Skip to main content
SpringerLink
Log in

Behavior Modeling and Simulation of an Inertial Sensor

  • Reference work entry
  • First Online:
Micro Electro Mechanical Systems

Part of the book series: Micro/Nano Technologies ((MNT))

  • 3059 Accesses

Abstract

Two macromodeling techniques for inertial sensors are discussed in this chapter. The first one is a parametric model order reduction (PMOR) method based on the implicit moment matching to accommodate the parameter variation. The second one is the trajectory piecewise-linear (TPWL) method which is developed for dealing with the strong nonlinearity. For each technique, its effectiveness is demonstrated by the applications to read devices characterization.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 799.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Antonova EE, Looman DC (2005) Finite elements for thermoelectric device analysis in ANSYS. In: 24th international conference on thermoelectrics, pp 215–218

    Google Scholar 

  • Astrid P (2004) Reduction of process simulation models: a proper orthogonal decomposition approach. Dissertation, Department of Electrical Engineering, Eindhoven University of Technology

    Google Scholar 

  • Bedyk W, Niessner M, Schrag G, Wachutka G, Margesin B, Faes A (2008) Automated extraction of multi-energy domain macromodels demonstrated on capacitive MEMS microphones. Sensors Actuators A Phys 145–146:263–270

    Article  Google Scholar 

  • Bond BN (2010) Stability-preserving model reduction for linear and nonlinear systems arising in analog circuit applications. Dissertation, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology

    Google Scholar 

  • Bond BN, Daniel L (2007) Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions. In: 2007 IEEE/ACM international conference on computer-aided design, pp 860–867

    Google Scholar 

  • Chang H, Zhang Y, Xu J, Yuan W (2009) Parametric model order reduction for squeeze film damping in perforated microstructures. Microsyst Technol 15(6):893–898

    Article  Google Scholar 

  • Chang H, Zhang Y, Xie J, Zhou Z,Yuan W (2010) Integrated behavior simulation and verification for a MEMS vibratory gyroscope using parametric model order reduction. J Microelectromech Syst 19(2)

    Article  Google Scholar 

  • Chatterjee AN, Aluru NR (2005) Combined circuit/device modeling and simulation of integrated microfluidic systems. J Microelectromech Syst 14(1):81–95

    Article  Google Scholar 

  • Chen J, Kang S-M(S), Zou J, Liu C, Schutt-Ainé JE (2005) Macromodeling of weakly nonlinear MEMS devices with Taylor-series expansion and Arnoldi approach. J Microelectromech Syst 14(4):441–451

    Google Scholar 

  • Cho YH, Pisano AP, Howe RT (1994) Viscous damping model for laterally oscillating microstructures. J Microelectromech Syst 3:81–87

    Article  Google Scholar 

  • Chowdhury I, Dasgupta SP (2003) Computation of Rayleigh damping coefficients for large systems. Electron J Geotech Eng 8:1–11

    Google Scholar 

  • Clark JV, Pister KSJ (2007) Modeling, simulation, and verification of an advanced micromirror using SUGAR. J Microelectromech Syst 16(6):1524–1536

    Article  Google Scholar 

  • Coventor Inc coventorWare ARCHITECT 2008

    Google Scholar 

  • Davis TA, Duff IS (1997) An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J Matrix Anal Appl 18(1):140–158

    Article  MathSciNet  Google Scholar 

  • Eid R, Salimbahrami B, Lohmann B, Rudnyi EB, Korvink JG (2007) Parametric order reduction of proportionally damped second-order systems. Sens Mater 19(3):149–164

    Google Scholar 

  • Freund RW (2000) Krylov-subspace methods for reduced-order modeling in circuit simulation. J Comput Appl Math 123(1–2):395–421

    Article  MathSciNet  Google Scholar 

  • Guo D, Chu FL (2001) The influence of rotation on vibration of a thick cylindrical shell. J Sound Vib 242(3):487–505

