In this paper we present an output feedback nonlinear control for position tracking of electro-hydraulic systems (EHSs)。 Although previous nonlinear control methods improved the position tracking perfor- mance of EHS, all of the methods require full state feedback。 However, due to cost and space limitations, it is not always possible to measure the full state of the EHS。 The proposed method consists of a high gain observer and a passivity-based controller。 The high gain observer is designed to estimate the full state, and the passivity-based control is implemented for position tracking。 In order to design the passivity- based controller with the high gain observer, a defined Lyapunov condition guarantee that the origin of the tacking error dynamics is exponentially stable by selecting the controller gain。 The stability of the closed-loop is studied using the singular perturbation theorem。 The performance of the proposed method is validated through simulations and  experiments。82308

1。Introduction

Electro-hydraulic systems (EHSs) are important in modern industrial automation and have been used in many kinds of mech- anizations, including robot and aircraft actuators and rolling mills。 Compared to their electrical counterparts, they also have a high power to weight ratio [1,2]。 Furthermore, they are able to rapidly generate very high forces。 However, EHSs exhibit significantly higher nonlinearities in their dynamics because of the compress- ibility of hydraulic fluid and the complex flow properties of servo valves。 Therefore, the investigation of position  control  for EHSs has been of great interest from both academic and industrial perspectives。

Various techniques have been used to control the position or force of an EHS。 Local linearization of the nonlinear dynamics about a nominal operating point was proposed in [1]。 However, the nonlinear behavior of the system requires the use of conserva- tive loop gain that sacrifices controller performance in favor of robustness。 In [3,4], the use of pressure feedback was proposed in order to improve the performance of proportional integral deriv- ative (PID) controllers in EHSs, but stability was not proven。 An indirect adaptive control incorporating a linear model of EHS was designed for position tracking [5] but use of the linear model re- sults in limitations on the efficiency of the controller。 Variable structure control (VSC) strategies have been studied for the control

⇑ Corresponding author。 Tel。: +82 2 2220 1724; fax: +82 2 2291  5307。

E-mail   addresses:   alukard@hanyang。ac。kr   (W。   Kim),  daehee@kitech。re。kr (D。 Won), shin211@hanyang。ac。kr (D。 Shin), cchung@hanyang。ac。kr (C。C。 Chung)。

of EHS in [6–10]。 The chattering in the control action, which is inherent in VSC, can easily excite high frequency modes and may result in the system instability。 Feedback linearization has also been used to develop EHS [11–13]。 Various methods based on Lyapunov function have been studied for EHS and the valve dynamics was considered to make EHS an input affine system。 Backstepping approaches were applied to EHS [14–20] for expo- nential convergence of the desired position or load pressure。 Although backstepping controllers are long and complex [15], the backstepping controllers can improve the position/force tracking performance of the EHS。 Passivity-based control is a design tech- nique that uses passivation to achieve the control objective [21]。 This technique has been successfully applied to a nonlinear model and was shown to be very effective for the EHS [21–25]。 The pas- sivity-based control is simpler and more straightforward than a backstepping algorithm since the synthetic inputs in the passiv- ity-based control are decoupled。 Thus, modeling error effects asso- ciated with the controller are compartmentalized [22]。 Although previous nonlinear control methods improved the position track- ing performance of EHSs, all of these methods require full state feedback。 However, it is not always possible to measure the full state of the EHS due to cost and space limitations。 Furthermore, measurement noise is associated with the pressure sensor and it is impossible to measure the spool position of the servo-valve un- less the position sensor is embedded in the servo-valve。 Thus, the estimation of the full state of the EHS is necessary。 Several observ- ers were designed to estimate the full state of active suspensions and EHS [26–29]。 Since only observer designs were studied, only the stabilities of the observers were proven。 Because the designs