湖南工程学院学报自然科学版

圣维南原理（Saint Venant’s Principle）是弹性力学的基础性原理，是法国力学家圣维南于1855年提出的。其内容是：分布于弹性体上一小块面积（或体积）内的荷载所引起的物体中的应力，在离荷载作用区稍远的地方，基本上只同荷载的合力和合力矩有关；荷载的具体分布只影响荷载作用区附近的应力分布。还有一种等价的提法：如果作用在弹性体某一小块面积（或体积）上的荷载的合力和合力矩都等于零，则在远离荷载作用区的地方，应力就小得几乎等于零。不少学者研究过圣维南原理的正确性，结果发现，它在大部分实际问题中成立。因此，圣维南原理中“原理”二字，只是一种习惯提法。在弹性力学的边值问题中，严格地说在面力给定的边界条件及位移给定的边界条件应该是逐点满足的，但在数学上要给出完全满足边界条件的解答是非常困难的。另一方面，工程中人们往往只知道作用于物体表面某一部分区域上的合力和合力矩，并不知道面力的具体分布形式。因此，在弹性力学问题的求解过程中，一些边界条件可以通过某种等效形式提出。这种等效将出带来数学上的某种近似，但人们在长期的实践中发现这种近似带来的误差是局部的，这是法国科学家圣维南首先提出的。要点一、进行替换的两个力系必须是刚体力学的“等效”力系；二、力系替换的表面必须小，在替换表面附近的解失去精度。1 李传习,夏桂云,张建仁;复式钢管砼空心柱的抗压刚度[J];重庆交通学院学报;2004年02期 2 王艳;陈淮;;大跨度悬臂拼装施工连续梁桥0号梁段局部应力分析[J];铁道科学与工程学报;2008年03期 3 杨臻;史天骄;费庆国;;钢管混凝土系杆拱桥空间建模技术及其动力特性分析[J];水利与建筑工程学报;2009年01期 4 杨群;刘小兵;;空间钢管混凝土管节点有限元分析[J];湖南工程学院学报(自然科学版);2009年02期 5 谢肖礼,赵国藩,胡安妮,邹存俊;钢管混凝土拱桥施工过程中考虑温度效应的预抬高量二阶分析[J];工程力学;2005年04期 6 陈政清;杨群;李寿英;李瑜;;钢管混凝土拱桥管节点有限元分析[J];钢结构;2007年09期 7 周晓华,蒋翔;钢管混凝土轴压刚度取值比较[J];公路;2003年S1期 8 王艳;朱倩;陈淮;;刚性索自锚式悬索桥主缆锚固区局部应力分析[J];公路;2012年07期 9 葛素娟;李静斌;;水南特大桥主桥0#块局部有限元分析[J];公路交通科技;2006年06期 10 姜增国;熊诚;谢睿杰;;京沪高速铁路斜交连续梁桥0号块空间应力分析[J];建材世界11 谢肖礼;钢管混凝土拱桥徐变收缩对任意形状拱肋截面应力重分布的影响[D];广西大学;2002年 12 彭文立;钢管拱肋缆索吊装施工控制及模糊推理系统的应用[D];广西大学;2005年 13 钟轶峰;中（下）承式系杆拱桥有限元分析与施工监控[D];重庆大学;2006年 14张玉芬;复式钢管混凝土轴压性能及节点抗震试验研究[D];长安大学;2010年

1、 题名： 新型双连杆双曲轴内燃机滑块偏转仿真研究作者： 谭理刚;杨靖;龚志辉来源： 《内燃机工程》 ISSN :1000-0925,2005,26(3):57-602、 题名： 直喷式发动机燃油喷射过程的多维模型仿真作者： 刘金武;杨靖;高为国;倪小丹来源： 《系统仿真学报 》ISSN :1004-731X,2004,16(3):525-5293、 题名： 虚拟样机技术在SL1126内燃机设计中的应用研究作者： 易际明;杨靖;张亮峰来源： 《计算机辅助设计与图形学学报》 ISSN :1003-9775,2004,16(7):1016-10194、 题名： 基于案例的SL1126内燃机方案设计作者： 易际明;杨靖;张亮峰来源： 《机械设计》 ISSN :1001-2354,2004,21(12):35-375、题名： 支持Top-Down Design的内燃机参数化建模作者： 易际明;杨靖;张亮峰来源： 《中国制造业信息化》 ISSN :1672-1616,2004,33(3):100-1026、 题名： 直喷式发动机喷雾模型研究进展作者： 刘金武;杨靖;高为国;倪小丹来源： 《内燃机工程》 ISSN :1000-0925,2005,26(1):81-847、 题名： 柴油机的性能改进及缸内工作过程的三维数值模拟作者： 杨靖;肖明伟;崔东晓;邓帮林;周剑来源： 《湖南大学学报. 自然科学版 》ISSN :1000-2472,2006,33(4):50-548、 题名： 内燃机燃烧过程仿真后处理输入文件Ipost的研究作者： 刘金武;杨靖;高为国;倪小丹来源： 《湖南工程学院学报》 自然科学版 ISSN :1671-119X,2003,13(3):34-369、 题名： 关联设计技术及其在内燃机CAD系统中的应用作者： 易际明;朱理;杨靖来源： 《机械设计与研究》 ISSN :1006-2343,2004,20(3):89-90,9510、题名： 基于μC/OS-Ⅱ嵌入式内核的排气分析仪开发研究作者： 谭理刚;杨靖;潘朝辉;龚金科来源：《湖南大学学报》自然科学版 ISSN :1000-2472,2005,32(4):43-4611、题名： CAD系统软件数据交换技术的实现作者： 张亮峰;杨靖;彭浩舸来源：《湖南工程学院学报》自然科学版ISSN :1671-119X,2004,14(4):38-4012、题名： 双连杆内燃机动态仿真作者： 易际明;杨靖来源： 《系统仿真学报》 ISSN :1004-731X,2004,16(12):2780-278213、题名： 提高智能排气分析仪精度的研究作者： 杨靖;潘朝晖;周剑来源： 《内燃机工程》 ISSN :1000-0925,2004,25(2):75-7814、题名： 105系列直喷式柴油机新燃烧系统开发作者： 杨靖;李克;潘朝浑来源： 《内燃机工程》 ISSN :1000-0925,2003,24(6):13-1615、题名： 面向装配的智能变型设计技术及应用研究作者： 易际明;杨靖来源： 《湖南工程学院学报》 自然科学版 ISSN :1671-119X,2005,15(1):25-2916、题名： SL1115单缸双连杆柴油机配气凸轮型线的设计作者： 李蓉;杨靖来源： 《小型内燃机与摩托车》 ISSN :1002-8277,2000,29(2):1917、题名：轻型汽油车改装柴油机后发动机悬置系统和冷却系统的优化作者： 杨靖;肖明伟；崔东晓；邓帮林来源： 《客车技术与研究》 ISSN :1000-2472,2006,28(2):4918、题名： 内燃机燃烧过程仿真计算的双精度系统设计作者： 刘金武;杨靖;倪小丹;黄麓升来源： 《湖南工程学院学报》 自然科学版 ISSN :1671-119X,2004,14(2):40-43

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Sensorless torque control scheme ofinduction motor for hybrid electric vehicleYan LIU 1,2, Cheng SHAO1( Institute of Advanced Control Technology, Dalian University of Technology, Dalian Liaoning 116024, China; of Information Engineering of Dalian University, Dalian Liaoning 116622, China)Abstract: In this paper, the sensorless torque robust tracking problem of the induction motor for hybrid electric vehicle(HEV) applications is addressed. Because motor parameter variations in HEV applications are larger than in industrialdrive system, the conventional field-oriented control (FOC) provides poor performance. Therefore, a new robust PI-basedextension of the FOC controller and a speed-flux observer based on sliding mode and Lyapunov theory are developed inorder to improve the overall performance. Simulation