激光切割機(jī)的傳動(dòng)控制可變結(jié)構(gòu)系統(tǒng)外文翻譯/中英文翻譯/外文文獻(xiàn)翻譯

徐州工程學(xué)院畢業(yè)設(shè)計(jì) 外文翻譯 學(xué)生姓名 劉星星 學(xué)院名稱 機(jī)電工程學(xué)院 專業(yè)名稱 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 指導(dǎo)教師 陳躍 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. 激光切割機(jī)的傳動(dòng)控制可變結(jié)構(gòu)系統(tǒng) 艾力斯霍斯，卡瑞爾詰責(zé)尼克，馬丁特布 馬里博爾大學(xué)機(jī)器人學(xué)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 2000 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 。激光切割機(jī)的 驅(qū)動(dòng) 機(jī)構(gòu) 是由帶傳動(dòng)機(jī)構(gòu)組成的。 彈性伺服機(jī)構(gòu)可以看成是一個(gè)彈簧連接的雙量機(jī)構(gòu)。由于存在彈力 ,摩擦力和干擾 ,利用可行的傳統(tǒng)的控制方 法得到的閉環(huán)回路是有限的。因此 , 利用可變系統(tǒng)結(jié)構(gòu)控制理論推導(dǎo)出運(yùn)動(dòng)控制算法。 算例分析表明文中有效控制 抑制機(jī)械振動(dòng)和保證系統(tǒng)補(bǔ)償?shù)牟淮_定性。 因此 ,確保準(zhǔn)確的位置跟蹤 。 簡(jiǎn)介： 對(duì)許多工業(yè)驅(qū)動(dòng)器，運(yùn)動(dòng)控制的性能具有非常重要性。最高的利益是快速動(dòng)態(tài)行為與準(zhǔn)確軌跡跟蹤。如應(yīng)用在機(jī)床必須滿足這些高的要求。激光切割機(jī)也是，它要求快速運(yùn)動(dòng)快速且高準(zhǔn)確度。這篇論文講述了激光切割機(jī)的一種低成本的建立在有兩個(gè)自由度的二維笛卡爾表基礎(chǔ)上的運(yùn)動(dòng)控制算法 (圖 1)。激光切割機(jī)的驅(qū)動(dòng)機(jī)構(gòu)由有一個(gè)正時(shí)帶的帶傳動(dòng)組成的。驅(qū)動(dòng)系統(tǒng)中的正時(shí)帶 具有吸引力是因?yàn)樗哂懈咚俣?、高效、遠(yuǎn)距離行進(jìn)和低成本特性 (霍斯 ,1996) 。另一方面 ,他們產(chǎn)生較多的不確定的動(dòng)態(tài)和更高的傳動(dòng)誤差。因此 ,傳動(dòng)帶遭受較低的重復(fù)性和準(zhǔn)確性。此外 ,帶傳動(dòng)動(dòng)力學(xué)包括很多諧振頻率，即反饋控制中的不穩(wěn)定因素。因此 ,傳統(tǒng)的控制方法像比例積分控制、比例微分控制或 比例積分微分控制 未達(dá)到可接受的性能。設(shè)備參數(shù)的變化、不確定的動(dòng)態(tài)和負(fù)載轉(zhuǎn)矩的干擾 ,以及機(jī)械振動(dòng)是必能保證系統(tǒng)的強(qiáng)穩(wěn)定性和系統(tǒng)的高性能的因素。在這片論文中講述了一種先進(jìn)的穩(wěn)定的運(yùn)動(dòng)控制方案 ,內(nèi)容涉及到正時(shí)帶驅(qū)動(dòng)的運(yùn)動(dòng)控制?？刂品桨?