edn. Reading, MA: Addison-Wesley.
Giorgio I Culla A Del Vescovo D (2009) Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network. Archive of Applied Mechanics 79(9): 859–879.
Hagood NW von Flotow A (1991) Damping of structural vibrations with piezoelectric materials and passive electrical networks. Journal of Sound and Vibration 146(2): 243–268.
Høgsberg J Krenk S (2017) Calibration of piezoelectric RL shunts with explicit residual mode correction. Journal of Sound and Vibration 386: 65–81.
Ikegame T Takagi K Inoue T (2019) Exact solutions to H∞ and H2 optimizations of passive resonant shunt circuit for electromagnetic or piezoelectric shunt damper. Journal of Vibration and Acoustics 141(3): 031015.
Lossouarn B Deü JF Kerschen G (2018) A fully passive nonlinear piezoelectric vibration absorber. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376(2127): 20170142.
Matten G Collet M Cogan S, et al. (2014) Synthetic impedance for adaptive piezoelectric metacomposite. Procedia Technology 15: 84–89.
Moheimani SOR Fleming AJ Behrens S (2003) On the feedback structure of wideband piezoelectric shunt damping systems. Smart Materials and Structures 12(1): 49–56.
Nečásek J Václavík J Marton P (2016) Digital synthetic impedance for application in vibration damping. Review of Scientific Instruments 87(2): 024704.
Nečásek J Václavík J Marton P (2017) Comparison of analog front-ends for digital synthetic impedance device. In: 2017 IEEE international workshop of electronics, control, measurement, signals and their application to mechatronics (ECMSM), Donostia, Spain, 24–26 May 2017, pp.1–4. New York: IEEE.
Niederberger D Fleming A Moheimani SOR, et al. (2004) Adaptive multi-mode resonant piezoelectric shunt damping. Smart Materials and Structures 13(5): 1025–1035.
Olgac N Elmali H (2000) Analysis and design of delayed resonator in discrete domain. Journal of Vibration and Control 6(2): 273–289.
Plíva Z Kolář M Došek P, et al. (2007) A piezoelectric elements and their electronics driving with help of FPGA circuits. Ferroelectrics 351(1): 187–195.
Preumont A (2011) Vibration Control of Active Structures, Solid Mechanics and Its Applications, vol. 179, 3rd edn. Dordrecht, The Netherlands: Springer.
Raze G Jadoul A Guichaux S, et al. (2020) A digital nonlinear piezoelectric tuned vibration absorber. Smart Materials and Structures 29(1): 015007.
Raze G Paknejad A Zhao G, et al. (2019) Suppression of delay-induced instabilities of digital piezoelectric vibration absorbers. In: Benjeddou A Mechbal N Deü JF (eds), Proceedings of the 9th ECCOMAS Thematic Conference on Smart Structures and Materials – SMART 2019. Barcelona: International Centre for Numerical Methods in Engineering (CIMNE), pp.991–1001.
Rosi G (2010) Control of sound radiation and transmission by means of passive piezoelectric networks: Modelling, optimization and experimental implementation. PhD Thesis, Université Pierre et Marie Curie, Paris VI.
Silva TMP (2018) Vibration attenuation in linear and nonlinear flexible structures via nonlinear piezoelectric shunt circuits. PhD Thesis, University of São Paulo, São Paulo.
Soltani P Kerschen G Tondreau G, et al. (2014) Piezoelectric vibration damping using resonant shunt circuits: An exact solution. Smart Materials and Structures 23(12): 125014.
Sugino C Ruzzene M Erturk A (2018) Design and analysis of piezoelectric metamaterial beams with synthetic impedance shunt circuits. IEEE/ASME Transactions on Mechatronics 23(5): 2144–2155.
Sugino C Ruzzene M Erturk A (2020) Digitally programmable resonant elastic metamaterials. Physical Review Applied 13(6): 1.
Thomas O Ducarne J Deü JF (2012) Performance of piezoelectric shunts for vibration reduction. Smart Materials and Structures 21(1): 015008.
Tustin A (1947) A method of analysing the behaviour of linear systems in terms of time series. Journal of the Institution of Electrical Engineers – Part II A: Automatic Regulators and Servo Mechanisms 94(1): 130–142.
Walton K Marshall JE (1987) Direct method for TDS stability analysis. IEE Proceedings D: Control Theory and Applications 134(2): 101.
Yi K Matten G Ouisse M, et al. (2020) Programmable metamaterials with digital synthetic impedance circuits for vibration control. Smart Materials and Structures 29(3): 035005.
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