results show that the proposed sensorless torque control scheme isrobust with respect to motor parameter variations and loading disturbances. In addition, the operating flux of the motor ischosen optimally to minimize the consumption of electric energy, which results in a significant reduction in energy lossesshown by : Hybrid electric vehicle; Induction motor; Torque tracking; Sliding mode1 IntroductionBeing confronted by the lack of energy and the increasinglyserious pollution, the automobile industry is seekingcleaner and more energy-efficient Hybrid ElectricVehicle (HEV) is one of the solutions. A HEV comprisesboth a Combustion Engine (CE) and an Electric Motor(EM). The coupling of these two components can be inparallel or in series. The most common type of HEV is theparallel type, in which both CE and EM contribute to thetraction force that moves the vehicle. Fig1 presents a diagramof the propulsion system of a parallel HEV [1].Fig. 1 Parallel HEV automobile propulsion order to have lower energy consumption and lower pollutantemissions, in a parallel HEV the CE is commonlyemployed at the state (n > 40 km/h or an emergency speedup), while the electric motor is operated at various operatingconditions and transient to supply the difference in torquebetween the torque command and the torque supplied bythe CE. Therefore fast and precise torque tracking of an EMover a wide range of speed is crucial for the overall performanceof a induction motor is well suited for the HEV applicationbecause of its robustness, low maintenance and lowprice. However, the development of a drive system basedon the induction motor is not straightforward because of thecomplexity of the control problem involved in the IM. Furthermore,motor parameter variations in HEV applicationsare larger than in industrial drive system during operation[2]. The conventional control technique ranging from theinexpensive constant voltage/frequency ratio strategy to thesophisticated sensorless control schemes are mostly ineffectivewhere accurate torque tracking is required due to theirdrawbacks, which are sensitive to change of the parametersof the general, a HEV operation can be continuing smoothlyfor the case of sensor failure, it is of significant to developsensorless control algorithms. In this paper, the developmentof a sensorless robust torque control system for HEVapplications is proposed. The field oriented control of the inductionmotor is commonly employed in HEV applicationsdue to its relative good dynamic response. However the classical(PI-based) field oriented control (CFOC) is sensitive toparameter variations and needs tuning of at least six controlparameters (a minimum of 3 PI controller gains). An improvedrobust PI-based controller is designed in this paper,Received 5 January 2005; revised 20 September work was supported in part by State Science and Technology Pursuing Project of China (No. 2001BA204B01).Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46 43which has less controller parameters to be tuned, and is robustto parameter variable parameters modelof the motor is considered and its parameters are continuouslyupdated while the motor is operating. Speed andflux observers are needed for the schemes. In this paper,the speed-flux observer is based on the sliding mode techniquedue to its superior robustness properties. The slidingmode observer structure allows for the simultaneous observationof rotor fluxes and rotor speed. Minimization of theconsumed energy is also considered by optimizing operatingflux of the The control problem in a HEV caseThe performance of electric drive system is one of thekey problems in a HEV application. Although the requirementsof various HEV drive system are different, all thesedrive systems are kinds of torque control systems. For anideal HEV, the torque requested by the supervisor controllermust be accurate and efficient. Another requirement is tomake the rotor flux track a certain reference λref . The referenceis commonly set to a value that generates maximumtorque and avoids magnetic saturation, and is weakened tolimit stator currents and voltages as rotor speed HEV applications, however, the flux reference is selectedto minimize the consumption of electrical energy as it is oneof the primary objectives in HEV applications. The controlproblem can therefore be stated as the following torque andflux tracking problems:minids,iqs,we Te(t) − Teref (t), (1)minids,iqs,we λdr(t) − λref (t), (2)minids,iqs,we λqr(t), (3)where λref is selected to minimize the consumption of electricalenergy. Teref is the torque command issued by thesupervisory controller while Te is the actual motor (3) reflects the constraint of field orientation commonlyencountered in the literature. In addition, for a HEVapplication the operating conditions will vary changes of parameters of the IM model need to be accountedfor in control due to they will considerably changeas the motor changes operating A variable parameters model of inductionmotor for HEV applicationsTo reduce the elements of storage (inductances), the inductionmotor model used in this research in stationary referenceframe is the Γ-model. Fig. 2 shows its q-axis (d-axisare similar). As noted in [3], the model is identical (withoutany loss of information) to the more common T-model inwhich the leakage inductance is separated in stator and rotorleakage [3]. With respect to the classical model, the newparameters are:Lm = L2mLr= γLm, Ll = Lls + γLlr,Rr = γ. 2 Induction motor model in stationary reference frame (q-axis).The following basic w−λr−is equations in synchronouslyrotating reference frame (d - q) can be derived from theabove model.⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩dλdrdt= −ηλdr + (we − wr)λqr + ηLmids,dλqrdt= −(we − wr)λdr − ηλqr + ηLmiqs,didsdt= ηβλdr+βwrλqr−γids+weiqs+1σLsVds,diqsdt=−βwrλdr+ηβλqr−weids−γiqs+1σLsVqs,dwrdt= μ(λdriqs − λqrids) −TLJ,dθdt= wr + ηLmiqsλdr= we,Te = μ(λdriqs − λqrids)(4)with constants defined as follows:μ = npJ, η = RrLm, σ = 1−LmLs, β =1Ll,γ = Rs + RrLl, Ls = Ll + Lm,where np is the number of poles pairs, J is the inertia of therotor. The motor parameters Lm, Ll, Rs, Rr were estimatedoffline [4]. Equation (5) shows the mappings between theparameters of the motor and the operating conditions (ids,iqs).Lm = a1i2ds + a2ids + a3, Ll = b1Is + b2,Rr = c1iqs + c2.(5)4 Sensorless torque control system designA simplified block diagram of the control diagram isshown in Fig. Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46Fig. 3 Control PI controller based FOC designThe PI controller is based on the Field Oriented Controller(FOC) scheme. When Te = Teref, λdr = λref , andλqr = 0 in synchronously rotating reference frame (d − q),the following FOC equations can be derived from the equations(4).⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ids = λrefLm+ λrefRr,iqs = Terefnpλref,we = wr + ηLmiqsλref.(6)From the Equation (6), the FOC controller has lower performancein the presence of parameter uncertainties, especiallyin a HEV application due to its inherent open loopdesign. Since the rotor flux dynamics in synchronous referenceframe (λq = 0) are linear and only dependent on thed-current input, the controller can be improved by addingtwo PI regulators on error signals λref − λdr and λqr − 0 asfollowids = λrefLm+ λrefRr+ KPd(λref − λdr)+KId (λref − λdr)dt, (7)iqs = Terefnpλref, (8)we = wr + ηLmiqsλref+ KPqλqr + KIq λqrdt. (9)The Equation (7) and (9) show that current (ids) can controlthe rotor flux magnitude and the speed of the d − q rotatingreference frame (we) can control its orientation correctlywith less sensitivity to motor parameter variations becauseof the two PI Stator voltage decoupling designBased on scalar decoupling theory [5], the stator voltagescommands are given in the form:⎧⎪⎪⎪⎨⎪⎪⎪⎩Uds = Rsids − weσLsiqs = Rsids − weLliqs,Uqs = Rsiqs + weσLsids + LmLrweλref= Rsiqs + weσLsids + weλref .