是在運(yùn)動(dòng)控制算法的基礎(chǔ)上由詰責(zé)尼克、科克和哈尼克 1994年研制出的。用變結(jié)構(gòu)系統(tǒng) (VSS)理論使其得到了強(qiáng)健的抵御與一個(gè)名義上的對(duì)象模型有關(guān)的干擾的性能。漸近線的擾動(dòng)的估算是控制方案的關(guān)鍵的部分。 然而 ,就像文章指出 , 因?yàn)槭菫閯傂詸C(jī)器人機(jī)制而研制的故不是穩(wěn)定諧振帶動(dòng)力學(xué)。因此 ,介紹了一種改進(jìn)后的會(huì)出現(xiàn)非剛性、彈性傳動(dòng)的振動(dòng)運(yùn)動(dòng)控制方案。因此 ,保證其低位置跟蹤誤差的快速反應(yīng)。 本文陳述如下。激光切割機(jī)的陳述和控制系統(tǒng)模型機(jī)械傳動(dòng)在文章的第二 節(jié)。在第三節(jié) ,對(duì)于關(guān)于系統(tǒng)彈性伺服機(jī)構(gòu) 可變結(jié)構(gòu)系統(tǒng)控制進(jìn)行了深入探 討 ,并對(duì)運(yùn)動(dòng)的起源控制方案進(jìn)行了闡述。第四節(jié)是實(shí)驗(yàn)結(jié)果和后續(xù)討論。摘要在第五部分總結(jié)和歸納了。 2.模型控制 2.1 .機(jī)床的描述 激光切割機(jī)包括 XY工作臺(tái)和激光系統(tǒng)（如圖 1）。 激光系統(tǒng)的基本組成 因此沒有考慮運(yùn)動(dòng)控制設(shè)計(jì)所以 電源設(shè)備被放置 在后臺(tái) 激光束 來源 即產(chǎn)生激光束 (激光器 ) 激光頭即引導(dǎo)激光到理想的剖切面 。 必須移坐標(biāo)軸且與放置激光頭在水平面里。采用兩個(gè)獨(dú)立的運(yùn)動(dòng)軸的驅(qū)動(dòng)系統(tǒng)實(shí)現(xiàn)這樣的水平面。他們提供沿卡迪爾 XY軸和 Z軸移動(dòng)。 X軸傳動(dòng)使激光頭沿 X軸方向的運(yùn)動(dòng)。 驅(qū)動(dòng)機(jī)構(gòu)激光頭以及激光器 放置在橋接器上 ,以確保激光束有一條高品質(zhì)的光路徑。 Y軸運(yùn)動(dòng)是由 Y傳動(dòng)提供的。激光頭代表 X驅(qū)動(dòng)的負(fù)荷 , 它負(fù)載了全部 X驅(qū)動(dòng)系統(tǒng)，包括激光頭和激光器，而 Y驅(qū)動(dòng)由電機(jī)來負(fù)載。 這些負(fù)載在無阻力的滑動(dòng)面滑過。 定位系統(tǒng)由運(yùn)動(dòng)控制器 ,放大器 ,直流電機(jī)與驅(qū)動(dòng)系統(tǒng)。 X驅(qū)動(dòng)機(jī)構(gòu)是由一變速箱以及帶傳動(dòng) (圖 2)。 當(dāng)帶傳動(dòng)由旋轉(zhuǎn)運(yùn)動(dòng)轉(zhuǎn)化為線性運(yùn)動(dòng)變速箱降低了電機(jī)的轉(zhuǎn)速。帶傳動(dòng)由正時(shí)帶和兩個(gè)滑輪組成讓皮帶運(yùn)動(dòng)的主動(dòng)輪和從動(dòng)輪。 Y驅(qū)動(dòng)機(jī)構(gòu)更為復(fù)雜。沉重的橋接器由兩條平行傳動(dòng)帶驅(qū)動(dòng) ；每個(gè)橋面都連接到其中一個(gè)傳動(dòng)帶上。傳動(dòng)機(jī)構(gòu)通過減 少馬達(dá)的速度的傳動(dòng)帶驅(qū)動(dòng)和變速箱來帶動(dòng)的主動(dòng)輪與傳動(dòng)系聯(lián)系。 