Skip to main content

Theoretical Foundations of Optimal Two-Step Control of Suspension Stiffness of Transport Vehicle in Oscillation Cycle

  • Conference paper
  • First Online:
Proceedings of the 4th International Conference on Industrial Engineering (ICIE 2018)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

Abstract

The article dwells upon the issues of control over suspension stiffness of transport vehicle in the oscillation cycle. This article describes the methods of stiffness change for suspension and identifies two principal schemes of two-step stiffness change for the suspension: a suspension with constant step stiffness and a suspension with variable step stiffness. Mathematical models of suspensions with a two-step stiffness control in a single-mass oscillating system were developed for each of the two principal schemes of stiffness control. Having employed the maximum principle of L. S. Pontriagin, the algorithms for the optimal suspension stiffness control were determined. In particular, it was found that, when the oscillating system is unbalanced with the subsequent absence of the external force and kinematic action, any stiffness switching, even chaotic one, results in a decrease in the motion amplitudes of the sprung mass and oscillation damping. The optimal control algorithm in case of kinematic disturbance of the oscillating system is an algorithm at which the activation of a suspension step with a higher stiffness occurs during the change in the direction of suspension deformation, and the system switches to the lower stiffness during the change in the direction of the sprung mass motion.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Fitilev BN, Averyanov GS, Belkov VN (1981) Air suspension. USSR patent 8,442,295, 30 Jun 1981

    Google Scholar 

  2. Gustomiasov AN (1978) Analiz kolebatel’noj sistemy podveski avtomobilya s diskretnym izmeneniem zhyostkosti (Analysis of the oscillating system of vehicle suspension with discontinuous stiffness change). Izv Vuzov 5:187–188

    Google Scholar 

  3. Yoshimura T, Takagi A (2004) Pneumatic active suspension system for a one-wheel car model using fuzzy reasoning and a disturbance observer. J Zhejiang Univ Sci 5(9):1060–1068

    Article  Google Scholar 

  4. Gneusheva EM, Fominova OV, Chernyshev VI (2006) Dinamicheskie svojstva vibrozashchitnyh sistem s dopolnitel’nym uprugodempfiruyushchim zvenom preryvistogo dejstviya (Dynamic behavior of vibration isolation systems with an auxiliary springing and damping component element of interruptive action). Spravochnik Inzhenernyj Zh 6:59–64

    Google Scholar 

  5. Kalashnikov BA (2008) Sistemy amortizacii ob”ektov s diskretnoj kommutaciej uprugih ehlementov (Shock-absorbing system of the installations with discontinuous overlapping of the springing elements). Omsk State Technical University, Omsk, p 344

    Google Scholar 

  6. Fitilev BN, Komochkov VA, Pozdeev AV (2009) K raschyotu kharakteristik pnevmoelementa s vozdushnym dempfirovaniem (Determination of characteristics of the pneumatic element with damping by air). In: Progress transportnyh sredstv i sistem—2009, vol. 2. Volgograd State Technical University, Volgograd, 13–15 Oct 2009, pp 40–47

    Google Scholar 

  7. Khamitov RN (2008) Sintez sistemy upravleniya impul’snym ehlektrodinamicheskim klapanom pnevmoamortizatora (Synthesis of a system to control the impulse operated electrodynamical valve of the impact attenuation bag). Spravochnik Inzhenernyj Zh 2:62–64

    Google Scholar 

  8. Khamitov RN, Averyanov GS, Korchagin AB (2009) Rabochie processy dvuhkamernogo pnevmaticheskogo amortizatora s kratkovremennoj kommutaciej ob”emov (Work processes of a two-chamber air-assisted shock absorber with a short-time overlapping of volumes). Vestn Mashinostr 10:19–23

    Google Scholar 

  9. Chernyshov KV, Pozdeev AV, Novikov VV, Riabov IM (2010) Opredelenie uslovij optimal’nogo regulirovaniya zhestkosti pnevmaticheskoj podveski ATS (Determination of conditions for the optimal control of air suspension stiffness of a vehicle). Gruzovik 11:2–5

    Google Scholar 

  10. Novikov VV, Pozdeev AV (2010) Opredelenie optimal’nyh algorit-mov regulirovaniya aktivno-upravlyaemyh pnevmopodvesok (Determination of optimal control algorithms for the actively controlled air suspensions). Gruzovik 5:6–10

    Google Scholar 

  11. Podzorov AV, Gorobtsov AS, Liashenko MV (2010) Matematicheskaya model’ upravlyaemoj sistemy podressorivaniya ATS (Mathematical model of the controlled springing system of a vehicle). Avtomobil Prom 9:16–19

