输送机系统反馈控制

1、输送机系统反馈控制雷雠铿空等副娇份个涔仅站摘要 当输送带改变它的现在状态时就会引起高强度的瞬间压力，尤其是在它启动和制动时。这些压力对系统来说是有害的, 通常会缩短带的寿命。而且在一些严重的情形下，他们甚至能造成带的跑偏、带和托棍的磨损，因此，在输送机启动和制动时对输送带进行控制是十分必要的。祸戤窆俚枘膈陷处砑轰朊讳在这篇文章中，介绍给大家的是一种能减少这种瞬间压力的反馈控制方法。一个非连续的速度信号传递给反馈系统，并对比一下在正常情况下开环系统和闭环系统的各步反馈情况。在这里我们讨论的议题之一是系统的可控制性，当采用闭环系统时这是一个重要的因素。导佬斓遣耒蛄芳罕选躞樘插1 介绍闼濉败玮峥诮此

2、桫岢盆缟瘙带式输送机技术一直是以远距离运输大量物体、成本低的方式运用的。在现如今，它被广泛地应用于许多领域，例如：矿山运输煤、铁、石灰石等等。这些技术在操作时遇到的困难是在输送带上产生的驻波，尤其在启动和制动时。这些驻波通常引起带子跑偏，带子和托棍磨损会影响带子的寿命，维护费用会在短期内剧增。 吡蔻擢吕淙扰臼诸佾扮里鞫 这项研究是为了使瞬间压力最小化并降低维护费用。克服这些压力的一个原始的方法是设计一个高度安全的输送带(F.O.S)，这对执行预期的F.O.S标准很有意义。然而，这会导致系统成本的提高。现在，被广泛应用的方法是通过控制带子的启动和制动来减少带子加速和减速的变化比率。这常常被认为是

3、安全的启动或制动。一些方法已经被采用并被研究。这些研究主要地把重心集中在机械和电学的带式运输机。现在，被应用的平稳启动法是打开所有的回路。在系统开始和结束的时这些方法通常是不管用的。它们也是要经过一段时间来选择适当的方法使其达到一个令人满意的工作情况。一些方法甚至可能不包括驾驶超载保护，这也提高了超载费用。 在这篇文章中，介绍了在电动机上的电子反馈控制，这是一个闭环式控制方法。一个相似的方法早已在HARRISON1的文章中被简短地讨论过了, HARRISON1利用硅控整流器控制直流电动机。然而，这个研究的落实方法是在交流电动机2上使用矢量控制。直流电动机通常比交流电动机贵，尤其当维护费用也考虑

4、时。所以，交流电动机被普遍用于工业的输送带上。因此，该研究在全文中更适用。 研究中的反馈控制系统通过测量输送带各段的速度来计算电动机所需的输出量，测量的速度经由通信电缆被传输到主控制站。 这些主控制站处理从控制器一起获得的数据。然后，这些处理过的数据被用在驱动装置(可变电压、可变频率驱动装置)上，采用矢量空间的观念控制交流电动机。使用反馈控制方法的好处主要在于人们最关注的是系统达到最好的工作状态，而不是我们通常使用的开环系统。通过让负载在反馈控制系统中被平分并减少压力。这个系统也可以通过限制最小输出量来避免超负载。反馈控制系统的应用很容易达到稳定的状态。利用电子学控制的优点是降低保护成本和易于

5、远程控制。由于系统装置的需要，系统欠缺也会增加设备成本，如测量输送带速度传送器，传递信息和用于信息处理的微处理机的通信设备。由于维护费用低，你需要长期付维修费用。笆荒鹈睃杭耗缃夸觇颓卞觊控制的第一步是为工厂创造一个好的数学模型。 一些方法在过去已经被学习。大多数方法是离散模型而不是那些存在致命缺点的连续模型。这种连续模型的结果是通常被以部分微分方程式的形式表达的，包含着非常复杂的关系。 同时，用于部分的微分方程式的输送装置的带子短暂性是非常难的。因此，连续模型还没有广泛地用在输送装置带子的分析上。晋掠痖硭惰鹱荛朗垡摧杌朕一个不连续模型把连续的带子分成一个有有限数字的片段而且假设相同的片段里面的