    Article  Google Scholar 

  • He J, Sætrom J, Durlofsky LJ (2011) Enhanced linearized reduced-order models for subsurface flow simulation. J Comput Phys 230(23):8313–8341

    Article  MathSciNet  Google Scholar 

  • Jing Q, Mukherjee T, Fedder GK (2002) Large-deflection beam model for schematic behavioral simulation in NODAS. Model Simul Microsyst:136–139

    Google Scholar 

  • Liu G, Wang A, Jiang T, Jiao J, Jang JB (2008) Effects of environmental temperature on the performance of a micromachined gyroscope. Microsyst Technol 14:199–204

    Article  Google Scholar 

  • Liu Y, Yuan W, Chang H (2014a) A global maximum error controller-based method for linearization point selection in trajectory piecewise-linear model order reduction. IEEE Trans Comput Aided Des Integr Circuits Syst 33(7):1100–1104

    Article  Google Scholar 

  • Liu Y, Yuan W, Chang H, Ma B (2014b) Compact thermoelectric coupled models of micromachined thermal sensors using trajectory piecewise-linear model order reduction. Microsyst Technol 20(1):73–82

    Article  Google Scholar 

  • Ma BH, Zhou BQ, Deng JJ, Yuan WZ (2008) On heat insulation of micro thermal sensor using FEA. Chin J Sensors Actuators 21(6):933–937

    Google Scholar 

  • Ma BH, Ren JZ, Yuan WZ (2010) Flexible thermal sensor array on PI film substrate for underwater applications. In: Proceedings of 23rd IEEE international conference MEMS, pp 679–682

    Google Scholar 

  • Mukherjee T, Fedder GK, Ramaswamy D, White J (2000) Emerging simulation approaches for micromachined devices. IEEE Trans Comput Aided Des Integr Circuits Syst 19(12):1572–1589

    Article  Google Scholar 

  • Nahvi SA, Nabi M, Janardhanan S (2012) Trajectory based methods for nonlinear mor: review and perspectives. In: 2012 I.E. ISPCC, pp 1–6

    Google Scholar 

  • Nayfeh H, Younis MI, Abdel-Rahman EM (2005) Macromodels for MEMS applications. Nonlinear Dyn 41(1–3):211–236

    Article  Google Scholar 

  • Painter CC, Shkel AM (2001) Structural and thermal analysis of a mems angular gyroscope. Proc SPIE Int Soc Opt Eng 4334:86–94

    Google Scholar 

  • Painter CC, Shkel AM (2003) Structural and thermal modeling of a z-axis rate integrating gyroscope. J Micromech Microeng 13:229–237

    Article  Google Scholar 

  • Reitz S et al (2003) System level modeling of microsystems using order reduction methods. Analog Integr Circ Sig Process 37(1):7–16

    Article  Google Scholar 

  • Rewienski M, White J (2003) A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Trans CAD 22(2):155–170

    Article  Google Scholar 

  • Rudnyi EB, Feng LH, Salleras M, Marco S, Korvink JG (2005) Error indicator to automatically generate dynamic compact parametric thermal models. In: THERMINIC 2005, 11th international workshop on thermal investigations of ICs and systems, Belgirate, pp 139–145

    Google Scholar 

  • Saad Y (2003) Iterative methods for sparse linear systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia

    Book  Google Scholar 

  • Schrag G, Wachutka G (2002) Physically based modeling of squeeze-film damping by mixed-level system simulation. Sensors Actuators A Phys 97–98:193–200

    Article  Google Scholar 

  • Schrag G, Wachutka G (2004) Accurate system-level damping model for highly perforated micromechanical devices. Sensors Actuators A Phys 111(2–3):222–228

    Article  Google Scholar 

  • Senturia SD (2001) Microsystem design. Kluwer Academic Publishers, Boston

    Google Scholar 

  • Simoncini V, Szyld DB (2007) Recent computational developments in Krylov subspace methods for linear systems. Numer Linear Algebra 14(1):1–59

