Skip to main content
SpringerLink
Log in

Review on macromodels of MEMS sensors and actuators

  • Review Paper
  • Published:
Microsystem Technologies Aims and scope Submit manuscript

Abstract

Macromodel for simulating static and dynamic behavior characteristic of MEMS has become a famous research focus. This review reports the progress on the recent development of macromodel of MEMS. The macromodel of MEMS is classed into numerical macromodel, analytical macromodel and macromodel in-system in this review. Numerical macromodel is the focus in this work and is discussed mainly from macromodel based on Galerkin method, macromodel based on trajectory piecewise-linear approach, macromodel based on proper orthogonal decomposition, macromodel based on Krylov subspace projection, macromodel based on mapping method, macromodel based on neural-network and so on. A variety of MEMS and microfluidic devices designed based on macromodel method are expounded and analyzed. This paper will provide an expedient and valuable reference to designers who research rapid simulation and optimal design of MEMS.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Ansari MA, Kim KY (2007) Application of the radial basis neural network to optimization of a micromixer. Chem Eng Technol 30(7):962–966

    Article  Google Scholar 

  • Arafat HN, Nayfeh AH, Faris W (2004) Natural frequencies of heated annular and circular plates. Int J Solids Struct 41(11):3031–3051

    Article  MATH  Google Scholar 

  • Bai Z (2002) Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl Numer Math 43(1):9–44

    Article  MathSciNet  MATH  Google Scholar 

  • Batra RC, Xiao J (2013) Finite deformations of curved laminated St. Venant-Kirchhoff beam using layer-wise third order shear and normal deformable beam theory (TSNDT). Compos Struct 97:147–164

    Article  Google Scholar 

  • Batra RC, Porfiri M, Spinello D (2008) Reduced-order models for microelectromechanical rectangular and circular plates incorporating the casimir force. Int J Solids Struct 45(11):3558–3583

    Article  MATH  Google Scholar 

  • Bechtold T, Salimbahrami B, Rudyni EB, Lohmann B, Korvink JG (2003) Krylov-subspace-based order reduction methods applied to generate compact thermo-electric models for MEMS. In: Technical proceedings of the 2003 nanotechnology conference and trade show (MSM 2003)(San Francisco, 23–27 Feb 2003), vol 2

  • Bechtold T, Schrag G, Feng L (2014) Enabling technologies for system-level simulation of MEMS. Electronics System-Integration Technology Conference (ESTC), IEEE, pp 1–6

  • Beck CL, Doyle J, Glover K (1996) Model reduction of multidimensional and uncertain systems. IEEE Trans Autom Control 41(10):1466–1477

    Article  MathSciNet  MATH  Google Scholar 

  • Bedekar AS, Wang Y, Krishnamoorthy S et al (2006) SYSTEM-level simulation of flow induced dispersion in lab-on-a-chip systems [M]. Design automation methods and tools for microfluidics-based biochips. Springer, Netherlands, pp 189–214

    Google Scholar 

  • Bedekar AS, Wang Y, Siddhaye SS et al (2007) Design software for application-specific microfluidic devices. Clin Chem 53(11):2023–2026

    Article  Google Scholar 

  • Benaissa B, Hocine NA, Belaidi I et al (2016) Crack identification using model reduction based on proper orthogonal decomposition coupled with radial basis functions. Struct and Multidiscip Optim 54(2):265–274

    Article  MathSciNet  Google Scholar 

  • Caruntu DI, Martinez I (2014) Reduced order model of parametric resonance of electrostatically actuated MEMS cantilever resonators. Int J Non-Linear Mech 66:28–32

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Chen J, Kang SMS, Zou J et al (2004) Reduced-order modeling of weakly nonlinear MEMS devices with Taylor-series expansion and Arnoldi approach. Microelectromech Syst J 13(3):441–451

    Article  Google Scholar 

  • Chen YH, Hsu CL, Tsai LC et al (2013) A reliability-oriented placement algorithm for reconfigurable digital microfluidic biochips using 3-D deferred decision making technique. IEEE Trans Comput Aided Des Integr Circuits Syst 32(8):1151–1162

    Article  Google Scholar 

  • Danczyk J, Suresh K (2007) An Efficient CAD-Integrated Multi-Dimensional Model for Microfluidic Simulations. ASME. International design engineering technical conferences and computers and information in engineering conference, American society of mechanical engineers, pp 921–928