(10)Because of fast and good flux tracking, poor dynamics decouplingperformance exerts less effect on the control Speed-flux observer designBased on the theory of negative feedback, the design ofspeed-flux observer must be robust to motor parameter speed-flux observer here is based on the slidingmode technique described in [6∼8]. The observer equationsare based on the induction motor current and flux equationsin stationary reference frame.⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩d˜idsdt= ηβ˜λdr + β ˜ wr˜λqr − γ˜ids +1LlVds,d˜iqsdt= −β ˜ wr˜λdr + ηβ˜λqr − γ˜iqs +1LlVqs,d˜λdrdt= −η˜λdr − ˜ wr˜λqr + ηLm˜ids,d˜λqrdt= ˜wr˜λ dr − η˜λqr + ηLm˜iqs.(11)Define a sliding surface as:s = (˜iqs − iqs)˜λdr − (˜ids − ids)˜λqr. (12)Let a Lyapunov function beV = . (13)After some algebraic derivation, it can be found that when˜ wr = w0sgn(s) with w0 chosen large enough at all time,then ˙V = ˙s · s 0. This shows that s will converge tozero in a finite time, implying the stator current estimatesand rotor flux estimates will converge to their real valuesin a finite time [8]. To find the equivalent value of estimatewr (the smoothed estimate of speed, since estimate wr is aswitching function), the equation must be solved [8]. Thisyields:˜ weq = wr˜λqrλqr + λdr˜λdr˜λ2qr +˜λ2dr −ηnp˜λqrλdr − λqr˜λdr˜λ2qr +˜λ2dr. (14)The equation implies that if the flux estimates converge totheir real values, the equivalent speed will be equal to thereal speed. But the Equation (14) for equivalent speed cannotbe used as given in the observer since it contains unknownterms. A low pass filter is used instead,˜ weq =11 + s · τ˜ wr. (15)Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46 45The same low pass filter is also introduced to the systeminput,which guarantees that the input matches the feedbackin selection of the speed gain w0 has two major constraints:1) The gain has to be large enough to insure that slidingmode can be ) A very large gain can yield to instability of the simulations, an adaptive gain of the slidingmode observer to the equivalent speed is = k1 ˜ weq + k2. (16)From Equation (11), the sliding mode observer structureallows for the simultaneous observation of rotor Flux reference optimal designThe flux reference can either be left constant or modifiedto accomplish certain requirements (minimum current,maximum efficiency, field weakening) [9,10]. In this paper,the flux reference is chosen to maximum efficiency at steadystate and is weaken for speeds above rated. The optimal efficiencyflux can be calculated as a function of the torquereference [9].λdr−opt = |Teref| · 4Rs · L2r/L2m + Rr. (17)Equation (17) states that if the torque request Teref iszero, Equation (8) presents a singularity. Moreover, theanalysis of Equation (17) does not consider the flux fact, for speeds above rated, it is necessary toweaken the flux so that the supply voltage limits are not improved optimum flux reference is then calculatedas:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩λref = λdr-opt,if λmin λdr-opt λdr-rated ·wratedwr-actual,λref = λmin, if λdr-opt λmin,λref = λdr-rated ·wratedwr-actual,if λdr-opt λdr-rated ·wratedwr-actual.