Sliding Mode Observation with Iterative Parameter Adaption for Fast-Switching Solenoid Valves

Part of the Mathematical Engineering book series (MATHENGIN)


Control of the armature motion of fast-switching solenoid valves is highly desired to reduce noise emission and wear of material. For feedback control, information of the current position and velocity of the armature are necessary. In mass production applications, however, position sensors are unavailable due to cost and fabrication reasons. Thus, position estimation by measuring merely electrical quantities is a key enabler for advanced control, and, hence, for efficient and robust operation of digital valves in advanced hydraulic applications. The work presented here addresses the problem of state estimation, i.e., position and velocity of the armature, by sole use of electrical measurements. The considered devices typically exhibit nonlinear and very fast dynamics, which makes observer design a challenging task. In view of the presence of parameter uncertainty and possible modeling inaccuracy, the robustness properties of sliding mode observation techniques are deployed here. The focus is on error convergence in the presence of several sources for modeling uncertainty and inaccuracy. Furthermore, the cyclic operation of switching solenoids is exploited to iteratively correct a critical parameter by taking into account the norm of the observation error of past switching cycles of the process. A thorough discussion on real-world experimental results highlights the usefulness of the proposed state observation approach.


Solenoid Valve Observer Design Observer Gain Error Convergence Copper Resistance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The support of this work by the German Federal Ministry of Education and Research under grant 03FH047PX2 is gratefully acknowledged. Furthermore, the authors would like to thank the anonymous reviewers for their invaluable comments and suggestions, as well as F. Straußberger for helpful discussions.