  • Danczyk J, Suresh K (2009) Algebraic dimensional reduction for microfluidic simulation. J Comput Inf Sci Eng 9(3):031001

    Article  Google Scholar 

  • Daniel L, Siong OC, Chay LS et al (2004) A multiparameter moment-matching model-reduction approach for generating geometrically parameterized interconnect performance models. Comput Aided Des Integr Circuits Syst IEEE Trans 23(5):678–693

    Article  Google Scholar 

  • Deshpande M (2001) Development of a reduced-order methodology in the design of microfluidic systems. AIAA, Aerospace sciences meeting and exhibit, Reno

    Book  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Gabbay LD, Mehner JE, Senturia SD (2000) Computer-aided generation of nonlinear reduced-order dynamic macromodels. I. Non-stress-stiffened case. J Microelectromech Syst 9(2):262–269

    Article  Google Scholar 

  • Gallivan K, Vandendorpe A, Van Dooren P (2003) Model reduction via truncation: an interpolation point of view. Linear Algebra Appl 375:115–134

    Article  MathSciNet  MATH  Google Scholar 

  • Gaonkar AK, Kulkarni SS (2015) Application of multilevel scheme and two level discretization for POD based model order reduction of nonlinear transient heat transfer problems. Comput Mech 55(1):179–191

    Article  MathSciNet  MATH  Google Scholar 

  • Gershon D, Calame JP, Birnboim A (2001) Complex permittivity measurements and mixing laws of porous alumina. J Appl Phys 89(12):8117–8120

    Article  Google Scholar 

  • Hagleitner C, Bonaccio T, Rothuizen H et al (2007) Modeling, design, and verification for the analog front-end of a MEMS-based parallel scanning-probe storage device. IEEE J Solid State Circuits 42(8):1779–1789

    Article  Google Scholar 

  • He J, Durlofsky LJ (2014) Reduced-order modeling for compositional simulation by use of trajectory piecewise linearization. SPE J 19(05):858–872

    Article  Google Scholar 

  • He X, Hauan S (2006) Microfluidic modeling and design for continuous flow in electrokinetic mixing-reaction channels. AIChE J 52(11):3842–3851

    Article  Google Scholar 

  • Homentcovschi D, Murray BT, Miles RN (2010) An analytical formula and FEM simulations for the viscous damping of a periodic perforated MEMS microstructure outside the lubrication approximation. Microfluid Nanofluid 9(4–5):865–879

    Article  Google Scholar 

  • Hung ES, Senturia SD (1999) Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs. J Microelectromech Syst 8(3):280–289

    Article  Google Scholar 

  • Jallouli A, Kacem N, Bourbon G et al (2016) Pull-in instability tuning in imperfect nonlinear circular microplates under electrostatic actuation. Phys Lett A 380(46):3886–3890

    Article  Google Scholar 

  • Jia W, Helenbrook BT, Cheng MC (2014a) Thermal modeling of multi-fin field effect transistor structure using proper orthogonal decomposition. Electron Devices IEEE Trans 61(8):2752–2759

    Article  Google Scholar 

  • Jia Y, Ma C, Xie S (2014b) A novel nonlinear macromodeling using time piecewise volterra series representation. IEEJ Trans Electr Electronic Eng 9(6):664–669

    Article  Google Scholar 

  • Juillard J (2014) A comparative study of reduced-order modeling techniques for nonlinear MEMS beams. Design, test, integration and packaging of MEMS, MOEMS (DTIP), Symposium on, IEEE, p 1–5

  • Kang TG, Singh MK, Kwon TH et al (2008) Chaotic mixing using periodic and aperiodic sequences of mixing protocols in a micromixer. Microfluid Nanofluid 4(6):589–599

    Article  Google Scholar 

  • Kedia S, Wang W (2015) Simulation, design, fabrication, and testing of a MEMS resettable circuit breaker. J Microelectromech Syst 24(1):232–240

    Article  Google Scholar 

  • Kim S, Clark WW, Wang QM (2005) Piezoelectric energy harvesting with a clamped circular plate: analysis. J Intell Mater Syst Struct 16(10):847–854

    Article  Google Scholar 

  • Krylov S, Ilic BR, Lulinsky S (2011) Bistability of curved microbeams actuated by fringing electrostatic fields. Nonlinear Dyn 66(3):403–426

