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Microsystem Technologies

, Volume 25, Issue 1, pp 57–68 | Cite as

Integral sliding mode control for nonlinear damped model of arch microbeams

  • Arman Rajaei
  • Amin Vahidi-Moghaddam
  • Moosa AyatiEmail author
  • Mostafa Baghani
Technical Paper
  • 60 Downloads

Abstract

In this paper, a second order integral sliding mode controller (SMC) and a two-dimensional integral sliding mode controller are designed for a nonlinear damped model of arch microbeam with two electrodes as a bistable system. The latest model of the arch microbeam is introduced in which the squeezed film damping effect is modeled through considering nonlinear terms. The actuating voltage is considered as the control effort of the system somehow expands as a combined static DC and harmonic AC voltage. The second order integral SMC and two-dimensional integral SMC are proposed as the robust controllers to stabilize the system in the presence of the uncertain parameter due to the damping coefficient. The controller formula, stability and convergence of the closed-loop system are derived and formulated for the arch microbeam. Simulation results and comparison of the proposed controllers are presented to demonstrate the performance of the designed control schemes for achieving set point tracking in the closed-loop system.

Notes

References

  1. Aliakbari S, Ayati M, Osman JH, Sam YM (2013) Second-order sliding mode fault-tolerant control of heat recovery steam generator boiler in combined cycle power plants. Appl Therm Eng 50(1):1326–1338CrossRefGoogle Scholar
  2. Alsaleem FM, Younis MI (2010) Stabilization of electrostatic MEMS resonators using a delayed feedback controller. Smart Mater Struct 19(3):035016CrossRefGoogle Scholar
  3. Alsaleem F, Younis MI (2011) Integrity analysis of electrically actuated resonators with delayed feedback controller. J Dyn Syst Meas Control 133(3):031011CrossRefGoogle Scholar
  4. Ayati M, Salmasi FR (2015) Fault detection and approximation for a class of linear impulsive systems using sliding-mode observer. Int J Adapt Control Signal Process 29(11):1427–1441MathSciNetCrossRefzbMATHGoogle Scholar
  5. Baghani M (2012) Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory. Int J Eng Sci 54:99–105CrossRefzbMATHGoogle Scholar
  6. Bartolini G, Ferrara A, Utkin VI (1995) Adaptive sliding mode control in discrete-time systems. Automatica 31(5):769–773MathSciNetCrossRefzbMATHGoogle Scholar
  7. Bouchaala AM (2018) Theoretical study of an electrostatically actuated torsional microsensor for biological applications. Microsyst Technol 24(2):1109–1114CrossRefGoogle Scholar
  8. Bouchaala A, Nayfeh AH, Younis MI (2017) Analytical study of the frequency shifts of micro and nano clamped–clamped beam resonators due to an added mass. Meccanica 52(1–2):333–348CrossRefzbMATHGoogle Scholar
  9. Chuang WC, Lee HL, Chang PZ, Hu YC (2010) Review on the modeling of electrostatic MEMS. Sensors 10(6):6149–6171CrossRefGoogle Scholar
  10. Daneshpajooh H, Zand MM (2015) Semi-analytic solutions to oscillatory behavior of initially curved micro/nano systems. J Mech Sci Technol 29(9):3855–3863CrossRefGoogle Scholar
  11. Fazlyab M, Pedram MZ, Salarieh H, Alasty A (2013) Parameter estimation and interval type-2 fuzzy sliding mode control of a z-axis MEMS gyroscope. ISA Trans 52(6):900–911CrossRefGoogle Scholar
  12. Ghanbari A, Moghanni-Bavil-Olyaei MR (2014) Adaptive fuzzy terminal sliding-mode control of MEMS z-axis gyroscope with extended Kalman filter observer. Syst Sci Control Eng Open Access J 2(1):183–191CrossRefGoogle Scholar
  13. Hosseini II, Zand MM, Lotfi M (2017) Dynamic pull-in and snap-through behavior in micro/nano mechanical memories considering squeeze film damping. Microsyst Technol 23(5):1423–1432CrossRefGoogle Scholar
  14. Huang HW, Liao HH, Yang YJ (2011) Characterization of an 2 × 2 SCB optical switch integrated with VOA. In: Nano/micro engineered and molecular systems (NEMS), 2011 IEEE international conference on, pp 607–610Google Scholar
  15. Krylov S, Dick N (2010) Dynamic stability of electrostatically actuated initially curved shallow micro beams. Contin Mech Thermodyn 22(6–8):445–468MathSciNetCrossRefzbMATHGoogle Scholar
  16. Kumar S, Chattoraj N, Sinha MK, Danu N (2017) Investigation of electrostatic actuation scheme for low voltage MEMS switch. In: Proceedings of the international conference on nano-electronics, circuits & communication systems, pp 167–176Google Scholar
  17. Lotfi M, Zand MM, Hosseini II, Baghani M, Dargazany R (2017) Transient behavior and dynamic pull-in instability of electrostatically-actuated fluid-conveying microbeams. Microsyst Technol 23(12):6015–6023CrossRefGoogle Scholar