    Article  MathSciNet  Google Scholar 

  • Striebel M, Rommes J (2011) Model order reduction of nonlinear systems in circuit simulation: status and applications. Lecture Notes in Electrical Engineering 74(2):289–301. In: Benner P, Hinze M, ter Maten EJW (eds)

    Article  MathSciNet  Google Scholar 

  • Tilmans H (1996) Equivalent circuit representation of electromechanical transducers: I. Lumped-parameter systems. J Micromech Microeng 6:157–176

    Article  Google Scholar 

  • Tiwary SK, Rutenbar RA (2005) Scalable trajectory methods for on-demand analog macromodel extraction. In: Proceedings of the 42nd annual design automation conference, pp 403–408

    Google Scholar 

  • Vandemeer JE 1998 Nodal design of actuators and sensors (NODAS). M.S. Thesis, Carnegie Mellon University

    Google Scholar 

  • Vasilyev D, Rewienski M, White J (2003) A TBR-based trajectory piecewise-linear algorithm for generating accurate low-order models for nonlinear analog circuits and MEMS. In: Proceedings of the 40th design automation conference, pp 490–495

    Google Scholar 

  • Veijola T, Kuisma H et al (1995) Equivalent-circuit model of the squeezed gas film in a silicon accelerometer. Sensors Actuators A Phys 48(3): 239–248

    Article  Google Scholar 

  • Veijola T, Turowski M (2001) Compact damping models for laterally moving microstructures with gas-rarefaction effects. J Microelectromech Syst 10:263–273

    Article  Google Scholar 

  • Voss T, Verhoeven A, Bechtold T, ter Maten EJW (2008) Model order reduction for nonlinear differential algebraic equations in circuit simulation. In: Bonilla LL, Moscoso M, Platero G, Vega JM (eds) Progress in industrial mathematics at ECMI 2006. Series mathematics in industry, vol 12. Heidelberg, Springer, pp 518–523

    Chapter  Google Scholar 

  • Yang Y-JJ, Yen P-C (2004) An efficient macromodeling methodology for lateral air damping effects. J Microelectromech Syst 13(3):812–828

    Google Scholar 

  • Yang YJ, Yu CJ 2002 Technical proceedings of the 2002 international conference on modeling and simulation of microsystems, pp 178–181

    Google Scholar 

  • Zhang Y, Kamalian R, Agogino AM et al (2005) Hierarchical MEMS synthesis and optimization. In: Proceedings of 12th SPIE annual international symposium: smart structures and materials, #5763–12

    Google Scholar 

  • Zhang R, Wang W, Dounavis A, Jullien GA (2008) Passive reduced-order macromodeling algorithm for microelectromechanical systems. J Microelectromech Syst 17(3):678–687

    Article  Google Scholar 

  • Zhou N, Agogino AM (2002) Automated design synthesis for micro-electro-mechanical systems (MEMS). In: Proceedings of the ASME design automation conference, Montreal, 29 Sept–2 Oct

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MOE Key Laboratory of Micro/Nano Systems for Aerospace, Northwestern Polytechnical University, 710072, Xi’an, China

    Honglong Chang & Jianbing Xie

  2. School of Arts and Sciences, Shaanxi University of Science and Technology, 710021, Xi’an, China

    Ying Liu

Authors
  1. Honglong Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianbing Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ying Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Honglong Chang .

Editor information

Editors and Affiliations

  1. Key Laboratory of MEMS of the Ministry of Education, Southeast University, Nanjing, Jiangsu, China

    Qing-An Huang

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Chang, H., Xie, J., Liu, Y. (2018). Behavior Modeling and Simulation of an Inertial Sensor. In: Huang, QA. (eds) Micro Electro Mechanical Systems. Micro/Nano Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-10-5945-2_5

Download citation

Publish with us

Policies and ethics

Search

Navigation