2 .2 假設(shè) 這臺(tái)機(jī)器驅(qū)動(dòng)代表一個(gè)復(fù)雜的非線性分布參數(shù)系統(tǒng)。高階系統(tǒng)擁有多項(xiàng)的能被驅(qū)動(dòng)器的階躍響應(yīng)觀測(cè)到的共振頻率 (見第 4部分 )。根據(jù)控制設(shè)計(jì)觀點(diǎn) ,困難產(chǎn)生于在所要控制帶寬 ( 10赫茲 )出現(xiàn)的機(jī)械振動(dòng)。另一方面 ,設(shè)計(jì)目的是得到一個(gè)高性能控制系統(tǒng)的同時(shí)降低控制器復(fù)雜性。因此 ,一個(gè)簡(jiǎn)單的數(shù)學(xué)模型將只考慮它的一階共振 ,而忽視了高階動(dòng)態(tài)。換句話說 ,控制設(shè)備的設(shè)計(jì)模型將密切配合真正系統(tǒng)頻率響應(yīng)直到第一階共振。其次 ,控制器設(shè)計(jì)應(yīng)充分地應(yīng)對(duì)多諧振峰值的大 幅下降直到保持系統(tǒng)的穩(wěn)定性的情況下的高階共振。因此 ,根據(jù)信號(hào)分析與驅(qū)動(dòng)裝置的特點(diǎn) ,假設(shè)可制定為如下 : 在電流控制方式里直流伺服系統(tǒng)的運(yùn)作確保在電機(jī)軸上有一個(gè)忽略的時(shí) 間常數(shù)的高動(dòng)態(tài)扭矩。 變速箱里的小間隙和取決于 應(yīng)用拉伸的正時(shí)帶 的帶傳動(dòng)機(jī)構(gòu)的間隙是可以忽略不計(jì)的。 電機(jī)軸和傳動(dòng)機(jī)構(gòu)中的主動(dòng)輪的剛性關(guān)聯(lián)是可采用的。 相對(duì)其他傳動(dòng)系統(tǒng)中的部件從動(dòng)帶輪的慣性是可以忽略不計(jì)的。 用以上假設(shè) ,動(dòng)態(tài)模型將縮減至一個(gè)有兩個(gè)傳動(dòng)輪的只包含一階共振的傳動(dòng)機(jī)構(gòu)。在控制設(shè)計(jì) ,由于傳動(dòng)機(jī)構(gòu)的可重復(fù)性和準(zhǔn)確性都比較低，負(fù)載的不 確定的位置必須加以考量。 沒有注意到的耦合的動(dòng)力學(xué) Y軸傳動(dòng)由于平行傳動(dòng) ,因此 ,雙履帶傳動(dòng)可看成同級(jí)別的單履帶傳動(dòng)。 2.3 帶傳動(dòng)模型 可用一個(gè)多質(zhì)子系統(tǒng)仿制帶傳動(dòng)機(jī)構(gòu)采用模態(tài)分析。 在帶傳動(dòng)機(jī)構(gòu)模型有著集中參數(shù)的、線性的、無質(zhì)量的彈簧表示履帶的彈性。根據(jù)以上的假設(shè)條件 ,可以得到輪 -車架系統(tǒng)模型。主動(dòng)輪、電機(jī)軸和減速機(jī)都被看作是驅(qū)動(dòng)執(zhí)行機(jī)構(gòu)的集中慣量。從動(dòng)輪及負(fù)載主要集中在負(fù)荷質(zhì)量上。慣量和負(fù)荷由彈簧聯(lián)系的。電機(jī)軸承、齒輪箱、傳動(dòng)機(jī)構(gòu)以及非模型的高階動(dòng)態(tài)里的摩擦力都被看作是一個(gè)影響著傳動(dòng)方面還有負(fù)載方面的不 為人知的干擾。輪 -車架系統(tǒng)的力學(xué)模型系統(tǒng)及其方案分別顯示在圖 3和圖 4。 皮帶的延展由于正時(shí)帶的固有彈性。但是 ,根據(jù)傳動(dòng)機(jī)構(gòu)的振動(dòng)分析 ,所得到的模型能夠調(diào)整。假設(shè)單位傳送值為常數(shù) (L=