Modeling, Identi?cation 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 thedevelopment 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 signi?cantly better tracking performance than the PIcontroller, while handling uncertain parameters related to internal leakage, friction, the ori?ce 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 nonlinearhydraulic-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 sti? 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, unchanicalparts, b) models usually contain strong non- known volumes in the ori?ce equation and temperature linear elements such as the ?ow in ori?ces, 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 oilcharacteristics depend on parameters such as shows that valve dynamics can be signi?cant and temperature and air content. should be included in the model-based controller. In Bonchis et al. (2002) present an experimental evalua- addition to the valve dynamics, the adaptive controller tion of ten di?erent controller algorithms for an NHMS. developed in this paper also handles internal leakage Theresults in the paper show that the simple PI con- and unknown friction in the cylinder, unknown voltroller performs reasonably well, and only a few of the umes in the ori?ce equation and temperature depenmodel-based controllers are able to improve the perfor- dent oil characteristics. mance. Section 2 contains the model description including an Adaptive backstepping is a model-based nonlinear con-experiment to determine the second order valve dytrol technique which has been recently applied to namics model, while sections 3 and 4 contain the conNHMS, see Zeng and Sepehri (2006, 2008). The back- trollers for two di?erent scenarios: without and with

doi:10.4173/mic.2010.1.3

c 2010 Norwegian Society of Automatic Control

Modeling, Identi?cation and Control valve dynamics while bothcontrollers contain the non- 2.1. Linear Friction Model linear ori?ce equation. Section 5 contains simulation results with the two di?erent backstepping controllers In this work the in?uence of valve dynamics is the main compared with a PI controller. Finally, section 6 con- focus of the paper. Extra states added by considering the dynamics of the friction model would complicate tains the conclusions.the study of the valve dynamics. In this regard the chosen friction model is linear:

2. Model Description
The tracking of the mass position y in the NHMS shown in Fig. 1 is considered.

Ff ric = ? y ?

(1)

The system in state space representation, with hydraulic units is: d+? A k y? y+ ? pL M M 10M 4?A 4? pL = ? ? y? ? cL pL Vt Vt ? 400 10?Cd wKv 1 ? p ? p L xv + Vt ? 2D 2 xv = ??v ¨…