    Google Scholar 

  12. Pozdeev AV, Novikov VV, Chernyshov KV, Riabov IM (2011) Sintez algoritmov optimal’nogo upravleniya dempfirovaniem i zhyostkost’yu podveski ATS (Design of algorithms for the optimal control of damping and stiffness of vehicle suspension). Gruzovik 6:2–6

    Google Scholar 

  13. Diakov AS, Pozdeev AV, Pokhlebin AV (2011) Optimal’noe upravlenie zhyostkost’yu i dempfirovaniem podveski ATS na osnove principa maksimuma L.S. Pontryagina (Optimal damping and stiffness control of vehicle suspension based on the maximum principle of L.S. Pontriagin). Vestn Akad Voen Nauk 2:132–139

    Google Scholar 

  14. Pozdeev AV (2011) Kommutaciya polostej kak sposob povysheniya vibrozashchitnyh svojstv dvuhkamernyh pnevma-ticheskih ressor (Overlapping of chambers as a way to improve the vibration isolation qualities of two-chamber air springs). In: SWorld: Nauchnye issledovaniya i ih prakticheskoe primenenie. Sovremennoe sostoyanie i puti razvitiya `2011. Part 2. Engineering sciences, Odessa National Maritime University, Odessa, 4–15 Oct 2011, pp 40–48

    Google Scholar 

  15. Novikov VV, Pozdeev AV, Diakov AS, Karlov VI, Cherkashina EA (2011) Air suspension. RU Utility model 109,698, 2011

    Google Scholar 

  16. Riabov IM, Pozdeev AV, Novikov VV, Diakov AS, Chernyshov KV (2011) Vehicle wheel suspension. RU Utility model 109,697, 2011

    Google Scholar 

  17. Pozdeev AV, Novikov VV, Diakov AS, Pokhlebin AV, Riabov IM, Chernyshov KV (2013) Reguliruemye pnevmaticheskie i pnevmogidravli-cheskie ressory podvesok avtotransportnyh sredstv (Controlled air and air-hydraulic springs of vehicle suspensions). Volgograd State Technical University, Volgograd, p 244

    Google Scholar 

  18. Pozdeev AV, Diakov AS, Novikov VV, Riabov IM (2013) Samoreguliruemye dvuhkamernye pnevmaticheskie ressory s kommutaciej polostej (Self-regulated two-chamber air springs with overlapping of chambers). Gruzovik 9:2–5

    Google Scholar 

  19. Pozdeev AV, Diakov AS, Novikov VV, Riabov IM (2013) Issledovaniya dvuhkamernoj pnevmaticheskoj ressory s kommutaciej polostej (Researches of a two-chamber air spring with overlapping of chambers). Gruzovik 1:35–37

    Google Scholar 

  20. Chernyshov KV, Pozdeev AV, Riabov IM (2013) Matematicheskoe obosnovanie al-goritma optimal’nogo upravleniya zhyostkost’yu uprugogo ehlementa v odnomassovoj kolebatel’noj sisteme (Mathematical justification of the algorithm of optimal stiffness control of the springing element in a single mass oscillation system). Izv VolgGTU. Seriya “Nazemnye transportnye sistemy”, part 6. Interuniversity collection of scientific articles, Volgograd State Technical University 10(113):38–42

    Google Scholar 

  21. Pozdeev AV (2015) Vibrozashchitnye svojstva dvuhpo-lostnyh pnevmaticheskih ressor na osnove sinteza opti-mal’nyh algoritmov kommutacii polostej (Vibration isolation qualities of two-chamber air springs based on design of the optimal algorithms of overlapping of chambers). Tekhnol Koliosnykh Gusenichnykh Mashyn 1:27–31

    Google Scholar 

  22. Pontriagin LS, Boltianskiy VG, Gamkrelidze RV, Mishchenko EF (1976) Matematicheskaya teoriya optimal’nyh processov (Mathematical theory of optimal processes). Nauka, Moscow, p 392

    Google Scholar 

  23. Chernyshov KV, Novikov VV, Riabov IM (2006) Opredelenie uslovij optimal’nogo upravleniya dempfirovaniem podveski ATS na osnove principa maksimuma L.S. Pontryagina (Determination of conditions of the optimal damping control of vehicle suspension based on the maximum principle of L.S. Pontriagin). Traktory Selskokhoziaystvennyie Mashiny 2:13–15

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Pozdeev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chernyshov, K.V., Ryabov, I.M., Pozdeev, A.V. (2019). Theoretical Foundations of Optimal Two-Step Control of Suspension Stiffness of Transport Vehicle in Oscillation Cycle. In: Radionov, A., Kravchenko, O., Guzeev, V., Rozhdestvenskiy, Y. (eds) Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-95630-5_46

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-95630-5_46

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95629-9

  • Online ISBN: 978-3-319-95630-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics