内容简介：: 河北建筑工程学院毕业设计（论文）外文资料翻译系别：机械工程系专业：机械设计制造及其自动化班级：机083 姓名：马宏亮学号： 2008307329 外文出处： Control Engineering Practice 10(2002) 697-711 附件：1、外文原文；2、外文资料翻译译文。指导教师评语：签字：年月日应用整体滑动面重型机器人挖掘机的延时控制摘要从下面的问题观点出发，挖掘机的控制是很困难的：机械结构的参数多样性，来自与地面接触的液压器的非线性和干扰。此外，挖掘机的尺寸越大，挖掘机的链接的长度和质量越大;重型挖掘机参数越多种多样。应用完整滑动原理制成的开关动作时间延迟控制器（TDCSA）应用在这篇论文中作为21吨重型挖掘机的控制器。通过分析实验，我们表明，对TDCSA的开关动作应用完整滑动面原理比使用PD型的滑动面原理要好。该控制器在以一个熟练操作者操作速度前提下被应用在了21吨挖掘机的直线运动中了。为凹凸不平的表面和大范围的接缝运动所设计的实验表明该控制器具有良好的性能。 2002 Elsevier科学有限公司保留所有权利。关键词：时间延时控制器；动作开关;机器人挖掘机；轨迹控制1.介绍液压挖掘机是一个多功能的施工机械。在建筑行业的工人使用它进行作业，如开挖，倾倒垃圾，整理，起重等等。然而，操作者必须被训练多年才能快速熟练的完成这些任务。液压挖掘机有三个链接：拉杆、动臂和铲斗;但操作者只有讲个胳膊。因此，对于初学者同时操作三个链接来完成工作不是容易的事。此外，因为操作者不得不承担各种各样的危险以及恶劣的工作环境，所以高级操作工的数量正在减少。出于这个原因，研究液压挖掘机的自动控制对改善生产力，效率，和安全是很有必要的。几位研究人员已经对液压挖掘机的自动化进行了研究（辛格，1997年）。在实现自动化的几个考验中，Bradley 和Seward（1998）开发了（LUCIE）并将它应用到了挖掘的自动化。 Stentz，Bares，Singh和Rowe（1998）开发了一个完整的卸载货物的系统并将它应用在了一个25吨的液压挖掘机上。Zhang和Li实现了一个13吨的液压挖掘机在工作速度下的直线运动的自动化。即使一个熟练的操作工在长时间直线操作的情况下也会产生疲劳从而造成生产力的下降。从下面的几个问题来看，液压挖掘机的控制是很困难的：机器构造参数的多样化,液压传动装置的各种非线性，与土地接触的不平衡性。在机械构造方面，惯性力和重力随接触缝的运动变化很大。大体积组装和复杂连接的液压传动装置有各种各样的非线性组成部分。出于这个原因，在挖掘机控制上存在各种各样困难。图 1 直线运动图 2 Robex210lc-3挖掘机为解决这些问题，一些研究工作已经被指导分组，他们可能被归为模仿研究或实验研究。就模仿研究来说，现在，Chiba和Takeda(1982)应用一个最好的控制方案来控制挖掘机的操作。Song和Koivo（1995）在大量变化参数基础上成功应用了提前反馈神经网络和一个PID控制器。在实验研究方面，Lee（1995）将一个模糊的应用错误反应原理的控制技术和它的衍生物在几何平面上相组合。Yokota,Sasao,和Ichiryu使用干扰观察器和PI控制器，并且将它应用到一个小型挖掘机上。Chang和Lee（2002）在挖掘机动态学基础上使用延时控制器(TDC)和补偿控制器，并且将它应用到一个13吨的挖掘机的直线运动上，并以0.5m/s的速度工作，这个工作速度是一个熟练的操作工的工作速度。然而，几乎所有的以上研究工作都被限制在了一个小型挖掘机的相对低速条件下。在上述实验研究工作中，只有Chang和Lee的在工作速度条件下表现的好。挖掘机的尺寸越大，它的长度和体积相关性就越多，并且重型挖掘机的参数越多。因此，重型挖掘机的控制相对小型挖掘机的控制变得更加困难。重型挖掘机需要一个良好的控制器。在这篇论文中，通过对直线运动的追踪控制实验，我们将延时控制器应用在一个21吨的挖掘机的控制上，并且是控制算法得以生效。另外，我们展示了使用ISS的TDCSA的优点。TDCSA由Chang和Park(1998)发明，由一个TDC和一个转换器组成。Chang和Park使用了带有PDSS的转换器，还应用了TDCSA。但是，我们应用ISS在转换机能上是为了改善控制功能。然而，Lee和Youu已经通过模拟二线操作控制系统，证明了他们的计算方法的无用性。相反，我们将继续开展在挖掘机方面的实验。这篇文章的余下部分是按下面的方式组织的。第二部分简要的分析挖掘机系统的特性。第三部分描述了控制器。所发明的控制器的有效性通过应用在一个21吨挖掘机的实验中得以证明，最后结论将在第五段得出。2. 挖掘机系统的概要这部分主要描述了挖掘机的特性。更多关于挖掘机模型的细节能在Chang和Lee的研究中发现。在这篇论文中，转动装置和行走装置并不被认为是直线运动。因为挖掘机由操纵装置和传动装置组成，这两部分的特点将会简要描述。2.1控制器在运动方程中，惯性力、重力和离心力随连接角度的变化而变化。在这些力当中，离心力对控制系统的影响较小。相比较而言，惯性力和重力变化很大，因为动臂和铲斗的重量在这项研究中重达2.67吨，并且连接点转角范围较大。在直线运动中，每个惯性力和重力变化范围都很大。图3中就展现了一个0角的斜坡。我们能观察到惯性力和重力变化很大。（a) 惯性力 (b) 重力图 3 动臂和斗杆的惯性力和重力2.2液压传动装置在这篇论文中应用的挖掘机的液压传动装置至少有三种非线性：阀特性、死区和时间滞后。2.2.1阀特性液压阀是将油由油泵转移到液压油缸中的装置。油的流量被流量系数、油缸的截面积和压力的大小所决定。因此，根据油缸的非线性截面积，油缸有不同的非线性特性。2.2.2死区在Robex210lc-3挖掘机中应用的卷盘阀的几何学是一个重叠的形状，正如在图4所示，这也引起了死区的非线性。这个重叠区域是为操作者的便利所设计。因此，当卷轴放在重叠区域时，这个阀便关闭，着引起了死区的非线性。这部分重叠区域大约占整个排水量的30%。2.2.3时间滞后因为泵的输出压力要达到推动连接物开启的压力。这一部分时间的消耗使得一个和死区相似的现象出现了。注意到这一现象在某种程度上是不同于在输送线路上的纯粹时间消耗的。这一现象只有当吊杆连接开始移动时才出现。当泵的输出压力达到阀开启压力时，它将消失。此外，这一现象能通过补偿器得到补偿，这一内容将在3.2部分介绍 3、控制器设计一个挖掘机有以下非线性：在操纵器上的惯性力和重力的多样性；阀特性的非线性；传动装置的死区和时间滞后性。这篇论文所讨论的在21吨挖掘机和13吨挖掘机之间的显著不同点存在于挖掘机各连接物的长度和体积。因此，21吨挖掘角度的数据的多样性比13吨的挖掘机更为严峻。需要一个比TDC更优良的控制器来控制21吨挖掘机的直线运动。为了控制21吨的挖掘机，我们已经考虑了比TDC更优良的TDCSA。然后，为了改善控制器的表现，我们应用了ISS来代替Chang和Park所应用的PDSS。在前面提到的非线性中，死区和时间滞后引起了大量追踪错误。因此，需要正确补偿方法。出于那个原因，我们设计了两种控制器:第一个是应用ISS作为根本控制的TDCSA，第二个是克服死区和时间滞后的补偿器。3.1TDCSA的设计3.1.1使用ISS的TDCSA为了将控制器应用到挖掘机上，（A.5)被重组成下列形式：注意到M是一个常量矩阵来代表我们熟知的角度，但是H(t)有专业术语组成，代表不确定性和时间多变的原因，表示如下:估计量 H(t)可以通过使用公式（1)和H(t)是一个连续作用这一事实而得到。更具体点，当L足够小时，然后，更多关于条件的稳定性和TDC的实际能在Youcef-Toumi和Ito和Hsia和Hao的研究中发现。TDCSA在对TDC实现滑动模型控制基础上增加了转换机能，表示如下：这里s代表滑动表面，Kw是一个转换矩阵。TDCSA有下面错误表示方法在公式（10)中，我们能看到转换机能能减少TDE的错误。3.1.2应用完整滑动表面的TDCSA的稳定性分析为了整个系统的稳定性分析，我们使用Lyapunto的第二种方法，如果Lyapunto功能被选为它的时间衍生物就可表示如下：因此，下面的条件是需要的来使Lyapunto得功能时间衍生物被消极的定义为换句话说，转换获得量的大小一定要比TD估计的错误量要大。3.1.3饱和度功能TDCSA使用转换机能补偿TDE的错误，但这个转换机能引起了一个交流问题。因此，我们使用一个饱和度功能来减少交流问题。这个饱和度问题能这样应用：这里是饱和度功能的边界线。最终，得到了一个拥有饱和度的功能的TDCSA，表示如下：如果选择了一个大的边界层，各种交流将会减少，但是追踪错误将会增加，所以合适的边界层的选择是必要的。3.1.4ISS的必要性和优势在这一部分通过与PDSS的比较，我们将学习ISS的必要性和优势。完整滑动面的必要性TDCSA有TDC和SMC的想换机能组成。由此它在比较预期的TDC的动力学的错误和滑动面衍生物方面变得很必要。更具体一点，ISS给出如下形式它的衍生物变成了通过比较，PDSS被表示为它的衍生物与图3是不同的。完整滑动面的优势对于边界层内的滑动面，使用PDSS的TDCSA的转换机能和使用ISS的TDCSA的转换机能得到了公式16和公式17将公式16和公式17分别比较，重组公式15便得到公式18和19从公式18和19中，每一个闭环错误动态学表示如下3.2补偿器设计补偿器是用来克服死区和时间滞后的。因为来自油缸卷轴的重叠区域的死区的尺寸是固定的，我们经TDCSA输入增加了死区尺寸，表示如下：为了补偿时间滞后，Chang和Lee根据油泵和液压缸的不同压力设计了补偿器。在这篇论文中，证如图7所示那样，我们给控制律增加了固定值，直到油泵的压力足够大来开启连接物。然后一旦连接物开始移动就慢慢减少油压直到0.整个有TDCSA输入和补偿输入所组成的控制输出有以下表现形式得出如下公式：注意是动臂和斗杆的输入控制量。4. 实验为了计算在真正情形下应用ISS的TDCSA,我们已经在重型挖掘机上进行了真实的测试。这项工作的主要焦点是在空地上的直线运动。当然，我们已经将这一直线运动通过铲斗和地面的接触应用到了刮平地面的上。过去的Hyundai Robex210lc-3挖掘机现在已经有了如下详细说明：重21吨，控制器总长度10.06m，吊杆、动臂和铲斗总重2.67吨。在这实验中，铲斗的平均速度设定在0.5m/s，只有专家级别的操作者能以这个速度进行工作。4.1实验设备图8展示了挖掘机的全部控制系统。吊杆、动臂和铲斗的轨道均在一个DSP的控制器中计算出来。每一个连接物的控制器输入根据控制律在一个DSP控制器中计算出来。通过使用产生的轨道和测量角度，得到的控制输入通过一个D/A转换器被转换，然后操纵电力部分的压力减小阀。从EPPR阀出来的先导压力使每一个主要阀的卷轴移动，因此使每一个连接物移动，在这里，DSP控制器的频率样本取为100赫兹。Control Engineering Practice 10 (2002) 697711Control of a heavy-duty robotic excavator using time delay controlwith integral sliding surfaceSung-Uk Lee*, Pyung Hun ChangDepartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Science Town, 373-1 Koosung-dong, Yusung-ku,Taejon 305-701, South KoreaReceived 22 March 2001; accepted 14 December 2001AbstractThe control of a robotic excavator is difficult from the standpoint of the following problems: parameter variations in mechanicalstructures, various nonlinearities in hydraulic actuators and disturbance due to the contact with the ground. In addition, the morethe size of robotic excavators increase, the more the length and mass of excavators links; the more the parameters of a heavy-dutyexcavator vary. A time-delay control with switching action (TDCSA) using an integral sliding surface is proposed in this paper forthe control of a 21-ton robotic excavator. Through analysis and experiments, we show that using an integral sliding surface for theswitching action of TDCSA is better than using a PD-type sliding surface. The proposed controller is applied to straight-linemotions of a 21-ton robotic excavator with a speed level at which skillful operators work. Experiments, which were designed forsurfaces with various inclinations and over broad ranges of joint motions, show that the proposed controller exhibits goodperformance. r 2002 Elsevier Science Ltd. All rights reserved.Keywords: Time-delay control; Robust control; Switching action; Robotic excavator; Trajectory control1. IntroductionA hydraulic excavator is a multi-functional construc-tion machine. Workers in the construction industry useit for tasks such as excavating, dumping, finishing,lifting work, etc. However, operators who controlhydraulic excavators must be trained for many yearsto do such work quickly and skillfully. A hydraulicexcavator has three links: boom, arm and bucket; andthe operator has two arms. Thus, it is not easy forbeginners to execute elaborate work that manipulatesthree links at the same time. Moreover, because theoperators have to run work in various dangerous anddirty environments, the number of skillful operators isever decreasing. For that reason, studying the automa-tion of hydraulic excavators is necessary for improvingproductivity, efficiency, and safety.The automation of hydraulic excavators has beenstudied by several researchers (Singh, 1997). Among theseveral tasks to be automated, Bradley and Seward(1998) developed the Lancaster University computerizedintelligent excavator (LUCIE) and used it to automatethe digging work. Stentz, Bares, Singh, and Rowe (1998)developed a complete system for loading trucks fullyautonomously on a 25-ton robotic excavator. Changand Lee (2002) automated straight-line motions on a 13-ton robotic excavator under working speed conditions.Here, the straight-line motion represents the importanttask of scraping or flattening the ground and serves as afundamental element used as a basis for developingmore complicated tasks. As illustrated in Fig. 1, the end-effector of the manipulator needs to be controlled totrack a linear path on the task surface. An operatorshould manipulate three links simultaneously to executeit. Though an operator is skillful, performing thestraight-line motions for a long time results in thefatigue of an operator and decreases productivity.The control of robotic excavator is difficult from thestandpoint of the following problems: parameter varia-tions in mechanical structures, various nonlinearities inhydraulic actuators, and disturbance due to the contactwith the ground. In mechanical structures, the inertial*Corresponding author. Tel.: +82-42-869-3266; fax: +82-42-869-5226.E-mail address: s sulee123cais.kaist.ac.kr (S.-U. Lee).0967-0661/02/$-see front matter r 2002 Elsevier Science Ltd. All rights reserved.PII: S 0967 -0661(02 )0 0027-8force and gravitational force varies largely with jointmotions. Hydraulic actuators, massively coupled andcomplexly connected, have various nonlinear compo-nents. For such reasons, various difficulties exist incontrolling a robotic excavator.To solve these problems, several research works havebeen performed, which may be categorized as eithersimulation studies or experimental studies. In terms ofsimulation studies, for instance, Chiba and Takeda(1982) applied an optimal control scheme to the controlof the manipulator of an excavator. Morita and Sakawa(1986) used PID control with feedforward control basedon inverse dynamics. Medanic, Yuan, and Medanic(1997)proposedapolarcontroller-basedvariablestructure control. Song and Koivo (1995) used afeedforward multiplayer neural network and a PIDcontroller over a wide range of parameter variations. Asfor experimental studies, Bradley and Seward (1998)used a high-level controller that was based on rulesobtained by observation of skilled operators, and a PIDlow-level motion controller that moved the end-effectorin response to a demand from the high-level controller.Lee (1993) used P control together with a fuzzy controltechnique that used response error and its derivative onthe phase