【文章內(nèi)容簡介】 oad mass. The inertia and the mass are linked by a spring. Friction present in the motor bearings, the gearbox, the beltdrive, and nonmodelled higherorder dynamics are considered as an unknown disturbance that affects the driving side as well as the load side. The mechanical model of the twomass system and its block scheme are shown in Figs. 3 and 4, respectively. The beltstretch occurs due to the inherent elasticity of the timing belts. However, according to a vibration analysis of beltdrives (Abrate, 1992), the obtained model could be rearranged. Assume the unit transmission constant (L=1). Then, the control plant model is presented by Fig. 5. The control plant consists of two parts connected in a cascaded structure. The first part is described by poorly damped dynamics due to the elastic belt. The second part consists of the loadside dynamics. The beltstretch τ forced by the applied torque q. The dynamics are described by Eq. (1) （ 1） where Hw(s) denotes the beltstretch dynamics transfer function， （ 2） and is the natural resonant frequency （ 3） and is hte disturbance that affects the belt. The loadside dynamics are （ 4） (4) where Fw denotes the force, which drives the load （ 5） Fig. 3. The mechanical model of the elastic drive. M is the load side mass。 J the driving side inertia。 K the spring stiffness。 the motor shaft angular position。 x the load position。 w the beltstretch。 τ the motor shaft torque。 the driving side disturbance torque。 the load side disturbance force。 the spring force and 184。 the transmission constant. Fig. 4. The block scheme of the mechanical model: symbol are as explained in Fig. 3. Fig. 5. The block scheme of the control plant. 3. The motion control algorithm The erroneous control model with structured and unstructured uncertainties demands a robust control law. VSS control ensures robust stability for the systems with a nonaccurate model, namely, it has been proven in the VSS theory that the closedloop behavior is determined by selection of a sliding manifold. The goal of the VSS control design is to find a control input so that the motion of the system states is restricted to the sliding manifold. If the system states are restricted to the sliding manifold then the sliding mode occurs. The conventional approach utilises discontinuous switching control to guarantee a sliding motion in the sliding mode. The sliding motion is governed by the reduced order system, which is not affected by system uncertainties. Consequently, the sliding motion is insensitive to disturbance and parameter variations (Utkin, 1992). The essential part of VSS control is its discontinuous control action. In the control of electrical motor drives power switching is normal. In this case, the conventional continuoustime/discontinuous VSS control approach can be successfully applied. However, in many control applications the discontinuous VSS control fails, and chattering arises (S[abanovicH, Jezernik, amp。 Wada, 1996。 Young, Utkin amp。 OG zguK ner, 1999). Chattering is an undesirable phenomenon in the control of mechanical systems, since the demanded performance cannot be achieved, or even worse―me chanical parts of the servo system can be destroyed. The main causes of the chattering are neglected highorder control plant dynamics, actuator dynamics, sensor noise, and puter controlled discretetime implementation in sampleddata systems. Since the main purpose of VSS control is to reject disturbances and to desensitise the system against unknown parametric perturbations, the need to evoke discontinuous feedback control vanishes if the disturbance is sufficiently pensated for, . by the use of a disturbance estimator (Jezernik et al., 1994。 Kawamura, Itoh amp。 Sakamoto, 1994). Jezernik has developed a control algorithm for a rigid robot mechanism by bining conventional VSS theory and the disturbance estimation approach. However, the rigid bod