    Article  MathSciNet  Google Scholar 

  • Kudryavtsev M, Hohlfeld D, Rudnyi EB et al (2014) Structure preserving model order reduction and system level simulation of MEMS piezoelectric energy harvester. Proceedings of the 5th electronics system-integration technology conference (ESTC)

  • Li P, Fang Y (2015) An analytical model for squeeze-film damping of perforated torsional microplates resonators. Sensors 15(4):7388–7411

    Article  Google Scholar 

  • Liang YC, Lin WZ, Lee HP et al (2001) A neural-network-based method of model reduction for the dynamic simulation of MEMS. J Micromech Microeng 11(3):226

    Article  Google Scholar 

  • Liang YC, Lin WZ, Lee HP et al (2002) Proper orthogonal decomposition and its applications—part II: model reduction for MEMS dynamical analysis. J Sound Vib 256(3):515–532

    Article  Google Scholar 

  • Liang D, Liu J, Zhou J et al (2016) Combustion characteristics and propulsive performance of boron/ammonium perchlorate mixtures in microtubes. J Energ Mater 34(3):297–317

    Article  Google Scholar 

  • Lienemann J, Billger D, Rudnyi EB, et al (2004) MEMS compact modeling meets model order reduction: examples of the application of Arnoldi methods to microsystem devices [C]. The technical proceedings of the 2004 nanotechnology conference and trade show, Nanotech, p 4

  • Lin WZ, Lee KH, Lim SP et al (2003a) Proper orthogonal decomposition and component mode synthesis in macromodel generation for the dynamic simulation of a complex MEMS device. J Micromech Microeng 13(5):646

    Article  Google Scholar 

  • Lin WZ, Lee KH, Lim SP (2003b) Proper orthogonal modes for macromodel generation for complex mems devices. Model Simul Microsyst MSM 3:368–371

    Google Scholar 

  • Liou DS, Hsieh YF, Kuo LS et al (2011) Modular component design for portable microfluidic devices. Microfluid Nanofluid 10(2):465–474

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lu K, Yu H, Chen Y et al (2015) A modified nonlinear POD method for order reduction based on transient time series. Nonlinear Dyn 79(2):1195–1206

    Article  MATH  Google Scholar 

  • Magrargle R, Hoburg JF, Mukherjee T (2006) Microfluidic injector models based on artificial neural networks. IEEE Trans Comput Aided Desi Integr Circuits Syst 24(2):378–385

    Article  Google Scholar 

  • Medina L, Gilat R, Krylov S (2014) Symmetry breaking in an initially curved pre-stressed micro beam loaded by a distributed electrostatic force. Int J Solids Struct 51(11):2047–2061

    Article  Google Scholar 

  • Medina L, Gilat R, Krylov S (2016) Bouncing and dynamic trapping of a bistable curved micro beam actuated by a suddenly applied electrostatic force. Commun Nonlinear Sci Numer Simul 36:273–284

    Article  MathSciNet  Google Scholar 

  • Milijic M, Marinkovic Z, Kim T (2014) Modeling and optimization of Ohmic series RF MEMS switches by using neural networks. In: Microwave conference (GeMIC), 2014 German. VDE, pp 1–4

  • Minhass WH, Pop P, Madsen J (2011) System-level modeling and synthesis of flow-based microfluidic biochips. Proceedings of the 14th International Conference on compilers, architectures and synthesis for embedded systems, pp 225–233

  • Mikulchenko O, Rasmussen A, Mayaram K (2000) A neural network based macromodel for microflow sensors. In: Proc MSM, pp 540–543

  • Mohammad TF, Ouakad HM (2016) Static, eigenvalue problem and bifurcation analysis of MEMS arches actuated by electrostatic fringing-fields. Microsyst Technol 22(1):193–206

    Article  Google Scholar 

  • Mohseni SS, Yazdanpanah MJ, Ranjbar N (2015) New strategies in model order reduction of trajectory piecewise–linear models. Int J Numer Model Electronic Netw Devices Fields 29(4):1–5

    Google Scholar 

  • Nayfeh AH, Younis MI (2003) A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping. J Micromech Microeng 14(2):170