plane. Sepehri, Lawrence, Sassani, andFrenette (1994) analyzed the phenomenon of couplingin the hydraulic actuator, and proposed a feedforwardscheme that compensates coupling and load variation byusing a simple valve model and measured pressure.Yokota, Sasao, and Ichiryu (1996) used disturbanceobserver and PI control, and applied it to a miniexcavator. Chang and Lee (2002) used time-delaycontrol (TDC) and compensators based on the dy-namics of the excavator and applied it to straight-linemotions of a 13-ton excavator with a bucket speed of0:5 m=s; a speed level at which skillful operators work.However, almost all the research works above tend tobe limited to experiments on a mini excavator underrelatively lower speed conditions. Among the experi-mental research works above, only that of Chang andLee (2002), which was performed on the control of aheavy-duty 13-ton robotic excavator, was performedunder working speed conditions. The more the size ofexcavators increase, the more the length and mass ofexcavators links increase, and the more the parametersof a heavy-duty excavator vary. Therefore, the controlof a heavy-duty excavator becomes more difficult thanthe control of a mini excavator. The control of a heavy-duty excavator (a 21-ton robotic excavator (Fig. 2) usedin this paper) requires a robust controller.In this paper, we apply time-delay control withswitching action (TDCSA) using an integral slidingsurface (ISS) to the control of a 21-ton robotic excavatorand validate the proposed control algorithm throughexperiments on a straight-line motion tracking control.In addition, we show the advantage of the TDCSA usingan ISS. TDCSA, which was proposed by Chang andPark (1998), consists of a TDC and a switching action.The switching action based on sliding mode control(SMC) compensates for the error of the time-delayestimation (TDE) and makes the TDC more robust.Chang and Park (1998) used a PD-type sliding surface(PDSS) for the switching action and applied the TDCSAusing a PDSS to a pneumatic system for compensatingthe stick-slip, but we use an ISS for the switching actionto improve the control performance in this paper(Slotine & Li, 1991; Utkin & Shi, 1996). As a similarcontroller, a new integral variable structure regulationcontroller, designed using an integral sliding surface anddisturbance observer, was proposed by Lee and Youn(1999). Lee and Youn, however, have demonstrated theusefulness of their proposed algorithm by simulationsabout regulation controls of a two-link manipulator. Incontrast, we will perform experiments on the control ofa robotic excavator.Fig. 1. Illustration of straight-line motion.Fig. 2. Appearance of Robex210LC-3 excavator.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711698The rest of this paper is organized as follows. Section2 will briefly analyze the characteristics of the roboticexcavator system, Section 3 presents the design ofcontroller. In Section 4, the effectiveness of the proposedcontroller will be verified through experiments on a 21-ton robotic excavator. Finally, conclusions will bedrawn in Section 5.2. Overview of robotic excavator systemThis section describes briefly the characteristics of therobotic excavator. More details about the model of arobotic excavator can be found in Chang and Lee(2002). In this paper, the swing motor together with thetraveling motor is not considered for straight-linemotion; only the boom, arm and bucket are considered.The mathematical model that is needed for designing acontroller is described in Appendix A. Since a roboticexcavator consists of a manipulator and actuators, thecharacteristic of these two parts will be described briefly.2.1. ManipulatorIn the dynamic equation (Eq. (A.1), the inertialforces and gravitational forces as well as the centrifugaland Coriolis forces vary nonlinearly with the change ofangles of the links, and have coupling elements betweenlinks. Among these terms, the centrifugal and Coriolisforces have a smaller effect on the control performance,since the velocity of each link is not that great. Incomparison, the inertial forces and gravitational forcesvary largely, since the total weight of boom, arm andbucket used in this research is 2:67 ton and the range ofjoint angles are broad. The size and variation in each ofthe inertial and the gravitational forces in a straight-linemotion with incline of 01 are shown in Fig. 3. We canobserve that the inertial forces and gravitational forcesvary largely.2.2. Hydraulic actuatorsThe hydraulic actuator of the robotic excavator usedin this paper has at least three kinds of nonlinearities asfollows: valve characteristics, dead zone and time lag.2.2.1. Valve characteristicsHydraulic valves are devices that transfer the flowfrom the pump to cylinder. From the general valve flowequation Q cdAffiffiffiffiffiffiffiDPp; the flow that is transferredfrom the