Abstract
Uncertainty in physical parameters of a tunable MEMS capacitor, as the main element of MEMS AC voltage reference (VRS), is a significant matter to be regarded in order to obtain a precise output voltage which could be ruined by disturbance and noise. Even though many attempts are done to make MEMS tunable capacitor with desired precise physical characteristics and improve accuracy of values in physical parametric properties, parametric uncertainties inevitably transpire in manufacturing process due to shortcomings in micromachining procedures. Not only does this paper take into account design of a PI adaptive sliding mode controller and its application for the MEMS AC VRS in such a way that it is competent of producing a stable precise regulated output voltage in the presence of uncertainties and exogenous disturbance, but also it conquers both terms of matched and unmatched uncertainties and disturbance which their upper bounds are limited but not known. The matched and unmatched disturbance may emerge in the device dynamics because of cross-talk, inertial coercions and electrostatic disturbing forces. The matched uncertainties, such as change in stiffness and damping factors, may exist because of alteration in manufacturing process or even operational situations. The simulation yields in the article are very convincing that the controller design has demonstrated a persuasive tracking performance and has resulted in a well regulation about the pull-in working point.
Similar content being viewed by others
References
Alwi H, Zolotas A, Edwards C, Grigoriadis K (2012) Sliding mode control design of an electrostatic microactuator using LPV schemes. In: American control conference (ACC), pp 875–880. https://doi.org/10.1109/ACC.2012.6314803
Blard F, Bounouh A, Bélières D, Camon H (2011) Very high stability achievement in MEMS based AC voltage references. In: IEEE 24th international conference on micro electro mechanical systems (MEMS), pp 656–659. https://doi.org/10.1109/MEMSYS.2011.5734510
Bounouh A, Camon H, Bélières D, Blard F, Ziadé F (2011) MEMS AC voltage reference for miniaturized instrumentation and metrology. Comput Stand interfaces 33(2):159–164. https://doi.org/10.1016/j.csi.2010.06.007, XVI IMEKO TC4 “Symposium exploring new frontiers of instrumentation and methods for electrical and electronic measurements” and XIII international workshop on ADC modelling and testing
Bounouh A, Camon H, Belieres D (2012) MEMS based AC voltage references with very high stability. In: Conference on precision electromagnetic measurements (CPEM), pp 552–553. https://doi.org/10.1109/CPEM.2012.6251048
Bounouh A, Camon H, Belieres D (2013) Wideband high stability MEMS-based AC voltage references. IEEE Trans Instrum Meas 62(6):1646–1651. https://doi.org/10.1109/TIM.2012.2225963
Brogan WL (1991) Modern control theory, 3rd edn. Prentice-Hall Inc, Upper Saddle River
Castan̋er L, Pons J, Nadal-Guardia R, Rodrıǵuez A (2001) Analysis of the extended operation range of electrostatic actuators by current-pulse drive. Sens Actuators A Phys 90(3):181–190. https://doi.org/10.1016/S0924-4247(01)00525-8
Chenarani H, Binazadeh T (2017) Flexible structure control of unmatched uncertain nonlinear systems via passivity-based sliding mode technique. Iran J Sci Technol Trans Electr Eng 41(1):1–11
Cherrat N, Boubertakh H, Arioui H (2018) Adaptive fuzzy PID control for a class of uncertain MIMO nonlinear systems with dead-zone inputs’ nonlinearities. Iran J Sci Technol Trans Electr Eng 42:21–39
Dastani K, Moghimi Zand M (2017) Dynamic and static pull-in instability of electrostatically actuated nano/micro membranes under the effects of casimir force and squeezed film damping. J Comput Appl Mech 47(2):219–230. https://doi.org/10.22059/jcamech.2017.224952.125
Ebrahimi B, Bahrami M (2006) Robust sliding-mode control of a MEMS optical switch. J Phys Conf Ser 34:728–733. https://doi.org/10.1088/1742-6596/34/1/120
Fei J (2010) Robust adaptive vibration tracking control for a micro-electro-mechanical systems vibratory gyroscope with bound estimation. IET Control Theory Appl 4(6):1019–1026. https://doi.org/10.1049/iet-cta.2008.0199
Fei J (ed) (2012) Advanced control design of MEMS vibratory gyroscope. Nova Science Publishers, New York
