【正文】 學(xué)院電氣工程系和計(jì)算機(jī)科學(xué)系 截稿于 1999 年 10 月 18日，出版與 2020 年 6月 2 日 . 內(nèi)容摘要﹕ 一種先進(jìn)的位置跟蹤控制算法已經(jīng)研制出來了， 并將其應(yīng)用在 激光切割機(jī)的數(shù)控運(yùn)動(dòng)控制器上 。 Kawamura, Itoh amp。 Young, Utkin amp。 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。 the load side disturbance force。 τ the motor shaft torque。 x the load position。 K the spring stiffness。 driven pulleys is negligible in parison to other ponents of the drive system. Using the assumptions above, dynamic modeling could be reduced to a twomass model of the beltdrives that only includes the first resonance. In the control design, the uncertain positioning of the load due to the low repeatability and accuracy of the beltdrive has to be considered as well. Note, that no attention is paid to the coupled dynamics of the Ydrive due to the parallel driving, thus, the double beltdrive is considered as an equivalent single beltdrive. . The beltdrive model The beltdrives could be modelled as a multimass system using modal analysis. In the beltdrive model with concentrated parameters, linear, massless springs characterize the elasticity of the belt. According to the assumptions above, a twomass model can be obtained. The drivingpulley, motor shaft and the speed reducer are considered as the concentrated inertia of the driving actuator. The drivenpulley and the load are concentrated in the load 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）