6、原动力基本相同，例如，在带子的一段里有相近的持续速度，伸度，压力等。这个假设引起在不连续模型间取离散值的误差，它赖于被用的带子片段的数字和模型的量子化。诧形讣崃嫉驳铀按烤焯癸靥用一个恰当的数学模型, 一个合理的控制策略能有利于得到有效的模拟结果。一个大的模拟误差总能导致错误的模拟输出和不正确的使用控制参量。使用流变学的模型描述输送带的纵向动态属性，凯尔文固体模型是一个弹簧与平行的一个黏弹性元件，它是对大多数带式输送机分析简单和相对地准确。当一个分散模型代表一条连续的传送带时引用量子化误差。对于使用的模型, 传送带的固有频率的相对误差与带被分段的数量成反比，依照由公式1-1：陵赉舌薇竦赓茯郎园不

7、焙扌 （1-1）钣漩蚓孙怊漉压劳嘿要癀蹋是连续的输送带固有频率, 是分散输送带固有频率，并且n是输送带段的数量。虽然使用大量输送带段数实现一个小量子化误差是可行的，但当这指数地增加和n增加时对模拟时间是不利的。位置速度被广泛应用于描述输送带的动力学方法上。但是这种方法导致一个系统线性时间变化。例如，在时间t输送带i段起初应用电动机的力。但是, 在时间t+1, 电动机的力不再在i段起作用而i+1段起作用。所以, 当带运行时检测段的位置必与时间有关。位置速度方法表达将必根据时间变化。明显地这种方法导致一个更加复杂的模型。在这研究中采取应变速度法，它开发一个线性时间不变式的系统。输送带各段的应力和速

8、度与地面保持同样。因此, 这种方法避免时间变化的问题并建立一个简单模型。沉召斯沽坜婺酵峄召夂确撼传送带的一个离散模型，从带的n段表示力，公式1-2描述了速度改变率，和v分别表示应力和速度，是应用于电动机的原动力。泼坯雌腹砝铈甫秣印舌坛么 (1-2)君漏寄部樾泮溘钕箧物姬菊公式1-3应力变化率：踏珐窍陡趵恋埃妾丝伽兮聚 （1-3）缯剃崖辰服哏枣丁饭骨葡达不同于剩余的段, 代替重量的重力是一个另外模型。所以, 它必须分开地被对待。在重力上速度和应力的变量依靠重量, 如k段，能用公式1-4和1-5分别表示：政盲芳居芥吻癍彰钛捱砧挽 (1-4)松租甭冖氮撙胜蓝裟拍匹蛏 (1-5)灵适挂彘猴镑券损扫髓茺

9、贿上面所有等式可以用公式1-6表示：吸趴尜印宿佟截殆甏诟妍缨 ，W= （1-6）容两腐娈蝎婺灞爽藤假币笙公式16的表示形式叫做张力速度模块，运用一个已知W和u数字方法解决张力速度模块，能获得每段带的张力和速度。RUNGE-KUTTA 方法就是使用数字化的一个例子。人们目标是为了发现输送带的各段张力或应力。通常用表示应力，公式1-7为一个固体模块表达式3：坍抽崾悱袍掉酊忝苤副隋驭 （1-7）廷馔嫱笺沸喝蚀楼圆倍妻群E是模数，是黏度系数。公式1-7 表示减少张力和速度最大值, 应力也减小。唾绵濂袋艾栉肾佛荀舀礼铭基于这点，创造了一个多输入多输出(MIMO) 系统。常用的控制MIMO系统的三个方法是

10、杆连接式、线性二次调节器(LQR) 11 和H无限12 。杆连接式方法要求一个准确模块, 这样杆可根据所用的模块被安置在需要的地点。否则, 不正确安置杆将会导致能源浪费和控制错误。使用分散式张力速度模块是连续操作装置的略计, 因此，许多不确定性总存在。在一些情况下杆连接式方法不会是一种好控制方法。H无限方法是一种好控制方法, 但是对管理者来说会相对地复杂的并导致一个高动态指令。选择LOR 方法取决于处理模块的错误能力和在使用中它的适应能力强。但是, 选择适当的控制参量对LOR是困难的。因为不适当的参量容易地形成一个振动系统, 即过调节反应, 选择控制参量必须相当谨慎。培矜痢溧恨全抗撞处溺痿墉图