(18)where λmin is a minimum value to avoid the division SimulationsThe rated parameters of the motor used in the simulationsare given byRs = Ω, Rr = Ω, Lls = 75 H,Llr = 105 H, Lm = mH, Ls = Lls + Lm,Lr = Llr + Lm, P = 4, Jmot = kgm2,J = Jmot +MR2tire/Rf, ρair = , Cd = = m2, Rf = , Cr = = m, M = 3000 kg, wbase = 5400 rpm,λdr−rated = shows the torque reference curve that representstypical operating behaviors in a hybrid electric . 4 The torque reference torque is modeled by considering the aerodynamic,rolling resistance and road grade forces. Its expression isgiven byTL = RtireRf(12ρairCdAfv2 +MCr cos αg +M sin αg).Figures in [5∼8] show the simulation results of thesystem of (considering variable motor parameters).Though a small estimation error can be noticed on the observedfluxes and speed, the torque tracking is still achievedat an acceptable level as shown in Figs. [5, 6, 8]. The torquecontrol over a wide range of speed presents less sensitivityto motor parameters presents the d and q components of the rotor flux λr is precisely orientated to d-axis because of theimproved PI shows clearly the real and observed speed in thedifferent phases of acceleration, constant and decelerationspeed with the motor control torque of . The variablemodel parameters exert less influence on speed shows the power loss when the rotor flux keeps constantor optimal state. A significant improvement in powerlosses is noticed due to reducing the flux reference duringthe periods of low torque . 5 Motor rotor flux λ Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46Fig. 6 Motor . 7 Power . 8 Motor ConclusionsThis paper has described a sensorless torque control systemfor a high-performance induction motor drive for aHEV case. The system allows for fast and good torquetracking over a wide range of speed even in the presence ofmotor parameters uncertainty. In this paper, the improvedPI-based FOC controllers show a good performance in therotor flux λdr magnitude and its orientation tracking. Thespeed-flux observer described here is based on the slidingmode technique, making it independent of the motor adaptation of the speed -flux observer is used tostabilize the observer when integration errors are present.

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Robotics education in the university* Rafael M. Inigo and Jose M. Angulo School of Engineering and Applied Science, University of Virginia, Charlottesville, Virginia 22901, USADept. de Informatica, Universidad de Deusto, Bilbao, Spain Available online 28 October 2004. The importance of automation and robotics in modern factories has required the introduction of courses on these subjects at the graduate and undergraduate levels in engineering schools. A comprehensive course on robotics must include the following subjects of fundamental importance: kinematics, dynamics, computer hardware and software, automatic control and machine vision. This paper describes the authors' experience in teaching a graduate robotics course at the University of Virginia and a short summer course at the Universidad de Deusto in Spain. Hands-on experience is a must in courses on robotics, and some simple yet effective systems designed and constructed by students are described. These include a program for transformation matrix manipulation, an operating system for manipulator control, and a simple three degrees of freedom programmable manipulator. The majority of the students who took both courses were electrical engineers, but mechanical engineers and computer scientists were also enrolled. Author Keywords: Robotics Education; Robotics Laboratory; Hardware; Software Development For Robotics Education *Parts of this paper were presented at the Second annual workshop on interactive computing, CAD/CAM: Electrical Engineering Education Washington,