【正文】 Lee, K. I. (2000b). Development of shift control algorithm using estimated turbine torque. ‘2000 SAE Transmission and Driveline Sympo。 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。 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。 Workman, M. (1998). Digital control of dynamic systems. Reading, MA: AddisonWesley.Hahn, J. O., amp。 . 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。 u) = CTh（x。 Zak, 1987。 Hedrick, 1989。 ηof the form in (16) guarantees that Ve≤eTpeQe for all |Ce|≥ε by the stability analysis similar to the one in Walcott amp。 Zak, 1987。 Workman, 1998):The hydraulic actuator model (4) refers to both the model (2) and the model (3) for simplicity, since the observer design procedure for the two identified actuator models are nearly identical. When the actuator transfer function (4) refers to (3), V(s)= U(s) is implicitly assumed, where V(s) is Laplace transformation of v defined in (3). Denoting the state variables of the hydraulic actuator as x2 and x3 gives an observer canonical form (Chen, 1984): With x1 = y。 60% duty cycle approximately corresponds to 0 bar pressure output.These observations raise an immediate concern that the bruteforce application of system identification (Ljung, 1999) may utterly fail to give a highfidelity model if a conventional model structure, ., ARX (autoregressive with exogenou s input) is adopted. In the steadystate, an ARX model approximates the nonlinear mapping in Fig. 3 by a straight line passing through the origin, by virtue of its linearity. A better approach would be to shift the origin to a point around which the input–output mapping is approximately symmetric. The new origin bees 60% duty cycle and 0 bar pressure output. Such a shift of the origin amounts to subtracting the input duty cycle by 60%. The relatively high signaltonoise ratio leads to the choice of the ARX model structure as a model set, due primarily to its simplicity:where uoffset is the aforementioned offset value for input data and na=nb are the orders of the model, which are determined later. Then, the step response of the hydraulic actuator is obtained in order to help to design the identification input. The natural frequency (in an approximate sense) turns out to be around 5 Hz. A safety factor of ‘2’results in the excitation frequency band of 10 Hz. 50 sinusoids with various binations of amplitudes and phases are generated within the 10Hz band. The length of data is chosen to be 1024 considering the frequency content of the model to be identified, and the sample rate of 100 Hz is used, which corresponds to the sampling rate of TCU in mercial vehicles. MATLAB System Identification Toolbox (Ljung, 1995) is used to process the data and to obtain