pump to cylinder is determined by flowcoefficient, the area of the valve and pressure difference.The area of a spool valve has a nonlinear shape asshown in Fig. 4. Therefore, valves have nonlinearcharacteristics according to the nonlinear area of thevalve andffiffiffiffiffiffiffiDPp:2.2.2. Dead zoneThe geometry of the spool valve used in a Ro-bex210LC-3 excavator is an overlapped shape as shownin Fig. 4 and causes the dead zone nonlinearity. Theoverlapped region is designed for the convenience of anoperator. Therefore, when the spool is displaced in theoverlapped region, the valve becomes closed: this causes02468_3000_2000_10000100020003000timesecforceNewton(a) Inertial forceboomarm02468_505101520x 104timesecforceNewton(b) Gravitational forceboomarmFig. 3. Inertial forces and gravitational forces of boom and arm.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711699the dead zone nonlinearity. The overlapped region isabout 30 percent of the whole spool displacement.2.2.3. Time lagA phenomenon similar to a dead zone occurs becauseof the time taken for the pump output pressure to reachthe pressure level that is sufficient to move the link. Notethat this phenomenon is somewhat different from thepure time delay often found in transmission lines. Fig. 5illustratesthisphenomenonwiththeexperimentalresults. In the presence of maximum control input, theboom does not move until the time is 0:13 s; when thepump pressure begins to exceed the pressure of theboom cylinder plus the offset pressure, as shown inFig. 5. This phenomenon occurs only when the boomlink begins to move and it does not exist any more oncethe pump output pressure reaches the pressure levelsufficient to move the link. Moreover, this phenomenoncan be compensated by the compensator which will beproposed in Section 3.2.3. Controller designA robotic excavator has the following nonlinearities:variations in the inertial and gravitational forces in themanipulator; and nonlinear valve characteristics, deadzone and time lag in the hydraulic actuator. Toovercome these aforementioned nonlinearities, Changand Lee (2002) suggested the TDC and compensatorsand used these to control a 13-ton robotic excavator, butwe need a more robust controller to control a 21-tonrobotic excavator effectively. The greatest differencebetween the 21-ton robotic excavator used in this paperand the 13-ton robotic excavator used in Chang and Lee(2002) exists in the length and mass of excavators links.The links of the former are one and half times the lengthand weight of those of the latter. Therefore, theparameter variations of a 21-ton excavator are moreserious than those of a 13-ton excavator. A more robustcontroller than TDC is required to control the straight-line motion of a 21-ton robotic excavator.For controlling a 21-ton robotic excavator, we haveconsidered TDCSA, which is more robust than TDC.Spool displacementVavleAreaoverlap regionFig. 4. Rough shapes for areas of spool valve.01050100150200(a) Pressures of pump and head side of boom cylindertimesecpressurebarpumphead side of boom cylinder01949698100102104106(b) Boom responsetimesecangledegFig. 5. Illustration of the nonlinearity due to time lag.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711700Then, instead of a PDSS used by Chang and Park(1998), we use an ISS in this paper for improving thecontrol performance (Slotine & Li, 1991; Utkin & Shi,1996).Among the aforementioned nonlinearities, however,the dead zone and the time lag cause the large trackingerrors. Hence, proper compensation is demanded. Forthat reason, we design the two controllers: first theTDCSA using an ISS as the baseline control and second,compensators to overcome the dead zone and thetime lag.3.1. Design of the TDCSA3.1.1. TDCSA using an ISSInordertoapplythecontrollertoaroboticexcavator, Eq. (A.5) is rearranged into the following:%M.lt %Ht ut:1Note that%M is a constant matrix representing theknown angle of MK; whereas%Ht consists of termsrepresenting uncertainties and time-varying factors,which are expressed as%Ht Ht MKt ?%M.lt:2Now we define the desired dynamics of the closed-loopsystem with the following error dynamic:. et Kv et Kpet 0;3where et ldt ? lt denotes the position error vectorwith ldt denoting the vector of desired piston displace-ments, Kvthe derivative gain matrix, and Kptheproportional gain matrix. The TDC law that meets therequirement is obtained asutdct %M.ldt Kv et Kpet? #Ht;4where#Ht denotes an estimate of%Ht:The estimated#Ht can be obtained by using bothEq. (1) and the fact that%Ht is usually a continuousfunction. More specifically, when L is small enough,then#HtE%Ht ? L ut ? L ?%M.lt ? L:5Combining Eq. (5) with Eq. (4), the TDC law isobtained as follows:utdct %M.ldt Kv et Kpet? utdct ? L ?