【正文】 parametric uncertainties (damping constant and friction coefficient) is performed. The input gain of the mechanical subsystem (which contains the friction coefficient) and the damping constant are set to be gy(x1)= g’y(x1)|| g’’y(x1)|| and c=c’c’’。 . the input gain and the damping constant maximally differs from that of the nominal dynamics known to the observer. In the HILS work, the value of the friction coefficient is chosen based on the real vehicle data, which include nominal, maximum and minimum values of the friction coefficient. The MSE’s of the observers are for the hydraulic actuator model (2) and for the hydraulic actuator model (3), respectively .Note that as shown above, the MSE’s of the pure predictors are for the hydraulic actuator model (2) and for the hydraulic actuator model (3), respectively, since the uncertainties of the mechanical subsystem do not affect the accuracy of the pure predictors. Next, the HILS with random torque estimation errors is performed. The torque estimation error is simulated with random numbers with magnitude bound . The results show that the MSE’s the observers induce are for the hydraulic actuator model (2) and for the hydraulic actuator model (3), respectively.Finally, the HILS results with bined uncertainties (constant input gain uncertainty and random torque estimation errors) are shown in Fig. 10. The pressure estimation errors are bounded within about bar except at several isolated points. Taking the pressure fluctuation of around bar into account, the observer seems to perform reasonably well, if not superb. As shown earlier, the HILS results with single uncertainty reveals the MSE of for the random torque estimation errors and for the constant input gain and damping constant uncertainty. For the bined uncertainties, the MSE of the observer with the model (3) is about 37% smaller than that of the pure predictor with the model (3), while the MSE of the observer with the model (2) is 74% smaller than that of its counterpart, which verifies the viability of the proposed observerbased approach over the pure prediction without the slip velocity feedback.There are some practical issues if the proposed observerbased approach is applied to an actual vehicle. First, it is worthwhile to note that the gap between the MSE’s of nominal and perturbed HILS results signifies room for improving the observer performance. As indicated by the HILS results, it is desirable to keep the parametric uncertainty such as friction coefficient and torque estimation errors as small as possible to achieve enhanced performance of the observer. For instance, recently developed torque estimation techniques such as Shin et al. (2000), Yi, and Srinivasanetal (1992) can be incorporated to improve the estimation accuracy of the proposed observer. It should also be noted that the HILS results with the model (3) show better performance than those with the model (2). Such an observation indicates that the observer may perform even better by using more refined model structures for the hydraulic actuator。 for example, the introduction of a nonlinear ARX (NARX) model structure to acmodate the nonlinear steadystate and dynamic behavior.6. Concluding remarksIn this paper, an observerbased algorithm is presented to monitor a hydraulic actuator which enables pressure estimation in a vehicle power transmission actuator together with a physical model for the mechanical subsystem provide a foundation upon which a robust observer may be designed to guarantee desired performance against parametric variations and torque estimation errors. The performance of the designed observer is verified via hardwareintheloop simulation results, which shows satisfactory pressure estimation accuracy. The proposed algorithm has potential to be widely applicable to advanced vehicle power transmission control and fault diagnosis.ReferencesChen, C. T. (1984). Linear system theory and design. London: Saunders College Publishing.Franklin, G. F., Powell, J. D., amp。 Workman, M. (1998). Digital control of dynamic systems. Reading, MA: AddisonWesley.Hahn, J. O., amp。 Lee, K. I. (2000). Nonlinear robust control of torque converter clutchslip system for passenger vehicles using advanced torque estimation algorithms. Vehicle System Dynamics, partially accepted for publication.Hahn, J. O. (1999). Fuzzy logic slip control of torque converter clutch system for passenger car considering road grade resistance. Master’s thesis, Department of Mechanical Design and Production Engineering, Seoul National University.Hibino, R., Osawa, M., Yamada, M., Kono, K., amp。 Tanaka, M. (1996). HN control design for torqueconverterclutchslip system. Proceedings of the 35th Conference Decision and Control, Kobe, Japan (pp. 1797–1802).Jauch, F. (1999). Modelbased application of a slipcontrolled converter lockup clutchin automatic car transmissions. ‘1999 SAE Transmission and Driveline Symposium, SAE 1999011057, Detroit, USA.Jung, G. H., Cho, B. H., amp。 Lee, K. I. (2000). Dynamic analysis and closedloop shifting control of EFautomatic transmission with proportional control solenoid valves. ‘2000 FISITA World Automotive Congress, F2000 A104, Seoul, Korea.Ljung, L. (1999). System identification: theory for the user. Englewood Cliffs, NJ: PrenticeHall.Ljung, L. (1995). System identification toolbox user’s guide. Natick, MA: MathWorks.Misawa, E. A., amp。 Hedrick, J. K. (1989). Nonlinear observers: A stateoftheart survey. Journal of Dynamic Systems, Measurement and Contro, 111, 344–351. Shin, B. K., Hahn, J. O., Yi, K., amp。 Lee, K. I. (2000a). A supervisorbased neuraladaptive shift controller for automatic transmissions considering throttle opening and driving load. KSME International Journal, 14(4), 418–425.Shin, B. K., Hahn, J. O., amp。 Lee, K. I. (2000b). Development of shift control algorithm using estimated turbine torque. ‘2000 SAE Transmission and Driveline Sympo