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Ouakad HM (2013) Structural behavior of microbeams actuated by out-of-plane electrostatic fringing-fields. ASME 2013 international mechanical engineering congress and exposition. American Society of Mechanical Engineers, p V010T11A014

  • Ouakad HM (2014) Static response and natural frequencies of microbeams actuated by out-of-plane electrostatic fringing-fields. Int J Non-Linear Mech 63:39–48

    Article  Google Scholar 

  • Ouakad HM (2015) Simple and accurate analytical solution to the post-buckling response of an electrostatically actuated MEMS curled cantilever. Microsyst Technol 1–8. doi:10.1007/s00542-015-2719-9

  • Ouakad HM (2016) Electrostatic fringing-fields effects on the structural behavior of MEMS shallow arches. Microsyst Technol 1–9. doi:10.1007/s00542-016-2985-1

  • Ouakad HM, Mohammad TF (2014) Static and bifurcation analysis of MEMS arches actuated by electrostatic fringing fields. Mechatronic and embedded systems and applications (MESA), IEEE/ASME 10th international conference, IEEE, pp 1–6

  • Ouakad HM, Younis MI (2010) The dynamic behavior of MEMS arch resonators actuated electrically. Int J Non-Linear Mech 45(7):704–713

    Article  Google Scholar 

  • Park HM, Lim JY (2009) A reduced-order model of the low-voltage cascade electroosmotic micropump. Microfluid Nanofluid 6(4):509–520

    Article  Google Scholar 

  • Penzl T (2006) Algorithms for model reduction of large dynamical systems. Linear Algebra Appl 415(2):322–343

    Article  MathSciNet  MATH  Google Scholar 

  • Pfeiffer AJ, Mukherjee T, Hauan S (2004) Simultaneous design and placement of multiplexed chemical processing systems on microchips. IEEE/ACM, International conference on computer aided design, pp 229–236

  • Pu X, Li W, Zhou Z (2014) Electrothermal-driven gap adjustable MEMS comb structure: modeling and simulation of the equivalent circuit macromodel. Microsyst Technol 20(6):1205–1212

    Article  Google Scholar 

  • Qiao R, Aluru NR (2002) A compact model for electroosmotic flows in microfluidic devices. J Micromech Microeng 12(5):625

    Article  Google Scholar 

  • Ravindran SS (2000) A reduced-order approach for optimal control of fluids using proper orthogonal decomposition. Int J Numer Methods Fluids 34(5):425–448

    Article  MathSciNet  MATH  Google Scholar 

  • Rewieński M, White J (2003) A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Trans Comput Aided Des Integr Circuits Syst 22(2):155–170

    Article  Google Scholar 

  • Rowley CW (2005) Model reduction for fluids, using balanced proper orthogonal decomposition. Int J Bifur Chaos 15(03):997–1013

    Article  MathSciNet  MATH  Google Scholar 

  • Saghir S, Younis MI (2016) An investigation of the static and dynamic behavior of electrically actuated rectangular microplates. Int J Non-Linear Mech 85:81–93

    Article  Google Scholar 

  • Santorelli J, Nabki F, Khazaka R (2014) Practical considerations for parameterized model order reduction of MEMS devices. New circuits and systems conference (NEWCAS), IEEE 12th International IEEE, pp 129–132

  • Singh MK, Kang TG, Meijer HEH et al (2008) The mapping method as a toolbox to analyze, design, and optimize micromixers. Microfluid Nanofluid 5(3):313–325

    Article  Google Scholar 

  • Stroock AD, McGraw GJ (1818) Investigation of the staggered herringbone mixer with a simple analytical model. Philos Trans R Soc Lond A Math Phys Eng Sci 2004(362):971–986

    Google Scholar 

  • Sun C, Tsang S, Huang HY (2015) An analytical model for flow rectification of a microdiffuser driven by an oscillating source. Microfluid Nanofluid 18(5–6):979–993

    Article  Google Scholar 

  • Turowski M, Chen Z, Przekwas A (2001) Automated generation of compact models for fluidic microsystems. Analog Integr Circuits Signal Process 29(1–2):27–36

    Article  Google Scholar 

  • Vasilyev D, Rewieński M, White J (2006) Macromodel generation for BioMEMS components using a stabilized balanced truncation plus trajectory piecewise linear approach design automation methods and tools for microfluidics-based biochips. Springer, Netherlands, pp 169–187

