【正文】 ons and torque estimation errors. The hardware intheloop studies demonstrate the viability of the proposed algorithm in the field of advanced vehicle power transmission control and fault diagnosis. C 2002 Elsevier Science Ltd. All rights reserved. Received 1 March2001。 Hydraulic actuator。 Zheng, Srinivasan, amp。 Hibino, Osawa, Yamada, Kono, amp。 Lee, 2000), etc. Despite the extensive research effort on control algorithms, it appears that the pressure information of a hydraulic actuator has not been fully utilized in vehicle power transmission control, largely due to the high cost of a pressure sensor. As a result, most practical controllers have been largely built upon the mechanical subsystem only, while neglecting the dynamics of a hydraulic actuator.Instead of directly measuring the pressure output of a hydraulic actuator, this paper proposes an indirect alternative to estimate the pressure output: an observer based approach. The main thrust of this paper is that the pressure output of a hydraulic actuator is ‘observable’ with the slip velocity measurement of the mechanical subsystem in a vehicle power transmission control system. In addition to the readily available slip velocity measurement, the observer design requires the models of hydraulic and mechanical subsystems whose accuracy directly impacts the observer performance. The mechanical subsystem is physically modeled with relative ease. The plexity of the hydraulic actuator dynamics does not allow a physical model amenable to observer design. Instead, system identification yields a simplified empirical model of the hydraulic actuator. Actual observer design focuses on guaranteeing robust stability against parametric variations and torque estimation errors that are bound to occur in a mechanical power transmission control system. Hardware intheloop simulation studies are conducted to examine the performance of the robust observerbased estimator for the hydraulic actuator pressure, which shows the viability of the proposed approach. The oute is a robust pressure estimator that relies on the readily available slip velocity measurement only and thus has a potential to be widely employed in vehicle power transmission control and fault diagnosis.This paper is organized as follows. Section 2 derives a physical model for the mechanical subsystem. Simplified empirical models are developed for a hydraulic actuator in Section 3. Section 4 deals with the observer design. The performance of the designed observer is examined in Section 5.2. Overview of a vehicle power transmission control systemA vehicle power transmission control system typically consists of two subsystems, a mechanical subsystem and a hydraulic actuator. The input and output of the system under consideration are the voltage signal to the hydraulic actuator and the slip velocity between the friction elements in the mechanical subsystem, respectively. The hydraulic actuator drives the friction elements and generates the slip velocity of the mechanical subsystem according to its pressure output. Fig. 1 shows a vehicle power transmission control system considered in this paper, a torque converter clutch slip control system. The mechanical subsystem consists of an engine, a torque converter, an automatic transmission with planetary gear sets, and wheels with a final reduction gear. The torque converter clutch generates friction torque acting upon the engine according to the hydraulic actuator pressure, which in turn determines the slip velocity between the engine and the turbine of the torque converter at a desired target value.In order to derive a physical model of the mechanical subsystem, the power transmission at each stage is examined. At the very first stage, the engine torque is transmitted to the impeller and is balanced by the reaction torque of the impeller and the friction torque from the torque converter clutch. The torque converter amplifies and transmits the impeller torque to the turbine. The turbine torque drives the automatic transmission system together with the friction torque of the torque converter clutch, while the driving load torque of the vehicle provides additional resistive force. Denoting the slip velocity between the engine and the turbine as the output of interest (y) results in Hahn amp。 the equivalent rotational inertia of the vehicle varies as the number of passengers changes, and only a rough bound on the friction coefficient is available.3. Identification of a hydraulic actuator. Motivation for empirical modelingFig. 2 shows the hydraulic actuator considered in this paper. It basically consists of three elements: a PWM type solenoid valve, a pressure modulator valve and a pressure control valve. The first and second regulating valves, not shown in , regulates the main pressure of the entire hydraulic circuit. The pressure modulator valve further decreases the output pressure of the first regulating valve (channel 7) to a lower pressure level.The output pressure of the pressure modulator valve at channel 9 is always regulated around bar in the steadystate by means of the feedback chamber 10 (Hahn, 1999). The voltage signal from the transmission control unit (TCU) drives the PWMtype solenoid valve so that the pressure at channel 11 assumes values between 0 bar and 4 bar. The pressure at channel 11 acts on the spool of the pressure control valve, which in turn generates engage/disengage pressures for the friction element in the mechanical subsystem. Since the engage/disengage pressures are applied to the same friction element from the opposite sides, the difference between engage and disengage pressures may be regarded as the output of the hydraulic actuator. A nonlinear mathematical model of the hydraulic actuator has been obtained in Hahn (1999) using the Newton’s second law of motion. Although the nonlinear model in Hahn (1999) matches the experimental results to a certain extent, it has some drawbacks when applied