AN INVESTIGATION OF THE EFFECT OF FEEDBACK CONTROL ON THE BIFURCATION STABILITY OF A NONLINEAR SERVOHYDRAULIC SYSTEM
Keywords:
Servo-hydraulic, bifurcation, feedback control, nonlinear systemAbstract
The Servo-hydraulic systems are commonly used for motion and force control and exhibit nonlinear dynamic phenomena. One such nonlinear phenomenon is the loss of stability via bifurcations. In this work, a computational and experimental investigation is performed to characterize with a higher degree of accuracy the effect of linear feedback control on the bifurcation stability of a nonlinear servo-hydraulic system. A low-order model of the experimental test stand is first developed, validated and analyzed. It is then shown that the use of an appropriate linear feedback control structure can improve the bifurcation stability of a nonlinear servo-hydraulic system. Parametric space investigation is conducted to study the bifurcation stability behavior of the system and stability boundaries are developed to demonstrate the effect of linear feedback on the nonlinear systems.
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References
Alleyne, A. and Liu, R. 1999. On the limitations of
force tracking control for hydraulic servosystems.
Journal of Dynamic Systems, Measurement and
Control, Transactions of the ASME, vol. 121, no. 2,
pp.122-137.
Burton, R. T. 1975. Analytical and experimental prediction
of limit cycle oscillations in an inertially
loaded hydraulic control valve. Ph.D. University of
Saskatchewan,
Blackburn, J. F., Reethof, G., and Shearer, J. L.
Fluid Power Control Massachusetts. The
MIT Press.
Cox, C. S. and French, I. G. 1986. Limit cycle prediction
conditions for a class of hydraulic control systems.
Journal of Dynamic Systems, Measurement
and Control, Transactions of the ASME, vol. 108,
pp. 17-23.
D’azzo, J. D. and Houpis, C.H. 1966. Feedback control
systems analysis and synthesi, McGraw-Hill.
Foster, K. and Kulkarni, M. M. 1968. Steady amplitude,
self excited oscillations of hydraulic spool
valves. Journal of Mechanical Engineering Science,
vol. 10, no. 4, pp. 306-317.
Fuerst, D., Hahn, H., and Hecker, E. 1997. Mathematical
modeling and parameter identification of a
planar servo-pneumatic test facility. Part I: Mathematical
modeling and computer simulation. Nonlinear
Dynamics, vol. 14, no. 3, pp. 249-268.
Guckenheimer, J. and Holmes, P. 1983. Nonlinear
oscillations, dynamical systems, and bifurcation of
vector fields. Springer.
Jordan, D.W., and Smith, P. 1999. Nonlinear Ordinary
Differential Equations: An Introduction to Dynamical
Systems. Third Edition, New York: Oxford
Univ. Press.
Kowta, S. 2003. Robust stability analysis of servohydraulic
system in parameter space. M.S. Thesis,
University of Cincinnati, Cincinnati, Ohio.Kremer, G. G. and Thomson, D.F. 1998. A bifurcation-
based procedure for designing and analyzing
robustly stable nonlinear hydraulic servo systems.
Proc. of Institution of Mechanical Engineers, vol.
, pp. 383-393.
Krutz, J.E. 2001. Design of hydraulic actuator test
stand for nonlinear analysis of hydraulic test stand.
Master’s thesis, University of Cincinnati, Cincinnati,
Ohio.
Lewis, E. E. and Stern, H. 1962. Design of Hydraulic
Control Systems. McGraw Hill Book Co.
Maccari, A. 2000. Saddle-node bifurcations of cycles
in a relief valve. Nonlinear Dynamics, vol. 22, no.
, pp.221-231.
McCloy, D. and Matrin, H.R. 1980. Control of Fluid
Power. John Wiley and Sons.
Merritt, H. E. 1967. Hydraulic Control Systems. John
Wiley and Sons.
Scheidl, R. and Manhartsgruber, B. 1998. On the
dynamic behavior of servo-hydraulic drives.
Nonlinear Dynamics, vol. 17, pp. 247-268.
Seydel R. 1994. Practical bifurcation and stability
analysis: from equilibrium to chaos. NY. Springer-
Verlag.
Shukla, A. and Thompson, D.F. 2001. Bifurcation
stability of servo-hydraulic systems. Proc. of
American Controls Conference, pp. 3943-3948. Arlington,
Virginia.
Shukla, A. and Thompson, D.F. 2002. Control of
Bifurcations in Multidimensional Parameter Space
for Servo-Hydraulic Systems. Proc. of the 2002
American Control Conf.. Anchorage, Alaska.
Strogatz, S. H. 2000. Nonlinear Dynamics and Chaos.
Preseus Publishing. Cambridge, MA.
Van Schothorst, G. 1997. Modelling of Long-stroke
Hydraulic Servo-systems for Flight-simulator Motion
Control and System Design. PhD Thesis. Delft
University of Technology. Netherlands.
Venkatasubramainian, V., Schattler, H., and Zaborszky,
J. 1995. Dynamics of large constrained
nonlinear systems - a taxonomy theory. Proc. of
IEEE, vol. 83, no. 11, pp. 178-191.
Viall, E. N. and Zhang, Q. 2000. Spool valve discharge
coefficient determination. Proc. of the 2002
American Control Conf., pp.491-495.
Viersma, T. J. 1980. Analysis, synthesis and design of
hydraulic servosystems and pipelines. NY. Elsevier.
Watton, J. 1988. Modelling of electrohydraulic systems
with transmission lines using modal appoximations.
Proc. of the IMechE. vol. 202, no. B3, pp
-163.
Wiggins, S. 1990. Introduction to Applied Nonlinear
Dynamical Systems and Chaos. Springer.
Yang W.C. and Tobler W.E. 1991. Dissipative model
approximation of fluid transmission lines using linear
friction models. Trans. Of ASME Journal of Dynamic
Systems, Measurement and Control, vol. 113,
no. 1, pp. 152-162.
Yau, Chin-Horng, Bajaj, Anil K., Nwokah, Osita D.
I. 1992. Active control of chaotic vibration in a constrained
flexible pipe conveying fluid. American
Society of Mechanical Engineers, Applied Mechanics
Division, AMD, vol. 152, pp. 93-108.