AN INVESTIGATION OF THE EFFECT OF FEEDBACK CONTROL ON THE BIFURCATION STABILITY OF A NONLINEAR SERVOHYDRAULIC SYSTEM

Authors

  • Amit Shukla Department of Mechanical and Manufacturing Engineering, Miami University, Oxford, Ohio 45056, USA
  • David F. Thompson Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, Ohio 45221, USA

Keywords:

Servo-hydraulic, bifurcation, feedback control, nonlinear system

Abstract

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.

Downloads

Download data is not yet available.

Author Biographies

Amit Shukla, Department of Mechanical and Manufacturing Engineering, Miami University, Oxford, Ohio 45056, USA

Amit Shukla is an Assistant Professor at Miami University in the Department of Mechanical and Manufacturing Engineering. He received the M.S. and Ph.D. in mechanical engineering from University of Cincinnati in 1998 and 2002, respectively. His research interests include stability analysis and control of nonlinear systems.

David F. Thompson, Department of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, Ohio 45221, USA

David F. Thompson is an Associate Professor at University of Cincinnati in the Department of Mechanical, Industrial and Nuclear Engineering. He received the M.S. degree from University of Michigan, Ann Arbor, in 1984 and the Ph.D. degree from Purdue University in 1990. His research interests include robust control design, nonlinear dynamics and optimal design with applications to transportation, propulsion, and power machinery.

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.

Downloads

Published

2005-08-01

How to Cite

Shukla, A., & Thompson, D. F. (2005). AN INVESTIGATION OF THE EFFECT OF FEEDBACK CONTROL ON THE BIFURCATION STABILITY OF A NONLINEAR SERVOHYDRAULIC SYSTEM. International Journal of Fluid Power, 6(2), 37–46. Retrieved from https://journals.riverpublishers.com/index.php/IJFP/article/view/570

Issue

Section

Original Article