11、1反馈控制系统的结构图。W表示带上装载物体的重量, e代表速度误差并且u是原动力。传送带通过张力速度模块描述它的动力性。一个PI 控制器参考速度被用于控制驱动。如先前提及的, 运用LQR 方法计算比例值。H 矩阵的目的将反馈状态数量从x 降低到x, x 代表各传送带段的张力和速度, x 只表示速度。这称递减状态反馈。整个反馈系统会将模块里的所有状态反馈给控制器。由于测量的张力困难, 仅用速度反馈。使用流速计容易得到速度。值得注意的是, 在这个反馈控制系统中速度是主要环节, 系统会给一个相应的递减状态反馈反应。潦戍唾绶敬翰胺夏凭萏腑啦图1：传送带系统反馈控制块图肤叟廨焘欢蠃担糠仑敏窳蛉郛柔枉煸锂

12、起抠鬃恹诽跫阝在设置控制器上必须被强调获取一定数量的技术。控制器的主要目标是在系统上达到最宜控制, 产生快速度变化反应、低稳定状态和瞬间应变。用比例控制器提高系统的反应。但是, 需要高控制作用力产生高比例输出。另外, 由于使用控制方法, 递减状态反馈会导致高比例输出并产生过调节反应, 并且导致高瞬应变, 好的控制器将对系统给出的零稳定状态的误差做成反应。一个小的输出会降低系统响应, 需要长时间到达零的稳定状态误差。但是, 大的输出量能产生不稳定系统。所以, 选择适当的控制器输出量能得到一个性能好的系统。当驱动输出比例总相等时，可达到最小瞬变应变,。通过设置相同驱动输出, 可达到极小的稳定状态应

13、变。这归结于在驱动装置之间均分了负载。并且, 限制控制装置输出力以致从驱动装置它不需要不合情理地大功率, 而且在实践中能防止超载驱动。郗赡狁驻聋恁橡塞虽戟钡必如果电源故障，所有电子控制器和电机将被关闭并导致输送带未管制停止。克服这个问题方法是使用某种蓄装置，譬如DC公共汽车整流器电容器，它能为控制器和电动机提供能量。不用太多能量就能完成带的停滞控制。这表明闭合回路控制能产生一个稳定性和性能好系统。大磁极有快速的反应即低过调节和短增时间。所以,，转移大杆只能浪费能量。然而，转移小杆能产生好的性能，从而元件的频率和的阻尼率增加。闭合回路系统产生一个平稳速度反应但是开环系统不稳定达到调整点时。结果也

14、表示开环系统与闭合回路系统比较能获得更短调节时间、低输出。一个闭合回路系统的短调节时间的方式为了增加比例量。高放大系统通过四次增加比例量，但不是整体的量。许多增量导致系统过调节或者甚至系统不稳定。系统主要目标是达到零的稳定状态误差。所以，一个好系统在瞬时状态期间不影响综合化，但仍然能达到零的稳定状态误差。小复杂杆开始控制造成一个振动反应。但是，期望快速的反应因为系统由高频率元件控制。这些是在杆的定位件和反应的之间关系11 。开环系统与闭合回路系统相比产生高瞬间应变。并且, 高输出闭合回路系统产生高瞬间应变。这是许多高速度变化率造成的。开环系统比闭合回路有更高的平稳性，在闭合回路系统中，两驱动装

15、置之间均分载荷。在整体传送带过程中它产生极小的稳定状态应变区别。拗力吁檩崞傩掀珉辖珊呈袖当应用反馈控制时，在研究中一个重要问题是系统的可控性。一个无法控制的系统通过控制器也不能影响的其状态，换句话说，系统无法影响模块的所有杆。这导致系统不能充分地控制反应。未控制的大杆对系统无影响，因为他们不能由控制器移动。但是, 按LOR 方法要求将有一个完全地可控制的系统。完成第一情况的完全地可控制的系统至少有二驱动装置控制传送带。第二，把传送带以一个好的和简单的方式划分成有限段，但这也许会产生一个无法控制的系统。可调性由传送带驱动装置的位置确定。由于带的紧线的重量，会产生移动的波形。这导致一个无法控制的系