    Google Scholar 

  • Wang Y, Lin Q, Mukherjee T (2004a) System-oriented dispersion models of general-shaped electrophoresis microchannels. Lab Chip 4(5):453–463

    Article  Google Scholar 

  • Wang Y, Lin Q, Mukherjee T (2004b) A model for Joule heating-induced dispersion in microchip electrophoresis. Lab Chip 4(6):625–631

    Article  Google Scholar 

  • Wang Y, Lin Q, Mukherjee T (2005) A model for laminar diffusion-based complex electrokinetic passive micromixers. Lab Chip 5(8):877–887

    Article  Google Scholar 

  • Wang Y, Lin Q, Mukherjee T (2006) Composable behavioral models and schematic-based simulation of electrokinetic lab-on-a-chip systems. Comput Aided Des Integr Circuits Syst IEEE Trans 25(2):258–273

    Article  Google Scholar 

  • Xie WC, Lee HP, Lim SP (2003) Nonlinear dynamic analysis of MEMS switches by nonlinear modal analysis. Nonlinear Dyn 31(3):243–256

    Article  MATH  Google Scholar 

  • Xie D, Xu M, Dowell EH (2014) Proper orthogonal decomposition reduced-order model for nonlinear aeroelastic oscillations. AIAA J 52(2):229–241

    Article  Google Scholar 

  • Xu T, Chakrabarty K (2007) A cross-referencing-based droplet manipulation method for high-throughput and pin-constrained digital microfluidic arrays. Design, automation & test in Europe conference & exhibition, Date’07, IEEE, pp 1–6

  • Yang YJJ, Kuo CW (2008) Generating scalable and modular macromodels for microchannels using the Galerkin-based technique. Comput Aided Des Integr Circuits Syst IEEE Trans 27(9):1545–1554

    Article  Google Scholar 

  • Yang YJJ, Yen PC (2005) An efficient macromodeling methodology for lateral air damping effects. Microelectromech Syst J 14(4):812–828

    Article  Google Scholar 

  • Yang YJ, Cheng SY, Shen KY (2004) Macromodeling of coupled-domain MEMS devices with electrostatic and electrothermal effects. J Micromech Microeng 14(8):1190

    Article  Google Scholar 

  • Yen PC, Yang YJ (2016) Guidelines of creating krylov-subspace macromodels for lateral viscous damping effects. A A 1(2):1

    Google Scholar 

  • Yi M, Bau HH (2003) The kinematics of bend-induced mixing in micro-conduits. Int J Heat Fluid Flow 24(5):645–656

    Article  Google Scholar 

  • Yin CY, Lu H, Bailey C et al (2005) Macro-micro modeling analysis for high density packaged flip chips. In: IEEE conference on high density microsystem design and packaging and component failure analysis, pp 1–4

  • Zaman MH, Bart SF, Rabinovich VL et al (1999) A technique for extraction of macro-models in system level simulation of inertial electro-mechanical micro-systems. In: Proceedings of MSM, vol 99, pp 163–67

  • Zhang T, Chakrabarty K, Fair RB (2004) Behavioral modeling and performance evaluation of microelectrofluidics-based PCR systems using SystemC. IEEE Trans Comput Aided Des Integr Circuits Syst 23(6):843–858

    Article  Google Scholar 

  • Zhang Z, Kamon M, Daniel L (2014a) Continuation-based pull-in and lift-off simulation algorithms for microelectromechanical devices. J Microelectromech Syst 23(5):1084–1093

    Article  Google Scholar 

  • Zhang WM, Yan H, Peng ZK et al (2014b) Electrostatic pull-in instability in MEMS/NEMS: a review. Sens Actuators A Phys 214:187–218

    Article  Google Scholar 

  • Zhao X, Abdel-Rahman EM, Nayfeh AH (2004) A reduced-order model for electrically actuated microplates. J Micromech Microeng 14(7):900

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Liaoning BaiQianWan Talents Program.

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering and Automation, Liaoning University of Technology, Jinzhou, 121001, China

    Xueye Chen & Zeyang Wu

Authors
  1. Xueye Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeyang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xueye Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, X., Wu, Z. Review on macromodels of MEMS sensors and actuators. Microsyst Technol 23, 4319–4332 (2017). https://doi.org/10.1007/s00542-016-3251-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00542-016-3251-2

Keywords

Search

Navigation