【正文】 bearing position cx determines the pressure between the flywheel disk and the clutch disk and, therefore, the transmitted torque during the slipping phases. The nonlinear characteristic ? ?ccTx that relates the throwout bearing position cx to the torque transmitted by the clutch is not easy to model. The clutch wear drastically influences such a characteristic and thus the torque transmission. Moreover, the clutch characteristic is also influenced by the dependence of the friction coefficient on both temperature [14] and slip speed. In particular, the negative variations of the friction coefficient with slip speed can induce torsional selfexcited vibrations of the driveline [15], [16]. The nominal nonlinear characteristic ? ?ccTx has been identified from the experimental tests described above. By representing the estimated values of the clutch torque obtained through (7) as a function of the corresponding values of the signal cx , the set of points reported in Fig. 2 (top diagram) is obtained. The absolute value of the clutch torque has been modeled by using the interpolation curve reported in bottom diagra m of Fig. 2 (curve b), and its variations (curves a and c) which model different clutch wear and have been used to test the controller robustness. Note that the wear changes the bearing position, say cx , at which the two disks e in contact and the transmitted torque bees different from zero. C. Clutch Actuator In AMTs, the electrohydraulic actuator is mainly posed of a hydraulic piston connected to a system of springs that keep the clutch closed when the piston does not apply any force (see Fig. 3). The piston is controlled by a threeport electrovalve that regulates the oil flow through the hydraulic circuit and then determines the force on the mechanical actuator. In standard mercial applications, the electrohydraulic actuator is used with a feedback control on the throwout bearing position. Usually a further inner control loop on the current is implemented. By identifying the parameters of the detailed actuator model proposed in [17], we now show that, for the goal of this paper, the actuator with a position feedback loop can be satisfactorily approximated by a firstorder linear system. 6 Fig. 2. Set of points ( ,ccxT? ) obtained from experimental data (top diagram) and clutch characteristics (bottom diagram) for positive slip speed with different wear. Curve a: new clutch. Curve b: medium wear. Curve c: high wear. Fig. 3. Hydraulic actuator scheme corresponding to the clutch engaged. The actuator model consists of a set of equations describing the dynamics of the electrovalve spool, the servocylinder piston, and the pressure variation in the mechanical actuator chamber. The motion of the valve spool is described by a force balance equation ? ? ? ?,v v m v o i l v v v v v k oM y F I y F p y b y K y K? ? ? ? ? ? (8) where vM is the spool mass, vy is the spool position, mF is the force caused by the solenoid current I , vb is the friction coefficient, Kv is the effective spring constant, and koF is the mechanical spring force due to the preload of the spring. The oil orce Foil is the Bernoulli’s force defined as [18] 7 ? ?? ?c osv v vF C wy p y???? (9) where ? is the discharging coefficient, vC is the velocity coefficient, w is the control port width, ? ?vy? is the jet angle described by a polynomial function of the spool position ? ?? ? 323 2 1 0v v v vy C y C y C y C? ? ? ? ? R, and the variation of pressure in the threeport electrovalve is defined as ? ?? ?, 0 _, 0 _LAATp p f o r L Ao p e n e d y c l u t c h o p e npp p f o r A T o p e n e d y c l u t c h c l o se? ? ? ????? ?? ? ? ??? where Lp is the line pressure, Tp is the tank pressure, and Ap is the oil pressure in the actuator chamber. The variation of the oil pressure Ap can be described by ? ?,A v p cp c tEp Q y p A xA x V ??? ? ???? (10) where E is the fluid bulk modul