16、统变得可控制。但是, 因为紧线器重量与传送带长度比较相对地小，波形不会转移。这产生一个微弱地可控制的系统。所以，使用传送带段的质数可避免无法控制的问题，即达到一个完全地可控系统。从可控性模块数寻找可控性度的方法。哺临洪捌抽鳗馗永蜀蜞捂胶在此文，介绍的反馈控制系统在传送带上使驻波减到最小。反馈控制系统比常用的开环控制系统有更好的性能。闭合回路系统能均分电机之间负载使应变减到最小，但是在开环系统中均分驱动装置之间的载荷是困难的。在电机之间一个轻微的差距会对负载产生不同的滑移和扭矩。闭合回路系统能容易地限制输出量避免超载驱动。这个反馈控制系统缺点是招致额外成本，它取决于需要的额外驱动装置。但是，衡量

17、其价值和性能，发现该系统值得实施。控制策略是在提高系统的性能上进一步研究。舻饭醮冀踞薅闾膨撺钥淆鲸蛊付射艋瘦欤卺饱嘱鲇愉厶Feedback control of convey systems兼簧寺贪妹化简唱税砗氵切Summary瓮韪槔征骇骂酣扮轰寇以燔High transient stresses are induced when a conveyor belt changes its current status, especially during starting and stopping. These stresses are harmful to the system, which

18、usually shorten the belt life span. And in some serious cases, they can even result in belt splice, belt and pulley structure damage. Therefore, controlled starting and stopping of the drives to the conveyor belt are always needed.尤聪艽怖莸哄佟吓酸铅藉桁In this paper, a feedback control method is introduced to

19、 reduce these transient stresses. A discrete strain-velocity model was developed which allows the analysis of the feedback control system to be performed. Comparisons between the step response of a normal open loop system and closed loop systems were made. One of the issues discussed here is the con

20、trollability of the system, which is an important factor when the closed loop system is implemented.罱逃蒌陬病电原啡药宜材疖1.Introduction粑嗪胤纬屹莉娅蔺愣卵查饕Belt conveyor technology is still the most cost-effective way of transporting bulk solids continuously over a long distance. In the present day, it is widely used

21、 in many fields such as mining industries to transport coal, iron ore, limestone ect. Problem with this technology is the development of the standing waves in the belt during operations, especially at starting and stopping. These standing waves induce stresses to the belt life span, by causing belt

22、splice or even belt and pulley structure damage. The cost of maintenance would be increased tremendously.灭茁坻迩娟馅绔捐皂缙杰吞Research is conducted to minimize the transient stresses and to lower the cost of maintenance. An initial method to overcome these stresses is to design the belt with a very high fact

23、or of safety (F.O.S), which typically has a value of ten to the desired operating F.O.S. However, this will incur high costs to the system. Nowaday, a widely used method reduces the rate of change of belt acceleration and deceleration (“jerk”or “shock”) by controlled starting and stopping of the dri

24、ves to the belt.酱筹瓦庭既蚁雇贻捷博侈髀This is also commonly known as soft starting or stopping. A number of approaches have been adopted and studied. These are mainly focused on mechanical and electrical soft starting stopping of the conveyor belts. Currently, the soft starting methods used are all open loop

25、approaches. These approaches normally do not give a good performance on starting and stopping of the system. They are also time consuming to set up properly to achieve a satisfactory performance. Some of these methods might not even consist of drive overload protection, which give rise to significan

26、t overload costs.萃惹偶挥翌糖锣害窘舁晁亠In this paper, a power electronic feedback control on the drive motors, which is a closed loop control method, is introduced. A similar method has been briefly discussed in an early paper by HARRISON 1, who uses Thysitor/SCR to control DC motor. However, the implementati

27、on approach in this research uses the vector control on AC motors 2 DC motors are generally more expensive than AC motors, especially when maintenance costs is taken into account. Therefore, AC motors are more commonly used on the conveyor belts in industry, hence, this research will be more applica

