激光切割机的传动控制可变结构系统外文翻译/中英文翻译/外文文献翻译

徐州工程学院毕业设计 外文翻译 学生姓名 刘星星 学院名称 机电工程学院 专业名称 机械设计制造及其自动化 指导教师 陈跃 2011 年 5 月 27 日 VSS motion control for a laser-cutting machine Ales Hace, Karel Jezernik*, Martin Terbuc University of Maribor, Faculty of Electrical Engineering and Computer Sciences, Institute of Robotics, Smetanova ul. 17, SI-2000 Maribor, Slovenia Received 18 October 1999； accepted 2 June 2000 Abstract An advanced position-tracking control algorithm has been developed and applied to a CNC motion controller in a laser-cutting machine. The drive trains of the laser-cutting machine are composed of belt-drives. The elastic servomechanism can be described by a two-mass system interconnected by a spring. Owing to the presence of elasticity, friction and disturbances, the closed-loop performance using a conventional control 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 compensation of the system uncertainties. Thus, accurate position tracking is guaranteed. ( 2001 Elsevier Science td. All rights reserved.) Keywords: Position control； Drives； Servomechanisms； Vibrations； Variable structure control； Chattering； Disturbance rejection； 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 low-cost laser-cutting machine that has been built on the base of a planar Cartesian table with two degrees-of-freedom (Fig. 1). The drive trains of the laser-cutting machine are composed of belt-drives 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 low-cost (Haus, 1996). On the other hand, they yield more uncertain dynamics and a higher transmission error ( Kagotani, Koyama & Ueda, 1993). Consequently, belt-drives suffer from lower repeatability and accuracy. Moreover, the belt-drive dynamics include more resonance frequencies, which are a destabilising factor in a feedback control (Moon, 1997). Therefore, a conventional control approach like PI, PD or PID control fails to achieve acceptable performance. Plant parameter variations, uncertain dynamics and load torque disturbances, as well as mechanical vibrations, are factors that have to be addressed to guarantee robust system stability and the high performance of the system. An advanced robust motion control scheme is introduced in this paper, which deals with the issues related to motion control of the drives with timing belts. The control scheme is developed on the basis of the motion control algorithm introduced by Jezernik, Curk and Harnik (1994). It possesses robust properties against the disturbances that are associated with a nominal plant model, as it has been developed with the use of the variable structure system (VSS) theory (Utkin, 1992). The crucial part of the control scheme is the asymptotic disturbance estimator. However, as shown in this paper, it fails to stabilise resonant belt dynamics, since it was developed for a rigid robot mechanism. Therefore, this paper introduces an improved motion control scheme, which suppresses the vibrations that would arise due to the non-rigid, elastic drive. Consequently, a rapid response with low position tracking error is guaranteed. The paper is set out as follows. The laser-cutting machine is presented and the control plant model of the machine drives is developed in Section 2. In Section 3, the VSS control regarding the elastic servomechanism is discussed and the derivation of the motion control scheme is described. Section 4 presents the experimental results and a follow-up discussion. The paper is summarized and concluded in Section 5. 