%M.lt ? L:6More details about the stability condition and the designof TDC can be found in Youcef-Toumi and Ito (1990)and Hsia and Gao (1990).L should be sufficiently small for TDC to meet thedesired error dynamics of Eq. (3). The valve used for L;however, is set to be that of the sampling time, whenTDC is implemented in a real-time controller. Thevariation of system nonlinearities and disturbances,occurred during the time delay L; caused TDE erroras follows:%Ht ?#Ht %Ht ?%Ht ? L DHt:7More specifically, the friction dynamics cause large TDEerror. Because of the TDE error, TDC does not have thedesired error dynamics of Eq. (3), but the followingerror dynamics:. et Kv et Kpet %M?1DHt;8where the right term %M?1DHt denotes the effect ofthe TDE error.The TDCSA is proposed by adding the switchingaction based on the sliding mode control to TDC, asfollows:utdcsat %M.ldt Kv et Kpet? utdcsat ? L?%M.lt ? L Kwsgns;9where s represents the sliding surface and Kwis aswitching gain matrix. The TDCSA has the followingerror dynamic:. et Kv et Kpet %M?1DHt ?%M?1Kwsgns: 10In Eq. (10), we see that the switching action can reducethe TDE error.In order to match the desired error dynamics (Eq. (4)with the sliding surface (s), we use the integral slidingsurface as follows:st et Kvet KpZt0et dt ? e0 ? Kve0; 11where the sliding surface (s) has the initial value of zeroand its derivative is equal to desired error dynamics(Eq. (3). The necessity and advantage of using anintegral sliding surface will be shown in Section .1.2. Stability analysis of TDCSA using an integralsliding surfaceFor the stability analysis of the overall system, we usethe second method of Lyapunov. If the Lyapunovfunction is selected as V 12sTs; its time derivative is asfollows:V sT s sT. e Kv e Kpe?sT.ld?%M?1u %M?1%H Kv e Kpe?sTf.ld?%M?1%M.ld Kv e Kpe #H Kwsgns?%M?1%H Kv e KpegsT?%M?1#H %M?1%H ?%M?1Kwsgns?sT%M?1DH ?%M?1Kwsgns?:12Therefore, the following condition is needed so that thetime derivative of the Lyapunov function should benegative definite:Kwii jDHijfor i 1;y;3:13S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711701In other words, the magnitude of the switching gainKw must be larger than that of the term due to the TDestimation error.3.1.3. Saturation functionTDCSA uses a switching action for compensating theTDE error, but the switching action in TDCSA causes achattering problem. Therefore, we use a saturationfunction to reduce the chattering problem (Slotine & Li,1991). A saturation function can be used as follows:satst;f stfif jstjof;sgnstotherwise;8 jDHij; the minimum tracking guarantee isjessijo%M?1iDHitKpi%M?1iKwili=fi:22For a constant right-hand side of Eq. (21), however, thesteady-statesolutionofEq. (21)iseit-0andRt0eit dt-0: Therefore, TDCSA using an ISS candrivethetrackingerrorsresultingfrombiasinuncertainties (such as constant and slowly varyingparametric errors) to zero.From Eqs. (20) and (21), the relationship in theLaplace domain between the TDE error and positionerror et is as follows:where p is the Laplace operator. Eq. (23) is that of theTDCSA using a PDSS and Eq. (24) is that of theTDCSA using an ISS. The bode plot of Eqs. (23) and(24) is shown in Fig. 6. The TDCSA using an ISS has thesame high-frequency behavior as the TDCSA using aPDSS and TDC. In the low-frequency range, however,TDCSA using an ISS has a lower gain than the othercontroller. Thus, the TDCSA using an ISS reduceseffectively the position error, which is caused by TDEerror in the low-frequency range, and then the TDCSAusing an ISS is more robust than the other controlleragainst the disturbances and variation of parameterswhich occur in the low-frequency range.3.2. Design of compensatorsCompensators are designed to overcome the deadzone and the time lag.Since the size of the dead zone coming from theoverlapped area of the spool valve is constant, we addthe size of the dead zone to TDCSA input as follows:u utdcsa ucomp1;25EipDHip%M?1ip2 Kvi%M?1iKwi=fip Kpi%M?1iKwili=fi;23EipDHip%M?1ipp3 Kvi%M?1iKwi=fip2 Kpi%M?1iKwiKvi=fip %M?1iKwiKpi=fi%M?1ipp %M?1iKwi=fip2 Kvip Kpi;2410_210_110010110210310_610_510_410_310_210_1|Ei(s)|/|delHi(s)|FrequencyHzMagnitudeTDC TDCSA using a integral sliding surfaceTDCSA using a PD type sliding surface Fig. 6. Bode diagram of closed-loop error dynamics.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711703where u denotes the overall control input and ucomp1the3 ? 