28、ble in this context.铨影啪舷藕袈闹趸珙锦梳朴The feedback control system in this research measures the velocities for each segment of the belt to calculate the output power needed for the motors. The velocities measured are transmitted, via a communication cable, to the master stations. These master stations pro

29、cess the data received together with the controller gains. The processed data are then being used on WF drives (variable voltage variable frequency drives), which adopt the concept of vector space to control the AC motors. The advantages of using a feedback control method are mainly concentrated on

30、achieving a better performance system than the open loop system which is currently in common use. Stresses can be minimized by allowing the load to be shared equally among drives in the feedback control system. This system can also limit the maximum output power to avoid drive overload. Zero steady

31、state error can be reached easily using the feedback control system. The advantages of using power electronics control are low cost of maintenance and the ease with which remote on-line monitoring can be achieved. A drawback of the system is a slight increase in installation costs due to the extra d

32、evices needed, such as transducers to measure the belt speed, communication devices to transfer data and microprocessors for data processing. This pays in the long run because of low maintenance costs.史隽麂邈鱼菅喋株骧鑫啪迤The first step towards control is to create a good mathematical model for the plant. A

33、number of approaches have been studied in the past 3-9. Most of these approaches use discrete models instead of continuous models due to an important disadvantage of the continuous models. The resultant solution from the continuous model, which is normally expressed in the form of partial differenti

34、al equations, contains very complex relationships. Also, it is very difficult to express the transient characteristics of the conveyor belt using partial differential equations. Therefore, continuous models have not been popularly used on the conveyor belt analysis.仲厢妲珏郧潞气蓄逦撵累舔A discrete model divid

35、es the continuous belt into a finite number of segments and assumes that the dynamics within the same segment are closely identical, i.e., approximately constant velocity, stretch, stress etc. within a segment of the belt. This assumption induces a quantization error in the discrete model, which dep

36、ends on the number of belt segments and the model used.囚螽榍镂弪惨溱露刖屹忱柑With a good mathematical model, a satisfactory control strategy can be applied to give valid simulation results. A large modeling error could always result in wrong simulation outputs and incorrect control parameters used.苌役骡报售艋舴眩枵肓猓

37、焰The rheological models used for describing the longitudinal dynamic properties of the belt have been studied by a number of researchers. The KELVIN solids model, which is a spring in parallel with a viscoelastic element, is most commonly used due to the fact that it is analytically simple and relat

38、ively accurate for most of the conveyor belt. Quantization error is induced when representing a continuous belt by a discrete model. For the model used, the relative error of the natural frequency of the belt is inversely proportional to the number of segments into which the belt has been divided, a

39、s illustrated by Eq. (1) 10父薛幢蟒合悱韩卷惑睇鹈臼 (1)锔茭妙醅坡锭曰仉焐磺京丝Where is, the natural frequency of continuous belt, is the natural frequency of discrete belt and n is the number of belt segments. Although it is desirable to use a large number of belt segments in order to achieve a small quantization error, t

40、he simulation time is a drawback as this increases exponentially as n increases.赃陇脶邬夕莓逃氨痊舂冒粕Position-velocity is the most widely used approach to describe the dynamics of the conveyor belt. However. this approach produces a linear time varying system. Which means the forces that apply to each segmen

41、t of a moving conveyor belt vary from time to time. For example, a motor force is initially applied to segment i of a moving conveyor belt at time t. However, at time t+1, the motor force would no longer be acting on segment I but on segment I+ 1. Therefore, the segments position must be monitored w

42、ith respect to time when the belt moves. The expressions for the position-velocity approach will also have to vary according to time. This approach will obviously result in a more complicated model. The strain-velocity approach is adopted in this research, which develops a linear time invariant syst

43、em. The strains and velocities for each segment of a moving conveyor belt always remain on the same spot with respect to the ground. Hence, this approach avoids the time varying issue and establishes a much simpler model.渔趿媵坠崩涞投圮媚固堕笙A discrete model of the conveyor belt. From the forces which act on

44、 the segment n of the belt, an equation for the rate of change of velocity can be described by Eq. (2), in terms of strain and velocity which are commonly denoted as and v respectively. is the motor force applied to the conveyor belt.袅浠珉忿蹁倨谮萄萦檀刍笛 (2)惑姊缬旱扭涿糌泥鹭篷拯巍The rate of change of strain is expres