  1. 1.
    Abry F, Brun X, Di Loreto M, Sesmat S, Bideaux É (2015) Piston position estimation for an electro-pneumatic actuator at standstill. Control Eng Pract 41:176–185CrossRefGoogle Scholar
  2. 2.
    Alessandri A, Cuneo M, Punta E (2010) State observers with first-/second-order sliding-mode for nonlinear systems with bounded noises. In: Proceedings of the 11th international workshop on variable structure systems (VSS), Mexico, pp 493–497Google Scholar
  3. 3.
    Alvarez J, Orlov YV, Acho L (2000) An invariance principle for discontinuous dynamic systems with application to a coulomb friction oscillator. ASME J Dyn Syst Meas Control 122(4):687–690Google Scholar
  4. 4.
    Braun T, Schwab M, Straußberger F, Reuter J (2014) State estimation for fast-switching solenoid valves—a nonlinear sliding-mode-observer approach. In: 19th IEEE international conference on methods and models in automation and robotics (MMAR14), Miedzyzdroje, pp 282–287Google Scholar
  5. 5.
    Braun T, Straußberger F, Reuter J (2015) State estimation for fast-switching solenoid valves: a study on practical nonlinear observers and new experimental results. In: 20th IEEE international conference on methods and models in automation and robotics (MMAR15), Miedzyzdroje, pp 862–867Google Scholar
  6. 6.
    Braun T, Straußberger F, Reuter J, Preissler G (2015) A semilinear distributed parameter approach for solenoid valve control including saturation effects. In: American control conference (ACC15), Chicago, pp 2600–2605Google Scholar
  7. 7.
    Danca M-F, Codreanu S (2002) On a possible approximation of discontinuous dynamical systems. Chaos Solitons Fractals 13(4):681–691MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Drakunov S (1992) Sliding-mode observers based on equivalent control method. In: Proceedings of the 31st IEEE conference on decision and control vol 2. Tucson, pp 2368–2369Google Scholar
  9. 9.
    Eyabi P, Washington G (2006) Modeling and sensorless control of an electromagnetic valve actuator. Mechatronics 16(3–4):159–175CrossRefGoogle Scholar
  10. 10.
    Filippov A (1988) Differential equations with discontinuous righthand sides. Mathematics and its applications. Kluwer Academic Publishers, DordrechtGoogle Scholar
  11. 11.
    Glück T (2013) Soft landing and self-sensing strategies for electromagnetic actuators. Modellierung und Regelung komplexer dynamischer Systeme. Shaker, AachenGoogle Scholar
  12. 12.
    Glück T, Kemmetmüller W, Kugi A (2011) Trajectory optimization for soft landing of fast-switching electromagnetic valves. In: Proceedings of the 18th IFAC world congress, Milano, pp 11532–11537Google Scholar
  13. 13.
    Glück T, Kemmetmüller W, Tump C, Kugi A (2011) A novel robust position estimator for self-sensing magnetic levitation systems based on least squares identification. Control Eng Pract 19(2):146–157CrossRefGoogle Scholar
  14. 14.
    Haddad W, Chellaboina V (2011) Nonlinear dynamical systems and control: a Lyapunov-based approach. Princeton University Press, PrincetonGoogle Scholar
  15. 15.
    Haskara I, Özgüner Ü (1999) Equivalent value filters in disturbance estimation and state observation. In: Young K, Özgüner Ü (eds) Variable structure systems. Sliding mode and nonlinear control. Volume 247 of lecture notes in control and information sciences. Springer, London, pp 167–179Google Scholar
  16. 16.
    Kallenbach E (2008) Elektromagnets: basics, dimensioning, design and application (in German). ViewegTeubner [GWV Fachverlage GmbH], Wiesbaden, 3rd ednGoogle Scholar
  17. 17.
    Khalil H (2002) Nonlinear systems. Prentice Hall PTR, Upper Saddle RiverGoogle Scholar
  18. 18.
    Kim I-S (2010) A technique for estimating the state of health of Lithium batteries through a dual-sliding-mode observer. IEEE Trans Power Electron 25(4):1013–1022CrossRefGoogle Scholar
  19. 19.
    Kogler H, Scheidl R (2008) Two basic concepts of hydraulic switching converters. In: Proceedings of the first workshop on digital fluid power DFP 2008, Tampere, pp 113–128Google Scholar
  20. 20.
    Linjama M (2011) Digital fluid power—state of the art. In: The Twelfth Scandinavian International conference on fluid power (SICFP), Tampere, pp 331–353Google Scholar
  21. 21.
    Lynch AF, Koch CB, Chladny R (2003) Nonlinear observer design for sensorless electromagnetic actuators. Dynamics of continuous discrete and impulsive systems-Series B-applications and algorithms, special issue, pp 317–322Google Scholar
  22. 22.
    Orlov Y (2009) Discontinuous systems: Lyapunov analysis and robust synthesis under uncertainty conditions. Communications and control engineering. Springer, LondonGoogle Scholar
  23. 23.
    Poznyak AS (2004) Deterministic output noise effects in sliding mode observation. In: Sabanovic A, Fridman LM, Spurgeon S (eds) Variable structure systems: from principles to implementation. IEE control engineering series vol 66. The Institution of Engineering and Technology (IET), London, pp 45–80Google Scholar
  24. 24.
    Reinertz O, Murrenhoff H (2009) Dynamic modeling of switching valves: an approach for one-dimensional simulation (in German). O+P Ölhydraulik und Pneumatik 16(4):152–155Google Scholar
  25. 25.
    Reuter J (2006) Flatness based control of a dual coil solenoid valve. In: 4th IFAC symposium on mechatronic systems. Ruprecht-Karls-University, Germany, pp 48–54Google Scholar
  26. 26.
    Shtessel Y, Edwards C, Fridman L, Levant A (2014) Sliding mode control and observation. Control engineering. Birkhäuser, BaselGoogle Scholar
  27. 27.
    Straußberger F, Schwab M, Braun T, Reuter J (2014) Position estimation in electro-magnetic actuators using a modified discrete time class a/b model reference approach. In: American control conference (ACC14), Portland, pp 3686–3691Google Scholar
  28. 28.
    Utkin V (1992) Sliding modes in control and optimization. Communications and control engineering. Springer, BerlinGoogle Scholar
  29. 29.
    Yaz E, Azemi A (1993) Variable structure observer with a boundary-layer for correlated noise/disturbance models and disturbance minimization. Int J Control 57(5):1191–1206MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Zeitz M (1977) Nonlinear observers for chemical reactors (in German). Fortschrittberichte der VDI-Zeitschriften; Nr. 27. VDI-Verlag, DüsseldorfGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of System Dynamics, Constance University of Applied SciencesKonstanzGermany

Personalised recommendations