1 vector whose elements are constants equivalent tothe dead zone of each link.To compensate for the time lag, Chang and Lee(2002) designed the compensator using the pressuredifference of the pump and cylinder. This compensatorincreases the pump pressure to cylinder pressure quicklyand works until pump pressure begins to exceed thepressure of the cylinder plus the offset pressure, but itneeds pressure sensors. In this paper, as shown in Fig. 7,we add the constant value ucomp2 to the control lawuntil the pump pressure is increased to the pressure levelsufficient to move the link, and then decrease the valueslowly to zero once the link begins to move.The whole control input, which now consists of theTDCSA input and the compensation inputs, is obtainedas follows:u utdcsa ucomp1 ucomp2:26Note that ucomp2is used for the control inputs of boomand arm.4. ExperimentTo evaluate TDCSA using an ISS in real circum-stance, we have experimented the method in a heavy-duty excavator carrying out realistic tasks. The task ofconcern is primarily a straight-line motion in free spaces;yet, we have applied the straight-line motion to scrapingthe ground with the bucket in contact with the ground.The excavator used is a Hyundai Robex210LC-3, whichhas the following specifications: it weights 21 ton; thetotal length of the manipulator is 10:06 m and the totalweight of boom, arm and bucket is 2:67 ton: In theexperiments, the average speed of the bucket is set to be0:5 m=s 4 m in 8 s), the speed level at which only anexpert operator can perform a task.4.1. Experimental setupFig. 8 shows the overall structure of the excavatorcontrol system. The trajectories of boom, arm andbucket for a task are calculated on a DSP controller.The angles of each links are measured with a resolverand then converted by an A/D converter for generatinga control input. The control input for each link iscalculated on a DSP controller according to the controllaw, by using the trajectories generated and the anglesmeasured. The control inputs obtained are convertedthrough a D/A converter and fed to operate the electri-proportional pressure reducing (EPPR) valve, whichtransforms the electrical signal into the hydraulicpressure signal. The pilot pressure from the EPPR valvemoves the spool of each main valve, thus making eachlink move. Here, the sampling frequency of a DSPcontroller is selected as 100 Hz:4.2. Trajectory generationTo automate the straight-line motion, the trajectoriesof the end-effector and the joint angle are needed.Once the incline of the task surface is given, the end-effector path is determined, and then the velocitytrajectory of the end-effector is determined by consider-ing the average speed of the end-effector. Here, thisvelocity profile is for the direction tangential to the tasksurface, with the velocity in its normal direction beingkept at 0 m=s: The displacement trajectory of theend-effector is obtained by integrating the velocitytrajectory.To control each link, the displacement trajectory ofthe end-effector is transformed into the joint angletrajectory of each link. Moreover, during a straight-linemotion, the constraint exists that the attack angle ofbucket (the angle of the bottom surface of bucket)is kept constant with respect to the task surface.The joint angles of boom and arm are calculated byDACTrajectoryGenerationControllerADCEPPRvalveExcavatorResolverDSPControllerAnglesFig. 8. Overall structure of control system.TimesecCompensatorInputCompensator for time lag(Ucomp2)Compensator for dead-zone(Ucomp1)Fig. 7. Compensator for dead zone and time lag.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711704using excavator kinematics from Fig. 9, as Eqs. (27)and (28):yboom sin?1x2a y2a L21? L222L1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2a y2ap? tan?1yaxa;27yarm cos?1x2a y2a? L21? L222L1L2;28where xaand yais the position of the bucket joint. Fromthe aforementioned constraint, the angle of the bucket isdetermined as follows:ybucket yinit? yboom? yarm;29where yinitis the sum of the boom angle, arm angle, andbucket angle in initial posture. From the above, we candetermine the joint trajectory of each link.We use the velocity trajectory obtained that meets thespecified average speed of 0:5 m=s as shown in Fig. 10.Then, the joint trajectories for three task surfaces withrespective inclines of ?301; 01 and 301 is shown inFig. 11. This trajectory is made to realize the practicethat straight-line motions are usually carried out from astretched posture to a folded one.4.3. Experimental resultsIn implementing the control law in Eq. (15), wedetermined each gain for utdcsaas follows:%M %M1000%M2000%M326643775;Kv2x1w10002x2w20002x3w326643775;Kpw21000w22000w2326643775;30where xiand widenote the damping coefficient and thefrequency for desired error dynamics of each link. Inaddition,%Miis selected in the stable range throughexperiments. The switching gain Kwi; satisfying thecondition of Kwii jDHij; is selected by tuning. Theboundary layer of the saturation function fi isFig. 9. Excavator kinematics.012345678_0.7_0.6_0.5_0.4_0.3_0.2_0.10End Effector velocity trajector ytimesecvelocitym/sFig. 10. End-effectors velocity trajectory for horizontal direction.