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Stability of Equilibria in a Four-dimensional Nonlinear Model of a Hydraulic Servomechanism

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Abstract

Starting from plysical laws a four-dimensional nonlinear model for mecano-hydraulic servomechanisms is deduced. The stability of its equilibria is analysed using a theorem of Lyapunov and Malkin to handle the critical case due to the presence of zero in the spectrum of the matrix of the linear part around equilibria. Stability diagrams are drawn and simulation results are presented through phase diagrams.

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References

  1. S.A. Ermakov, T.S. Klaptsova and G.G. Smirnov, Synthesis of electrohydraulic tracking systems with observers (in Russian). Pnevmatika i Gidravlika12 (1986) 45–54.

    Google Scholar 

  2. H.V. Panasian, Reduced order observers applied to state and parameter estimation of hydro-mechanical servoactuators. J. Guidance, Control Dyn.9 (1986) 249–251.

    Google Scholar 

  3. R.H. Ingenbleek, A nonlinear discrete-time observer based control scheme and its application to hydraulic drives. In: Proc. 2nd Europ. Control Conf.(1993) pp. 215–219.

  4. H. Hahn, A. Piepenbrink and K.-D. Leimbach, Input output linearization control of an electro-servohydraulic actuator. In: Proceedings of 3-rd IEEE Conference on Control Applications.Glasgow (1994) pp. 995–1000.

  5. G. Vossoughi and M. Donath, Dynamic feedback linearization for electrohydraulically actuated control systems. Trans. ASME, J. Dyn. Syst.,Measurement Control117 (1995) 468–477.

    Google Scholar 

  6. A.R. Plummer, Feedback linearization for acceleration control of electrohydraulic actuators. Proc. Inst. Mech. Engs.211 (1997) 395–406.

    Google Scholar 

  7. E. Richard and R.Outbib, Feedback stabilization of an electrohydraulic systems. In: Proc. 3rd Europ. Control Conf.Rome (1995) pp. 330–334.

  8. J.E. Bobrow and K. Lum, Adaptive, high band-width control of a hydraulic actuator. Trans. ASME, J. Dyn. Syst.,Measurements Control118 (1996) 714–720.

    Google Scholar 

  9. I. Ursu, G. Tecuceanu, F. Ursu, T. Sireteanu and M. Vladimirescu, From robust control to antiwindup compensation of electrohydraulic servoactuator. Aircraft Engng. Aerosp. Technol.70 (1998) 259–264.

    Google Scholar 

  10. I. Ursu, F. Ursu and T. Sireteanu, About absolute stable symthesis of electrohydraulic servo. Technical Papers of AIAA Guidance, Navigation and Control Conference2 (1999) 848–858.

    Google Scholar 

  11. I. Ursu, F. Ursu and L. Iorga, Neuro fuzzy symthesis of flight control electrohydraulic servo. Aircraft Engng. Aerosp. Technol.73 (2001) 465–471.

    Google Scholar 

  12. H.E. Merritt, Hydraulic Control Systems. New York: John Wiley & Sons (1967) 368pp.

    Google Scholar 

  13. M. Guillon, L'asservissement Hydraulique et Électrohydraulique. Paris: Dunod, tome I and II (1972) 241–291pp.

    Google Scholar 

  14. N.S. Gamynin, Hydraulic Automatic Control Systems(in Russian). Moskow: Mashinostroenie (1972) 376pp.

    Google Scholar 

  15. N.S. Gamynin, Iu. K. Jdanov and A.L. Klimashin, Dynamics of Fast Hydraulic Servoactuators(in Russian). Moskow: Mashinostroenie (1979) 80pp.

    Google Scholar 

  16. V.M. Popov, Hyperstability of Control Systems. Bucharest: Romanian Academy Publishing House and Berlin: Springer-Verlag (1973) 400pp.

