【正文】 ntrol approach is limited. Therefore, the motion control algorithm is derived using the variable system structure control theory. It is shown that the proposed control e!ectively suppresses the mechanical vibrations and ensures pensation of the system uncertainties. Thus, accurate position tracking is guaranteed. ( 2020 Elsevier Science 184。 Drives。 Vibrations。 Chattering。 Robust control1. Introduction For many industrial drives, the performance of motion control is of particular importance. Rapid dynamic behaviour and accurate position trajectory tracking are of the highest interest. Applications such as machine tools have to satisfy these high demands. Rapid movement with high accuracy at high speed is demanded for laser cutting machines too. This paper describes motion control algorithm for a lowcost lasercutting machine that has been built on the base of a planar Cartesian table with two degreesoffreedom (Fig. 1). The drive trains of the lasercutting machine are posed of beltdrives with a timing belt. The use of timing belts in the drive system is attractive because of their high speed, high efficiency, long travel lengths and lowcost (Haus, 1996). On the other hand, they yield more uncertain dynamics and a higher transmission error ( Kagotani, Koyama amp。 ● the laserbeam source, which generates the laser beam (the lasergenerator)。 XY axes of 2 and 1m, respectively. The Xdrive provides the motion of the laserhead in Xdirection. The drive and the laserhead as well as the lasergenerator are placed on the bridge to ensure a highquality optical path for the laserbeam. The movement of the bridge along the Yaxis is provided by the Ydrive. The laserhead represents the Xdrive load, while the Ydrive is loaded by the bridge, which carries the plete Xdrive system, the laserhead, and the lasergenerator. The loads slide over the frictionless slide surface. The positioning system consists of the motion controller, the amplifiers, the DCmotors and the drive trains. The Xdrive train is posed of a gearbox and a beltdrive (Fig. 2). The gearbox reduces the motor speed, while the beltdrive converts rotary motion into linear motion. The beltdrive consists of a timing belt and of two pulleys: a driving pulley and a driven pulley that stretch the belt. The Ydrive train is more plex. The heavy bridge is driven by two parallel beltdrives。 step response (see Section 4). From a control design perspective, difficulties arise from mechanical vibrations that are met in the desired control bandwidth (~10 Hz). On the other hand, the design objective is to have a highperformance control system while simultaneously reducing the plexity of the controller. Therefore, a simple mathematical model would only consider the firstorder resonance and neglect highorder dynamics. In other words, the design model of the control plant will closely match the frequency response of the real system up to the first resonance. Next, the controller should be adequately designed to cope with the higherorder resonance in such a way that the resonance peaks drop significantly to maintain the system stability. Thus, according to the signal analysis and the drives39。 ●the small backlash in the gearboxes and the backlash of the beltdrives due to the applied pretension of the timing belts is negligible。 ●the inertia of the beltdrives39。 J the driving side inertia。 the motor shaft angular position。 w the beltstretch。 the driving side disturbance torque。 the spring force and 184。 Wada, 1996。 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。 Sakamoto, 1994). Jezernik has developed a control algorithm for a rigid r