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711705properly chosen by tuning, without the chattering. Then,the magnitude of ucomp2is to be tuned from a small valueuntil satisfactory performance is achieved.4.3.1. Noncontact conditionIn free spaces, we experimented with three controllers:TDC, TDCSA using a PDSS and TDCSA using an ISS;for task surfaces with inclines of ?301; 01 and 301;respectively. Here, among the gains of the TDCSA, thedesired error dynamics are the identical with those ofTDC. The switching gain of the TDCSA using an ISS isidentical with that of the TDCSA using a PDSS.Fig. 12 shows the experimental results for TDC. Asshown in Fig. 12, the vertical distance error of the end-effector is within 73 cm for the task surface with anincline of ?301: For the task surface with an incline of301; however, the vertical distance error is within76 cm:Accordingtothetasksurfaceandjointpositions, the tracking error of the boom varies greatly.Namely, the control performance for the TDC variesgreatly with the task surface and joint positions.The experimental results for the TDCSA using aPDSS and for the TDCSA using an ISS are shown inFigs. 13 and 14, respectively. The control performanceof TDCSA is better than that of TDC. The controlperformance of TDCSA does not vary greatly with thetask surface and joint positions. The whole verticaldistance error of the end-effector is within 74 cm forTDCSA using an ISS, whereas the vertical distanceerror is over 74 cm for TDCSA using a PDSS.Fig. 15 shows the experimental results of the abovethree controllers for the task surface with an incline of01; and Fig. 16 shows the power spectral density of thetracking errors in Fig. 15. In Fig. 15, the difference dueto TDCSA using an ISS is not that significant; yet thereexists a noticeable trend. As shown in Fig. 16, TDCSAusing an ISS results in the DC components of the powerspectral densities considerably smaller than those of theother two controllers. This trend is a direct outcome ofthe offset of the tracking error of TDCSA using an ISSsmaller than those of the other two controllers. A closeinspection of the tracking errors in Fig. 15 (a) revealsthat the tracking error due to TDCSA using an ISStends to fluctuate around zero, whereas those due to theother controllers tend to drift from zero. These resultssuggest that TDCSA using an ISS can decrease theoffset of the tracking error effectively, which still occursfor TDC and TDCSA using a PDSS.4.3.2. Contact conditionThe above experiments do not involve any contactwith the ground; but the straight-line motion in freespaces. Therefore digging or excavating work is not ourimmediate concern. Nevertheless, we have applied thestraight-line motion to leveling work, scraping theground with the bucket in contact with the ground.When leveling work is being done, friction due to thecontact behaves as a disturbance to position control ofTDCSA using an ISS. Since TDCSA using an ISS has02468405060708090100(a) Boom angledegreetimesec02468406080100120140(b) Arm angledegreetimesec02468020406080100120(c) Bucket angletimesecdegreeFig. 11. Angle trajectories for task surface (solid line stands for incline of 01; dashed line for incline of 301; and dotted line for incline of ?301).S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711706shown effectiveness in rejecting the disturbances, it doesnot require additional force control scheme.We have applied TDCSA using an ISS to levelingworks for the ground surfaces with inclines of ?301; 01and 301; respectively. The soil used at the experimentsis classified into gravel (GP group)poorly gradedgravel and graded-sand mixturesby the United SoilClassification, a generally used classification in civil02468_6_4_20246time(sec)errorcm(a) Bucket vertical error02468_1_0.500.51time(sec)errordeg.(b) Boom angle error02468_2_1012time(sec)errordeg.(c) Arm angle error02468_3_2_1012time(sec)errordeg.(d) Bucket angle errorFig. 13. Experimental results of TDCSA using a PDSS for task surface (solid line stands for incline of 01; dashed line for incline of 301; and dottedline for incline of ?301).02468_6_4_20246time(sec)errorcm(a) Bucket vertical error02468_1_0.500.51time(sec)errordeg.(b) Boom angle error02468_2_1012time(sec)errordeg.(c) Arm angle error02468_3_2_1012time(sec)errordeg.(d) Bucket angle errorFig. 12. Experimental results of TDC for task surface (solid line stands for incline of 01; dashed line for incline of 301; and dotted line for inclineof ?301).S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711707engineering(Bowles, 1982).Fig. 17 (a)shows theexperimental results that the bucket vertical error ismostly within 74 cm for three task surfaces, which issimilar to the results for non-contact condition. On thecontacting condition, the ground will prevent the bucketvertical error from having the large error of (-) directionby supporting the end-effector of the excavator, and thefriction force between the end-effector and the ground02468_6_4_20246time(sec)errorcm(a) Bucket vertical error02468_1_0.500.51time(sec)errordeg.