2. The control plant 2.1. The machine description The laser-cutting machine consists of the XY horizontal table and a laser system (Fig. 1). The fundamental components of the laser system are: the power supply unit, which is placed off the table and thus is not considered in the motion control design； the laser-beam source, which generates the laser beam (the laser-generator)； the laser-head, which directs the laser beam onto the desired position in the cutting plane. Fig. 1. The machine and the controller hardware. The table has to move and position the laser head in a horizontal plane. This is achieved by the means of a drive system with two independent motion axes. They provide movement along the Cartesians XY axes of 2 and 1m, respectively. The X-drive provides the motion of the laser-head in X-direction. The drive and the laser-head as well as the laser-generator are placed on the bridge to ensure a high-quality optical path for the laser-beam. The movement of the bridge along the Y-axis is provided by the Y-drive. The laser-head represents the X-drive load, while the Y-drive is loaded by the bridge, which carries the complete X-drive system, the laser-head, and the laser-generator. The loads slide over the frictionless slide surface. The positioning system consists of the motion controller, the amplifiers, the DC-motors and the drive trains. The X-drive train is composed of a gearbox and a belt-drive (Fig. 2). The gearbox reduces the motor speed, while the belt-drive converts rotary motion into linear motion. The belt-drive consists of a timing belt and of two pulleys: a driving pulley and a driven pulley that stretch the belt. The Y-drive train is more complex. The heavy bridge is driven by two parallel belt-drives； each bridge-side is connected to one of the belt-drives. The driving pulleys of the belt-drives are linked to the driving axis, which is driven via the additional belt-drive and the gearbox is used to reduce the speed of the motor. Fig. 2. The drive. 2.2. Assumptions The machine drives represent a complex non-linear distributed parameter system. The high-order system possesses several resonant frequencies that can be observed by the drives 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 high-performance control system while simultaneously reducing the complexity of the controller. Therefore, a simple mathematical model would only consider the first-order resonance and neglect high-order 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 higher-order resonance in such a way that the resonance peaks drop significantly to maintain the system stability. Thus, according to the signal analysis and the drives features, the following assumptions could be made: the DC-servos operating in the current control mode ensure a high-dynamic torque response on the motor axis with a negligible time constant； the small backlash in the gearboxes and the backlash of the belt-drives due to the applied pre-tension of the timing belts is negligible； a rigid link between a motor shaft and a driving pulley of the belt-drive could be adopted； the inertia of the belt-drives driven pulleys is negligible in comparison to other components of the drive system. Using the assumptions above, dynamic modeling could be reduced to a two-mass model of the belt-drives 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 belt-drive has to be considered as well. Note, that no attention is paid to the coupled dynamics of the Y-drive due to the parallel driving, thus, the double belt-drive is considered as an equivalent single belt-drive. 2.3. The belt-drive model The belt-drives could be modelled as a multi-mass system using modal analysis. In the belt-drive model with concentrated parameters, linear, massless springs characterize the elasticity of the belt. According to the assumptions above, a two-mass model can be obtained. The driving-pulley, motor shaft and the speed reducer are considered as the concentrated inertia of the driving actuator. The driven-pulley 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 belt-drive, and non-modelled higher-order dynamics are considered as an unknown disturbance that affects the driving side as well as the load side. The mechanical model of the two-mass system and its block scheme are shown in Figs. 3 and 4, respectively. The belt-stretch