    Google Scholar 

  17. A. Halanay and C.A. Safta, Periodic motions for loaded two control edges hydraulic copying systems. Comp. Methods Appl. Mech. Engng.158 (1998) 367–374.

    Google Scholar 

  18. A. Halanay and C.A. Safta, Stability and accuracy of steady-state motions in loaded copying system: an analytical approach. Comp. Assist. Mech. Engng. Sci.6 (1999) 107–113.

    Google Scholar 

  19. G.G. Kremer and D.F. Thompson, A bifurcation-based procedure for designing and analyzing robustly stable non-linear hydraulic servo systems. Proc. Inst. Mech. Engng.212 (1998) 283–394.

    Google Scholar 

  20. A. Halanay and C.A. Safta, Existence and stability of normal motions in loaded hydraulic copying systems with periodic and composed inputs. ZAMM80 (2000) 93–101.

    Google Scholar 

  21. I. Ursu and F. Ursu, Active and Semiactive Control.Bucharest: Romanian Academy Publishing House (2002) 356pp.

    Google Scholar 

  22. P.K.C. Wang, Analytical design of electrohydraulic servomechanism. IEEE, Transactions on Automatic ControlAC-8 (1963) 15–27.

    Google Scholar 

  23. J.F. Blackburn, J.L. Shearer and G. Reethof, Fluid Power Control. Boston: Technology Press ofM.I.T. (1960) 710pp.

    Google Scholar 

  24. V.A. Hohlov, Electrohydraulic Servosystems.Moskow: Nauka (1964) 231pp.

    Google Scholar 

  25. I. Ursu and F. Ursu, On mathematical modeling of hydraulic servo (in Romanian). Studii ¸si cercetări de mecanică aplicată56 (1997) 337–358.

    Google Scholar 

  26. I. Ursu, T. Popescu, M. Vladimirescu and R.D. Costin, On some linearization methods of the generalized flowrate characteristic of the hydraulic servomechanisms. Revue Roumaine des Sciences Techniques, Série de Mécanique Appliquée9 (1994) 207–217.

    Google Scholar 

  27. I.G. Malkin, Theory of Stability of Motion(in Russian). Moskow: Nauka (1996) 530pp

    Google Scholar 

  28. A. Lyapunov, General Problem of Stability of Motion(in Russian). Moskow: G.I.T.T.L. (1950) 471pp.

    Google Scholar 

  29. I. Ursu, Theoretical and experimental data concerning qualification testing and flight clearance for aircraft servomechanism SMHR (in Romanian). INCREST-ReportN-5303 (1984).

  30. * * * Air 8520/A, Conditions d'homologation des servocommandes hydrauliques de gouvernes. Edition Nr. 2 du 23 juillet 1973, Ministère des Armées, Direction techniques des constructions aéronautiques.

  31. Y. Kuznetzov, Elements of Applied Biffurcation Theory. Berlin: Springer-Verlag (1995) 515p.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics I, University Politehnica of Bucharest, Splaiul Independenţei 313, RO-060042, Bucharest, Romania

    A. Halanay

  2. University Politehnica of Bucharest, Splaiul Independenţei 313, RO-060042, Bucharest, Romania

    C.A. Safta

  3. `Elie Carafoli' National Institute for Aerospace Research, Bd. Iuliu Maniu 220, RO-061099, Bucharest, Romania

    I. Ursu & F. Ursu

Authors
  1. A. Halanay
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  2. C.A. Safta
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  3. I. Ursu
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  4. F. Ursu
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Correspondence to A. Halanay.

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Halanay, A., Safta, C., Ursu, I. et al. Stability of Equilibria in a Four-dimensional Nonlinear Model of a Hydraulic Servomechanism. Journal of Engineering Mathematics 49, 391–405 (2004). https://doi.org/10.1023/B:ENGI.0000032810.53387.d9

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  • DOI: https://doi.org/10.1023/B:ENGI.0000032810.53387.d9

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