Fei J, Batur C (2009) A novel adaptive sliding mode control with application to MEMS gyroscope. ISA Trans 48(1):73–78. https://doi.org/10.1016/j.isatra.2008.10.008
Fei J, Xin M, Juan W (2013) Adaptive fuzzy sliding mode control using adaptive sliding gain for MEMS gyroscope. Trans Inst Meas Control 35(4):551–558. https://doi.org/10.1177/0142331212455451
Hailu Z (2017) High quality factor RF MEMS tunable capacitor. Microsyst Technol 23(8):3719–3730. https://doi.org/10.1007/s00542-016-3181-z
Han C, Choi D, Yang H, Yoon Y, Yoon J (2013) Voltage-controlled \(C{-}V\) response tuning in a parallel plate mems variable capacitor. J Microelectromech Syst 22(6):1403–1413. https://doi.org/10.1109/JMEMS.2013.2257987
Hashemipoor SS, Suratgar AA, Fard A, Hashemipoor SM (2009) Designing a robust MEMS AC voltage reference source using artificial neural network. In: ICCSIT 2009. 2nd IEEE international conference on computer science and information technology, pp 184–187. https://doi.org/10.1109/ICCSIT.2009.5234416
Hassani FA, Payam AF, Fathipour M (2010) Design of a smart MEMS accelerometer using nonlinear control principles. Smart Struct Syst 6(1):1–16. https://doi.org/10.12989/sss.2010.6.1.001
Juan W, Fei J (2013) Adaptive fuzzy approach for non-linearity compensation in MEMS gyroscope. Trans Inst Meas Control 35(8):1008–1015. https://doi.org/10.1177/0142331212472224
Karami F, Salarieh H, Shabani R (2014) Tracking and shape control of a micro-cantilever using electrostatic actuation. Int J Eng Trans C Asp 27(9):1439–1448
Kärkkäinen AM (2006) MEMS based voltage references. Ph.D. thesis, VTT Technical Research Centre of Finland, Vuorimiehentie 3, P.O. Box 1000, FI-02044 VTT, Finland, dissertation for the degree of Doctor of Philosophy to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in the Large Seminar Hall of Micronova at Helsinki University of Technology
Kärkkäinen A, Oja A, Kyynäräinen J, Kuisma H, Seppä H (2004a) Stability of electrostatic actuation of MEMS. Phys Scr T114:193. https://doi.org/10.1088/0031-8949/2004/T114/048
Kärkkäinen A, Pesonen N, Suhonen M, Kyynarainen J, Oja A, Manninen A, Tisnek N, Seppa H (2004b) AC voltage reference based on a capacitive micromechanical component. In: Conference on precision electromagnetic measurements digest, pp 119–120. https://doi.org/10.1109/CPEM.2004.305489
Kärkkäinen A, Pekko P, Dekker J, Pesonen N, Suhonen M, Oja A, Kyynäräinen J, Seppä H (2005) Stable SOI micromachined electrostatic AC voltage reference. Microsyst Technol 12(1–2):169–172. https://doi.org/10.1007/s00542-005-0005-y
Khalil H, Education P (2015) Nonlinear systems. Always learning, Pearson Education International Incorporated. https://books.google.com/books?id=Gt2HAQAACAAJ. Accessed 9 June 2019
Kuttler K (2012) Linear algebra: theory and applications. Open textbook library, The Saylor Foundation. https://books.google.nl/books?id=TIVPAgAAQBAJ. Accessed 9 June 2019
Mehrnezhad A, Suratgar A, Khatami S, Sobhiyeh S (2013) A mathematical dynamic model for static and dynamic behaviours of MEMS-based AC voltage reference source. In: 21st Iranian conference on electrical engineering (ICEE), pp 1–5. https://doi.org/10.1109/IranianCEE.2013.6599714
Menbari B, Suratgar AA (2006) A low- power low-voltage VCO with wide range tuning controlled by adaptive neural network. In: IEEE international frequency control symposium and exposition, pp 567–574. https://doi.org/10.1109/FREQ.2006.275449
Mobki H, Sadeghi M, Rezazadeh G (2015) State estimation of MEMs capacitor using taylor expansion. Int J Eng Trans B Appl 28(5):764–770. https://doi.org/10.5829/idosi.ije.2015.28.05b.15
Mohabbatian N, Abbaspour Sani E (2012) Design and simulation of RF-MEMS tunable capacitors using multiple voltage sources. MEMS, NANO and smart systems. Trans Tech Publications, Advanced Materials Research, vol 403, pp 4137–4140. https://doi.org/10.4028/www.scientific.net/AMR.403-408.4137
Moreira E, Cabral J, Gaspar J, Rocha L (2016) Low-voltage, high-tuning range MEMS variable capacitor using closed-loop control. Procedia Eng 168:1551–1554. https://doi.org/10.1016/j.proeng.2016.11.458. Proceedings of the 30th anniversary Eurosensors conference—Eurosensors 2016, 4–7 Sepember 2016, Budapest, Hungary