occurs due to the inherent elasticity of the timing belts. However, according to a vibration analysis of belt-drives (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 load-side dynamics. The belt-stretch forced by the applied torque q. The dynamics are described by Eq. (1) （ 1） where Hw(s) denotes the belt-stretch dynamics transfer function， （ 2） and is the natural resonant frequency （ 3） and is hte disturbance that affects the belt. The load-side 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 belt-stretch； the motor shaft torque； the driving side disturbance torque； the load side disturbance force； the spring force and 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 non-accurate model, namely, it has been proven in the VSS theory that the closed-loop 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 continuous-time/discontinuous VSS control approach can be successfully applied. However, in many control applications the discontinuous VSS control fails, and chattering arises (SabanovicH, Jezernik, & Wada, 1996； Young, Utkin & OG zguK ner, 1999). Chattering is an undesirable phenomenon in the control of mechanical systems, since the demanded performance cannot be achieved, or even worsemechanical parts of the servo system can be destroyed. The main causes of the chattering are neglected high-order control plant dynamics, actuator dynamics, sensor noise, and computer controlled discrete-time implementation in sampled-data 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 compensated for, e.g. by the use of a disturbance estimator (Jezernik et al., 1994； Kawamura, Itoh & Sakamoto, 1994). Jezernik has developed a control algorithm for a rigid robot mechanism by combining conventional VSS theory and the disturbance estimation approach. However, the rigid body assumption, which neglects the presence of distributed or concentrated elasticity, can make that control input frequencies of the switcher excite neglected resonant modes. Furthermore, in discrete-time systems discontinuous control fails to ensure the sliding mode and has to be replaced by continuous control (Young et al., 1999). Avoiding discontinuous-feedback control issues associated with unmodelled dynamics and related chattering are no longer critical. Chattering becomes a non-issue. In plants where control actuators have limited bandwidth there are two possibilities: actuator bandwidth is outside the required closed-loop bandwidth, or, the desired closed-loop bandwidth is beyond the actuator bandwidth. In the fist case, the actuator dynamics are to be considered as the non-modelled dynamics. Consequently, the sliding mode using discontinuous VSS control cannot occur, because the control plant input is continuous. Therefore, the disturbance estimation approach is preferred rather than VSS disturbance rejection. In the second case, the actuator dynamics are to be lumped together with the plant. The matching conditions (DrazenovicH, 1969) for disturbance rejection and insensitivity to parameter variations in the sliding mode are violated. This results from having dominant dynamics inserted between the physical input to the plant and the controller output. When unmatched disturbances exist the VSS control cannot guarantee the invariant sliding motion. This restriction may be relaxed by introducing a high-order sliding mode control in which the sliding manifold is chosen so that the associated transfer function has a relative degree larger than one (Fridman & Levant, 1996). Such a control scheme has been used in a number of recently developed VSS control designs, e.g. in Bartolini, Ferrara and Usai (1998). In the latter, the second-order sliding mode control is invoked to create a dynamical controller that eliminates the chattering problem by passing discontinuous control action onto a derivative of the control input. The system to be controlled is given by Eqs. (1) (5) and the