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A dynamical envelope model for vibratory gyroscopes

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Abstract

In this contribution, a method will be presented to derive an envelope model for vibratory gyroscopes capturing the essential “slow” dynamics (envelope) of the system. The methodology will be exemplarily carried out for a capacitive gyroscope with electrostatic actuators and sensors. The resulting envelope model can be utilized for both transient and steady state simulations with the advantage of a significantly increased simulation speed. Especially for the sensor design and optimization, where usually very complex mathematical models are used, efficient steady state simulations are of certain interest. Another great advantage of this approach is that the steady state solutions in terms of the envelope model are constant. Thus, for the controller design, a linearization of the nonlinear envelope model around the steady state solution yields a linear time-invariant system allowing for the application of the powerful methods known from linear control theory.

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References

  • Alper S, Akin T (2001) A symmetric surface micromachined gyroscope with decoupled oscillation modes. In: The 11th international conference on solid-state sensors and actuators, Munich, pp 456–459

  • Ayazi F, Zaman MF, Sharma A (2008) Vibrating gyroscopes. In: Gianchandani YB, Tabata O, Zappe H (eds) Comprehensive microsystems, vol 2. Elsevier, Amsterdam, pp 181–208

    Google Scholar 

  • Bernstein J, Cho S, King AT, Kourepenis A, Maciel P, Weinberg M (1993) A micromachincd comb-drive tuning fork rate gyroscopce. In: Proceedings MEMS, pp 143–148

  • Bhave SA, Seeger JI, Jiang X, Boser BE, Howe RT, Yasaitis J (2003) An integrated vertical-drive, in-plane-sense microgyroscope. In: Digest of technical papers of the 12th international conference on solid-state sensors, sctuators and microsystems, Boston, pp 171–174

  • Braxmaier M, Gaißer A, Link T, Schumacher A, Simon I, Frech J, Sandmaier H, Lang W (2003) Cross-coupling of the oscillation modes of vibratory gyroscopes. In: Digest of technical papers of the 12th international conference on solid-state sensors, actuators and microsystems, Boston, pp 167–170

  • Caliskan VA, Verghese GC, Stankovic AM (1996) Multi-frequency averaging of DC/DC converters. In: IEEE workshop on computers in power electronics, Portland, pp 113–119

  • Egretzberger M, Kugi A (2009) An envelope model to describe the sensor dynamics of vibratory gyroscopes. In: Proceedings of the SPIE, smart sensors, actuators and MEMS IV, Dresden, vol 7362

  • Feldman P, Roychowdhury J (1996) Computation of circuit waveform envelopes using an effcient, matrix-decomposed harmonic balance algorithm. In: Digest of technical papers of the ICCAD, IEEE/ACM international conference, San Jose, pp 295–300

  • Günthner S (2006) Entwurf und Charakterisierung von mikromechanischen Drehratensensoren in Silizium. In: Aktuelle Berichte aus der Mikrosystemtechnik, Shaker Verlag, Aachen

  • Günthner S, Egretzberger M, Kugi A, Kapser K, Hartmann B, Schmid U, Seidel H (2005) Compensation of parasitic effects for a silicon tuning fork gyroscope. IEEE Sens J 6:596–604

    Article  Google Scholar 

  • Juneau T, Pisano AP, Smith JH (1997) Dual axis operation of a micromachined rate gyroscope. In: The 9th international conference on solid-state sensors, actuators and microsystems, Chicago, vol 2, pp 883–886

  • Kanso E, Szeri AJ, Pisano AP (2004) Cross-coupling errors of micromachined gyroscopes. J Micromech Syst 13:323–331

    Article  Google Scholar 

  • Kokotovic P, Khalil HK, O’Reilly J (1986) Singular perturbation methods in control: analysis and design. Academic Press, Philadelphia

    MATH  Google Scholar 

  • Kuisma H, Ryhänen T, Lahdenperä J, Punkka E, Routsalainen S, Silanpää T, Seppä H (1997) A bulk micromachined angular rate sensor. In: The 9th international conference on solid-state sensors, actuators and microsystems, Chicago, pp 875–878

  • Loveday PW, Rogers CA (2002) The influence of control system design on the performance of vibratory gyroscopes. J Sound Vib 255:417–432

    Article  MathSciNet  Google Scholar 

  • Maenaka K, Fujita T, Konishi Y, Maeda M (1996) Analysis of a highly sensitive silicon gyroscope with cantilever beam as vibrating mass. Sens Actuators A 54:568–573

    Article  Google Scholar 

  • Mair F, Egretzberger M, Kugi A (2009) A tool for the automatic modeling of capacitive MEMS gyroscopes. In: Proceedings of the 6th Vienna international conference on mathematical modelling, Vienna, pp 2228–2235

  • Merz P, Pilz W, Senger F, Reimer K, Grouchko M, Pandhumsoporn T, Bosch W, Cofer A, Lassig S (2007) Impact of Si DRIE on vibratory MEMS gyroscope performance. In: The 14th international conference on solid-state sensors, actuators and microsystems, Lyon, pp 1187–1190

  • Piyabongkarn D, Rajamani R, Greminger M (2005) The development of a MEMS gyroscope for absolute angle measurement. IEEE Trans Control Syst Technol 13:185–195

    Article  Google Scholar 

  • Reid JG (1983) Linear system fundamentals. McGraw-Hill, New York

    Google Scholar 

  • Sassen S, Voss R, Schalk J, Stenzel E, Gleissner T, Grünberger R, Neubauer F, Ficker W, Kupke W, Bauer K, Rose M (2000) Tuning fork silicon angular rate sensor with enhanced performance for automotive applications. Sens Actuators A 83:80–84

    Article  Google Scholar 

  • Seeger JI, Boser BE (2003) Charge control of parallel-plate, electrostatic actuators and the tip-in instability. J Micromech Syst 12:656–671

    Article  Google Scholar 

  • Seshia AA, Howe RT, Montaguet S (2002) An integrated microelectromechanical resonant output gyroscope. In: The 15th IEEE international conference on micro electro mechanical systems, Las Vegas, pp 722–726

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Acknowledgments

This work was funded by the German BMBF as part of the EURIPIDES project RESTLES (project no. V3EUR015).

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Correspondence to Markus Egretzberger.

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Egretzberger, M., Kugi, A. A dynamical envelope model for vibratory gyroscopes. Microsyst Technol 16, 777–786 (2010). https://doi.org/10.1007/s00542-009-0979-y

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  • DOI: https://doi.org/10.1007/s00542-009-0979-y

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