45、s in Eq.(3)能盎蹈失悌柁拶挨锋钽粱孪 (3)狡竺灿猝浏报剂馍仨钳蜞返Unlike the rest of the segments, the gravity take up weight has a different model. Therefore, it has to be treated separately. The derivative of velocity and derivative of strain on the gravity take up weight, say segment k, can be described by Eqs. (4) and (5)

46、 respectively;榷孜缮离捞妍卅蟆鲞镖竣尔 (4)蛀碰当呵菊铝白蚧悲捣坎侬 (5)趺仑钲游炉儆璨趟闭蚶窀炅All the equations above can be presented in a form equivalent to a standard statespace representation, as in Eq. (6):聱肓仵尘糜恒呻资飒玳证釜 W= (6)粳酲怄菰壳肥忠锩等岱仿纭This expression, Eq. (6), is called the Strain-Velocity model. By solving the Strain-Velocity

47、model using a numerical method a given W and u, the strains and velocities for each segment the belt can be obtained. An example of the numerical methods used would be RUNGE-KUTTA method. The man aim is to find tension or stress for each segment of the belt. The stress, commonly denoted by , for a s

48、olid model can be expressed by Eq. (7) 3;灭瘁邵摇钙懈猹滟澄愕堂鲜 (7)欣潴勇伦涵业澜握蕉榀庄呢where E is YOUNGS modulus and is the viscosity coefficient. Eq. (7) shows that by reducing the maximum strains and velocities, the stresses can be minimized.拦齑胁湓璧鲎遄钲贰熔汉匹In this point, a Multiple Input-Multiple Output (MIMO) system

49、has been created. The three methods that are commonly used to control a MIMO system are pole placement, Linear Quadratic Regulator (LQR) 11 and H-infinity 12. The pole placement method requires an accurate model such that poles can be placed at desired locations according to the model used. Otherwis

50、e, incorrect placing of poles would result in a waste of energy and controlling errors. The discrete Strain-Velocity model used is an approximation of the continuous plant, therefore, an amount of uncertainty always exists. The pole placement method would not be a good control approach in this case.

51、 TheH-infinity method is a good control approach, but is relatively complicated and results in a very high dynamic order for the controller. The LOR method is chosen due to the robustness capability of handling modeling error and its ease in use. However, choosing appropriate control parameters for

52、LOR is difficult. Since inappropriate parameters would easily result in an oscillatory system, i.e. response with overshoots, the control parameters have to be chosen extremely carefully.若燹园掴副镏军悚鲅硖怠扃Fig.1; illustrates the block diagram of a feedback control system. W represents the weight of the loa

53、d on the belt, e represents the velocities errors and u is the motors force. The plant, i.e. the conveyor belt, has its dynamics described by the Strain Velocity model. A P1 (proportional and integral) controller with speed reference, V is used to control the drives. As mentioned previously, the LQR

54、 method is applied to calculate the proportional and integral gain. The purpose of H matrix is to reduce the number of feedback states from x to x, where x represents the strains and velocities of each belt segment, and x represents the velocities only. This is called the reduced-state feedback. A f

55、ull-state feedback system would have all the states in the model being fed back to the controller. Due to the difficulty in measuring strains, only velocities are fed back. Velocities can easily be measured using tachometers. It should be noted that as the velocities are the main concerns of the sta

56、tes in this feedback control system, the system would still give a similar response with the reduced-state feedback.咸粲炻等权鼽狠镑鸺貌呢僬Fig3: Block diagram of feedback control of a conveyor system 後乏驰芟旄瑰妾栅爱鹑砌使 A number of techniques on setting the controller gains have to be emphasized. The main aim of the

57、controller is to achieve an optimum control on the system, which produces fast response on velocity changes and, low steady state and transient stresses. The use of proportional controller is to speed up the response of the system. However, large control efforts are needed to produce high proportion

58、al gains. In addition, due to the control method used, reduced-state feedback would cause the high proportional gains to produce high overshoots response, and results in high transient stresses, The integral controller gives a zero steady state error response to the system. A small integral gain slows down the system response, where it takes a long period of