Modeling, Identification and Control, Vol. 31, No. 1, 2010, pp. 35–44, ISSN 1890–1328

Adaptive Backstepping Control of Nonlinear Hydraulic-Mechanical System Including Valve Dynamics
M. Choux G. Hovland
E-mail:

Mechatronics Group, Department of Engineering, University of Agder, N-4898 Grimstad, Norway. {martin.choux,geir.hovland}@uia.no

Abstract The main contribution of the paper is the development of an adaptive backstepping controller for a nonlinear hydraulic-mechanical system considering valve dynamics. The paper also compares the performance of two variants of an adaptive backstepping tracking controller with a simple PI controller. The results show that the backstepping controller considering valve dynamics achieves significantly better tracking performance than the PI controller, while handling uncertain parameters related to internal leakage, friction, the orifice equation and oil characteristics. Keywords: adaptive observer backstepping, state feedback, nonlinear hydraulic-mechanical system, valve dynamics

1. Introduction

stepping controller was not included in the survey of Bonchis et al. (2002). Hence, it would be of interControl of nonlinear hydraulic-mechanical systems est to compare the backstepping and the PI controller (NHMS) is challenging for several reasons: a) the sys- for an NHMS. In Zeng and Sepehri (2006, 2008) the tem model is normally stiff with fast dynamics for the authors presented an adaptive controller to handle inhydraulics and relatively slow dynamics for the me- ternal leakage and unknown friction in a cylinder, unchanical parts, b) models usually contain strong non- known volumes in the orifice equation and temperature linear elements such as the flow in orifices, friction, dependent oil characteristics. valve overlap and input saturation, c) valves contain One physical phenomenon not considered in Zeng and non-measurable states (position and velocity) and d) Sepehri (2006, 2008) is valve dynamics. Section 2.2 the oil