Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 349489, 15 pages
doi:10.1155/2010/349489
Research Article

Influence of Control Valve Delay and Dead Zone on the Stability of a Simple Hydraulic Positioning System

Bálint Magyar,1 Csaba Hős,2 and Gábor Stépán1

1Department of Applied Mechanics, Budapest University of Technology and Economics, Pf. 91, Budapest 1521, Hungary
2Department of Hydrodynamic Systems, Budapest University of Technology and Economics, Pf. 91, Budapest 1521, Hungary

Received 4 March 2010; Accepted 17 June 2010

Academic Editor: Carlo Cattani

Copyright © 2010 Bálint Magyar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the PI control of a highly simplified dynamic model of a hydraulic cylinder. It is assumed that the hydraulic fluid is incompressible and that the pump provides constant flow rates, which results in the possibility of velocity control. Two types of anomalies are taken into account: (a) the time delay due to the controller computations and the internal pressure dynamics and (b) the dead zone of the controller valve. This results in a nonlinear system are described by a piecewise linear discontinuous map. Nonlinear behavior of the system is explored and the practically globally stable parameter domains are identified.