  18. Medina L, Gilat R, Krylov S (2012) Symmetry breaking in an initially curved micro beam loaded by a distributed electrostatic force. Int J Solids Struct 49(13):1864–1876CrossRefGoogle Scholar
  19. Medina L, Gilat R, Krylov S (2017) Modeling strategies of electrostatically actuated initially curved bistable micro plates. Int J Solids Struct 118:1–13CrossRefzbMATHGoogle Scholar
  20. Meghni B, Dib D, Azar AT (2017) A second-order sliding mode and fuzzy logic control to optimal energy management in wind turbine with battery storage. Neural Comput Appl 28(6):1417–1434CrossRefGoogle Scholar
  21. Park S, Hah D (2008) Pre-shaped buckled-beam actuators: theory and experiments. Sens Actuators A 148(1):186–192CrossRefGoogle Scholar
  22. Rabanim S, Amir E, Krylov S (2011) Bistable threshold sensor with mechanically nonlinear self-limiting suspension and electrostatic actuation. In: ASME 2011 international design engineering technical conferences and computers and information in engineering conference, pp 135–144Google Scholar
  23. Rahnavard M, Hairi-Yazdi MR, Ayati M (2017) On the development of a sliding mode observer-based fault diagnosis scheme for a wind turbine benchmark model. Energy Equip Syst 5(1):13–26Google Scholar
  24. Rega G, Lenci S (2015) A global dynamics perspective for system safety from macro-to nanomechanics: analysis, control, and design engineering. Appl Mech Rev 67(5):050802CrossRefGoogle Scholar
  25. Roozegar M, Ayati M, Mahjoob MJ (2017) Mathematical modelling and control of a nonholonomic spherical robot on a variable-slope inclined plane using terminal sliding mode control. Nonlinear Dyn 90(2):971–981MathSciNetCrossRefGoogle Scholar
  26. Senturia SD (2007) Microsystem design. Springer Science & Business Media, BerlinGoogle Scholar
  27. Slotine JJ, Li W (1991) Applied nonlinear control. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  28. Tajaddodianfar F, Pishkenari HN, Hairi-Yazdi MR (2016) Prediction of chaos in electrostatically actuated arch micro-nano resonators: analytical approach. Commun Nonlinear Sci Numer Simul 30(1):182–195MathSciNetCrossRefzbMATHGoogle Scholar
  29. Utkin V, Guldner J, Shi J (2009) Sliding mode control in electro-mechanical systems. CRC Press, Boca RatonCrossRefGoogle Scholar
  30. Vagia M (2012) A frequency independent approximation and a sliding mode control scheme for a system of a micro-cantilever beam. ISA Trans 51(2):325–332CrossRefGoogle Scholar
  31. Vagia M, Tzes A (2008) Robust PID control design for an electrostatic micromechanical actuator with structured uncertainty. IET Control Theory Appl 2(5):365–373MathSciNetCrossRefGoogle Scholar
  32. Vagia M, Tzes A (2013) Design of a robust controller and modeling aspects of a micro cantilever beam with fringing and squeezed gas film damping effects. Mechatronics 23(1):67–79CrossRefGoogle Scholar
  33. Vahidi-Moghaddam A, Rajaei A, Vatankhah R, Hairi-Yazdi MR (2018) Terminal sliding mode control with non-symmetric input saturation for vibration suppression of electrostatically actuated nanobeams in the presence of Casimir force. Appl Math Model 60:416–434MathSciNetCrossRefGoogle Scholar
  34. Varadan VK, Vinoy KJ, Jose KA (2003) RF MEMS and their applications. Wiley, New YorkGoogle Scholar
  35. Vatankhah R, Asemani MH (2017) Output feedback control of piezoelectrically actuated non-classical micro-beams using TS fuzzy model. J Frankl Inst 354(2):1042–1065MathSciNetCrossRefzbMATHGoogle Scholar
  36. Vatankhah R, Karami F, Salarieh H (2015) Observer-based vibration control of non-classical microcantilevers using extended Kalman filters. Appl Math Model 39(19):5986–5996MathSciNetCrossRefGoogle Scholar
  37. Yau HT, Wang CC, Hsieh CT, Cho CC (2011) Nonlinear analysis and control of the uncertain micro-electro-mechanical system by using a fuzzy sliding mode control design. Comput Math Appl 61(8):1912–1916MathSciNetCrossRefzbMATHGoogle Scholar
  38. Zhankui S, Sun K (2013) Nonlinear and chaos control of a micro-electro-mechanical system by using second-order fast terminal sliding mode control. Commun Nonlinear Sci Numer Simul 18(9):2540–2548MathSciNetCrossRefzbMATHGoogle Scholar
  39. Zhao F, Trimble MD (2017) 4H-SiC electrostatic microactuator with optically controlled actuation. Microsyst Technol 23(12):5631–5634CrossRefGoogle Scholar
  40. Zolotas AC, Tzes A, Vagia M (2007) Robust control design for an uncertain electrostatic micro-mechanical system via loop shaping. In: Control conference (ECC), 2007 European, pp 389–394Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShiraz UniversityShirazIran
  2. 2.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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