(b) Boom angle error02468_2_1012time(sec)errordeg.(c) Arm angle error02468_3_21012time(sec)errordeg.(d) Bucket angle errorFig. 14. Experimental results of TDCSA using an ISS for task surface (solid line stands for incline of 01; dashed line for incline of 301; and dotted linefor incline of ?301).02468_3_2_1012345time(sec)errorcm(a) Bucket vertical error02468_0.4_0.6time(sec)errordeg.(b) Boom angle error02468_1.5_1_0.500.51time(sec)errordeg.(c) Arm angle error02468_2_1.5_1_0.500.51time(sec)errordeg.(d) Bucket angle errorFig. 15. Experimental results for task surface with incline of 01 (solid line stands for TDCSA using an ISS; dashed line for TDCSA using a PDSS;and dotted line for TDC).S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711708deteriorates the control performance of the arm link;however, it does not affect largely the error of the bucketvertical error due to the posture of the excavator. Theseresults verify that the position control approach basedon the TDCSA is effective in handling the contactcondition.From the experimental results of applying TDCSAusing an ISS to a 21-ton robotic excavator, the vertical00.81050010001500FreqHzPower spectral density(a) Bucket vertical error00.8102468FreqHzPower spectral density(b) Boom error00.810102030405060FreqHzPower spectral density(c) Arm error00.81010203040FreqHzPower spectral density(d) Bucket errorFig. 16. Power spectral density of tracking errors for task surface with incline of 01 (solid line stands for TDCSA using an ISS; dashed line forTDCSA using a PDSS; and dotted line for TDC).02468_6_4_20246time(sec)errorcm(a) Bucket vertical error02468_1_0.500.51time(sec)errordeg.(b) Boom angle error02468_2_1012time(sec)errordeg.(c) Arm angle error02468_3_2_1012time(sec)errordeg.(d) Bucket angle errorFig. 17. Experimental results for TDCSA using an ISS for task surface in contact the end-effector with the ground (solid line stands for incline of 01;dashed line for incline of 301; and dotted line for incline of ?301).S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711709distance error of the end-effector is mostly within74 cm for the task surfaces with inclines of 0;?301and 301; respectively. Considering that the accuracyachieved by an expert operator is usually within an errorof 75 cm at 0:5 m=s speed level, these results verifygood tracking performance of our proposed control law.5. ConclusionA TDCSA using an ISS was proposed in this paperfor the control of a 21-ton robotic excavator. Fromanalysis, we observed that the proposed control is morerobust against the disturbances and the parametervariations, which occur in the low-frequency range,than that of TDC and TDCSA using a PDSS. Throughexperiments, we observed that TDCSA using an ISS iseffective enough to control a 21-ton robotic excavator;and that our proposed control achieves better trackingperformances than an expert operator does. Consideringthat the experiments have been made over a broadmotion range, under realistic working speed conditions,and on task surfaces with various inclines, we canconfirm the validity of our proposed control algorithm.Appendix A. Dynamic modeling of the excavator systemWe will obtain the brief model of the roboticexcavator to design the controller. More details aboutthe model of a robotic excavator can be found in Changand Lee (2002).The dynamics of the manipulator consisting of boom,arm and bucket can be mathematically modeled asfollows:F Mll.l Vll;l Gll Frll;l;A:1where F denotes the 3 ? 1 vector of forces acting on thepistons in the cylinders, and l is the 3 ? 1 vector, eachelement of which represents the piston displacementrelative to the cylinder responsible for each link. Mll isthe 3 ? 3 inertial matrix, Vll;l is the 3 ? 1 vector ofcentrifugal and Coriolis terms, Gll is the 3 ? 1 vectorof gravity terms, and Frll;l is the 3 ? 1 vectorconsisting of various friction terms.Fig. 18 shows the hydraulic actuator circuit of aHyundai Robex210LC-3. In Fig. 18, the flow frompump 1 is divided and supplied to the boom cylinderand the bucket cylinder, via main valves; whereas pump2 supplies flow to the arm cylinder. Fig. 19 shows one setof a main valve and cylinder pertaining to a specific link.Now, consider the divide above, ignoring the com-pressibility of oil at junctions (a)(c) in Fig. 19. Then,from the continuity equation of flow at junctions (a)(c)and a linearized valve flow equation (Chang & Lee,2002), one can obtain linearized relationships of at eachlink as follows:Kpa ai0Kpa ci0Kpb biKpb ciKpc aiKpc biKpc ci26643775PaiPbiPci26643775Aaili? Ku aiui? Qrm aiAbili? Ku biui? Qrm biQsec i? Ku ciui? Kpc diPdi? Qrm ai26643775;A:2Fig. 18. Overall structure of the hydraulic circuit for boom, arm andbucket.Fig. 19. Detailed structure of the hydraulic circuit pertaining to a link(boom, arm and bucket).S.-U. Lee,

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