system output is the load position. The control objective is the position trajectory tracking. The control algorithm that is proposed in this paper has been developed following the idea of the VSS motion control presented by Jezernik. Since the elastic belt-drive behaves as a low bandwidth actuator, the conventional VSS control algorithm failed to achieve the prescribed control objective. Thus, the robust position trajectory tracking control algorithm presented in the paper has been derived using second-order sliding mode control. In order to eliminate the chattering problem and preserve robustness, the control algorithm uses the continuous control law. Following the VSS disturbance estimation approach, it will be shown that the disturbance estimation feature of the proposed motion control algorithm is similar to the control approach of Jezernik (Jezernik et al., 1994). Additionally, the proposed control algorithm considers the actuator dynamics in order to reshape the poorly damped actuator bandwidth. Consequently, the proposed motion controller consists of a robust position-tracking controller in the outer loop and a vibration controller in the inner loop (Fig. 6). This section is organized as follows. Section 3.1 presents the proposed VSS control design. Section 3.2 describes the derivation of the robust position controller.Section 3.3 provides a description of the vibration controller. Finally, the proposed control scheme is described in Section 3.4. 激光切割机的传动控制可变结构系统 艾力斯霍斯，卡瑞尔诘责尼克，马丁特布 马里博尔大学机器人学学院电气工程系和计算机科学系 截稿于 1999 年 10 月 18日，出版与 2000 年 6月 2日 . 内容摘要 一种先进的位置跟踪控制算法已经研制出来了， 并将其应用在 激光切割机的数控运动控制器上 。激光切割机的 驱动 机构 是由带传动机构组成的。 弹性伺服机构可以看成是一个弹簧连接的双量机构。由于存在弹力 ,摩擦力和干扰 ,利用可行的传统的控制方 法得到的闭环回路是有限的。因此 , 利用可变系统结构控制理论推导出运动控制算法。 算例分析表明文中有效控制 抑制机械振动和保证系统补偿的不确定性。 因此 ,确保准确的位置跟踪 。 简介： 对许多工业驱动器，运动控制的性能具有非常重要性。最高的利益是快速动态行为与准确轨迹跟踪。如应用在机床必须满足这些高的要求。激光切割机也是，它要求快速运动快速且高准确度。这篇论文讲述了激光切割机的一种低成本的建立在有两个自由度的二维笛卡尔表基础上的运动控制算法 (图 1)。激光切割机的驱动机构由有一个正时带的带传动组成的。驱动系统中的正时带 具有吸引力是因为它具有高速度、高效、远距离行进和低成本特性 (霍斯 ,1996) 。另一方面 ,他们产生较多的不确定的动态和更高的传动误差。因此 ,传动带遭受较低的重复性和准确性。此外 ,带传动动力学包括很多谐振频率，即反馈控制中的不稳定因素。因此 ,传统的控制方法像比例积分控制、比例微分控制或 比例积分微分控制 未达到可接受的性能。设备参数的变化、不确定的动态和负载转矩的干扰 ,以及机械振动是必能保证系统的强稳定性和系统的高性能的因素。在这片论文中讲述了一种先进的稳定的运动控制方案 ,内容涉及到正时带驱动的运动控制。控制方案 是在运动控制算法的基础上由诘责尼克、科克和哈尼克 1994年研制出的。用变结构系统 (VSS)理论使其得到了强健的抵御与一个名义上的对象模型有关的干扰的性能。渐近线的扰动的估算是控制方案的关键的部分。 然而 ,就像文章指出 , 因为是为刚性机器人机制而研制的故不是稳定谐振带动力学。因此 ,介绍了一种改进后的会出现非刚性、弹性传动的振动运动控制方案。因此 ,保证其低位置跟踪误差的快速反应。 本文陈述如下。激光切割机的陈述和控制系统模型机械传动在文章的第二 节。在第三节 ,对于关于系统弹性伺服机构 可变结构系统控制进行了深入探 讨 ,并对运动的起源控制方案进行了阐述。第四节是实验结果和后续讨论。摘要在第五部分总结和归纳了。 2.模型控制 2.1 .机床的描述 激光切割机包括 XY工作台和激光系统（如图 1）。 激光系统的基本组成 因此没有考虑运动控制设计所以 电源设备被放置 在后台 激光束 来源 即产生激光束 (激光器 ) 激光头即引导激光到理想的剖切面 。 必须移坐标轴且与放置激光头在水平面里。采用两个独立的运动轴的驱动系统实现这样的水平面。他们提供沿卡迪尔 XY轴和 Z轴移动。 X轴传动使激光头沿 X轴方向的运动。 驱动机构激光头以及激光器 放置在桥接器上 ,以确保激光束有一条高品质的光路径。 Y轴运动是由 Y传动提供的。激光头代表 X驱动的负荷 , 它负载了全部 X驱动系统，包括激光头和激光器，而 Y驱动由电机来负载。 这些负载在无阻力的滑动面滑过。 定位系统由运动控制器 ,放大器 ,直流电机与驱动系统。 X驱动机构是由一变速箱以及带传动 (图 2)。 当带传动由旋转运动转化为线性运动变速箱降低了电机的转速。带传动由正时带和两个滑轮组成让皮带运动的主动轮和从动轮。 Y驱动机构更为复杂。沉重的桥接器由两条平行传动带驱动 ；每个桥面都连接到其中一个传动带上。传动机构通过减 少马达的速度的传动带驱动和变速箱来带动的主动轮与传动系联系。 2 .2 假设 这台机器驱动代表一个复杂的非线性分布参数系统。高阶系统拥有多项的能被驱动器的阶跃响应观测到的共振频率 (见第 4部分 )。根据控制设计观点 ,困难产生于在所要控制带宽 ( 10赫兹 )出现的机械振动。另一方面 ,设计目的是得到一个高性能控制系统的同时降低控制器复杂性。因此 ,一个简单的数学模型将只考虑它的一阶共振 ,而忽视了高阶动态。换句话说 ,控制设备的设计模型将密切配合真正系统频率响应直到第一阶共振。其次 ,控制器设计应充分地应对多谐振峰值的大 幅下降直到保持系统的稳定性的情况下的高阶共振。因此 ,根据信号分析与驱动装置的特点 ,假设可制定为如下 : 在电流控制方式里直流伺服系统的运作确保在电机轴上有一个忽略的时 间常数的高动态扭矩。 变速箱里的小间隙和取决于 应用拉伸的正时带 的带传动机构的间隙是可以忽略不计的。 电机轴和传动机构中的主动轮的刚性关联是可采用的。 相对其他传动系统中的部件从动带轮的惯性是可以忽略不计的。 用以上假设 ,动态模型将缩减至一个有两个传动轮的只包含一阶共振的传动机构。在控制设计 ,由于传动机构的可重复性和准确性都比较低，负载的不 确定的位置必须加以考量。 没有注意到的耦合的动力学 Y轴传动由于平行传动 ,因此 ,双履带传动可看成同级别的单履带传动。 2.3 带传动模型 可用一个多质子系统仿制带传动机构采用模态分析。 在带传动机构模型有着集中参数的、线性的、无质量的弹簧表示履带的弹性。根据以上的假设条件 ,可以得到轮 -车架系统模型。主动轮、电机轴和减速机都被看作是驱动执行机构的集中惯量。从动轮及负载主要集中在负荷质量上。惯量和负荷由弹簧联系的。电机轴承、齿轮箱、传动机构以及非模型的高阶动态里的摩擦力都被看作是一个影响着传动方面还有负载方面的不 为人知的干扰。轮 -车架系统的力学模型系统及其方案分别显示在图 3和图 4。 皮带的延展由于正时带的固有弹性。但是 ,根据传动机构的振动分析 ,所得到的模型能够调整。假设单位传送值为常数 (L=