Nguyen HD, Hah D, Patterson PR, Chao R, Piyawattanametha W, Lau EK, Wu MC (2004) Angular vertical comb-driven tunable capacitor with high-tuning capabilities. J Microelectromech Syst 13(3):406–413. https://doi.org/10.1109/JMEMS.2004.828741
Owusu KO, Lewis FL (2007) Solving the “pull-in” instability problem of electrostatic microactuators using nonlinear control techniques. In: 2nd IEEE international conference on nano/micro engineered and molecular systems, pp 1190–1195. https://doi.org/10.1109/NEMS.2007.352232
Pugh C (2003) Real mathematical analysis. Undergraduate texts in mathematics. Springer, New York, p 155. https://books.google.com/books?id=R_ZetzxFHVwC. Accessed 9 June 2019
Rajaei A, Vahidi-Moghaddam A, Ayati M, Baghani M (2019) Integral sliding mode control for nonlinear damped model of arch microbeams. Microsyst Technol 25(1):57–68. https://doi.org/10.1007/s00542-018-3931-1
Ranjbar E, Suratgar AA (2018) A composite adaptive controller design for 3-DOF MEMS vibratory gyroscopes capable of measuring angular velocity. Iran J Sci Technol Trans Electr Eng. https://doi.org/10.1007/s40998-018-0101-5
Ranjbar E, Mehrnezhad A, Suratgar A, Khatami S (2014) Adaptive control of MEMS-based AC voltage reference source. In: 22nd Iranian conference on electrical engineering (ICEE), pp 1336–1341. https://doi.org/10.1109/IranianCEE.2014.6999741
Ranjbar E, Mehrnezhad A, Suratgar AA (2017) Adaptive sliding mode control of MEMS AC voltage reference source. J Control Sci Eng. https://doi.org/10.1155/2017/9425190
Salah M, Al-Jarrah A, Tatlicioglu E (2011) Nonlinear control techniques for micro electrostatic actuators in the presence of parasitics and parametric uncertainties. In: Proceedings of the 13th IASTED international conference on control and applications, CA 2011. https://doi.org/10.2316/P.2011.729-105
Shavezipur M, Hashemi S, Nieva P, Khajepour A (2010) Development of a triangular-plate MEMS tunable capacitor with linear capacitance–voltage response. Microelectron Eng 87(9):1721–1727. https://doi.org/10.1016/j.mee.2009.09.011. 11th SEMATECH surface preparation and cleaning conference
Slotine J, Li W (1991) Applied nonlinear control. Prentice Hall, Upper Saddle River
Suhonen M, Seppa H, Oja A, Heinila M, Nakki I (1998) AC and DC voltage standards based on silicon micromechanics. In: Conference on precision electromagnetic measurements digest, pp 23–24. https://doi.org/10.1109/CPEM.1998.699739
Suratgar AA, Hashemipoor SS, Hoseini H (2009) Noise effect reduction on a MEMS-based AC voltage reference source using artificial neural network. In: ICCSIT 2009. 2nd IEEE international conference on computer science and information technology, pp 179–183. https://doi.org/10.1109/ICCSIT.2009.5234415
Teymoori M, Ahangarkolaei JM (2016) A tunable capacitor based on MEMS technology for RF applications. Eng Technol Appl Sci Res 6(3):982–986
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):325–332. https://doi.org/10.1016/j.isatra.2011.11.002
Vagia M (2013) How to extend the travel range of a nanobeam with a robust adaptive control scheme: a dynamic surface design approach. ISA Trans 52(1):78–87. https://doi.org/10.1016/j.isatra.2012.09.001
Wu D, Fei J (2016) Adaptive neural sliding control of MEMS gyroscope with robust feedback compensator. Trans Inst Meas Control 38(4):414–424. https://doi.org/10.1177/0142331215585879
Yoon J-B, Nguyen CT (2000) A high-Q tunable micromechanical capacitor with movable dielectric for RF applications. In: International electron devices meeting 2000. Technical digest. IEDM (Cat. No.00CH37138), pp 489–492. https://doi.org/10.1109/IEDM.2000.904362
Zhang WM, Yan H, Peng ZK, Meng G (2014) Electrostatic pull-in instability in MEMS/NEMS: a review. Sens Actuators A Phys 214:187–218. https://doi.org/10.1016/j.sna.2014.04.025
Zhu Y, Yuce MR, Moheimani SOR (2009) A low-loss MEMS tunable capacitor with movable dielectric. In: SENSORS, 2009 IEEE, pp 651–654. https://doi.org/10.1109/ICSENS.2009.5398334
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ranjbar, E., Yaghoubi, M. & Suratgar, A.A. Adaptive Sliding Mode Controller Design for a Tunable Capacitor Susceptible to Unknown Upper-Bounded Uncertainties and Disturbance. Iran J Sci Technol Trans Electr Eng 44, 327–346 (2020). https://doi.org/10.1007/s40998-019-00220-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40998-019-00220-8