外文翻譯--輸送機系統(tǒng)反饋控制

1、<p><b>　　輸送機系統(tǒng)反饋控制</b></p><p>　　摘要 當(dāng)輸送帶改變它的現(xiàn)在狀態(tài)時就會引起高強度的瞬間壓力，尤其是在它啟動和制動時。這些壓力對系統(tǒng)來說是有害的, 通常會縮短帶的壽命。而且在一些嚴(yán)重的情形下，他們甚至能造成帶的跑偏、帶和托棍的磨損，因此，在輸送機啟動和制動時對輸送帶進行控制是十分必要的。</p><p>　　在這篇文章

2、中，介紹給大家的是一種能減少這種瞬間壓力的反饋控制方法。一個非連續(xù)的速度信號傳遞給反饋系統(tǒng)，并對比一下在正常情況下開環(huán)系統(tǒng)和閉環(huán)系統(tǒng)的各步反饋情況。在這里我們討論的議題之一是系統(tǒng)的可控制性，當(dāng)采用閉環(huán)系統(tǒng)時這是一個重要的因素。</p><p><b>　　1 介紹</b></p><p>　　帶式輸送機技術(shù)一直是以遠(yuǎn)距離運輸大量物體、成本低的方式運用的。在現(xiàn)如今，它被

3、廣泛地應(yīng)用于許多領(lǐng)域，例如：礦山運輸煤、鐵、石灰石等等。這些技術(shù)在操作時遇到的困難是在輸送帶上產(chǎn)生的駐波，尤其在啟動和制動時。這些駐波通常引起帶子跑偏，帶子和托棍磨損會影響帶子的壽命，維護費用會在短期內(nèi)劇增。 </p><p>　　這項研究是為了使瞬間壓力最小化并降低維護費用。克服這些壓力的一個原始的方法是設(shè)計一個高度安全的輸送帶(F.O.S)，這對執(zhí)行預(yù)期的F.O.S標(biāo)準(zhǔn)很有意義。然而，這會導(dǎo)致系統(tǒng)成本的提高

4、?，F(xiàn)在，被廣泛應(yīng)用的方法是通過控制帶子的啟動和制動來減少帶子加速和減速的變化比率。這常常被認(rèn)為是安全的啟動或制動。一些方法已經(jīng)被采用并被研究。這些研究主要地把重心集中在機械和電學(xué)的帶式運輸機?，F(xiàn)在，被應(yīng)用的平穩(wěn)啟動法是打開所有的回路。在系統(tǒng)開始和結(jié)束的時這些方法通常是不管用的。它們也是要經(jīng)過一段時間來選擇適當(dāng)?shù)姆椒ㄊ蛊溥_到一個令人滿意的工作情況。一些方法甚至可能不包括駕駛超載保護，這也提高了超載費用。 在這篇文章中，介紹了在電動

5、機上的電子反饋控制，這是一個閉環(huán)式控制方法。一個相似的方法早已在HARRISON[1]的文章中被簡短地討論過了, HARRISON[1]利用硅控整流器控制直流電動機。然而，這個研究的落實方法是在交流電動機[2]上使用矢量控制。直流電動機通常比交流電動機貴，尤其當(dāng)維護費用也考慮時。所以，交流電動機被普遍用于工業(yè)的輸送帶上。因此，該研究在全文中更適用。 研究中的反饋控制系</p><p>　　控制的第一步是為

6、工廠創(chuàng)造一個好的數(shù)學(xué)模型。 一些方法在過去已經(jīng)被學(xué)習(xí)。大多數(shù)方法是離散模型而不是那些存在致命缺點的連續(xù)模型。這種連續(xù)模型的結(jié)果是通常被以部分微分方程式的形式表達的，包含著非常復(fù)雜的關(guān)系。 同時，用于部分的微分方程式的輸送裝置的帶子短暫性是非常難的。因此，連續(xù)模型還沒有廣泛地用在輸送裝置帶子的分析上。</p><p>　　一個不連續(xù)模型把連續(xù)的帶子分成一個有有限數(shù)字的片段而且假設(shè)相同的片段里面的原動力基本相同，例如

7、，在帶子的一段里有相近的持續(xù)速度，伸度，壓力等。這個假設(shè)引起在不連續(xù)模型間取離散值的誤差，它賴于被用的帶子片段的數(shù)字和模型的量子化。</p><p>　　用一個恰當(dāng)?shù)臄?shù)學(xué)模型, 一個合理的控制策略能有利于得到有效的模擬結(jié)果。一個大的模擬誤差總能導(dǎo)致錯誤的模擬輸出和不正確的使用控制參量。使用流變學(xué)的模型描述輸送帶的縱向動態(tài)屬性，凱爾文固體模型是一個彈簧與平行的一個黏彈性元件，它是對大多數(shù)帶式輸送機分析簡單和相對地準(zhǔn)

8、確。當(dāng)一個分散模型代表一條連續(xù)的傳送帶時引用量子化誤差。對于使用的模型, 傳送帶的固有頻率的相對誤差與帶被分段的數(shù)量成反比，依照由公式1-1：</p><p><b>　?。?-1）</b></p><p>　　是連續(xù)的輸送帶固有頻率, 是分散輸送帶固有頻率，并且n是輸送帶段的數(shù)量。雖然使用大量輸送帶段數(shù)實現(xiàn)一個小量子化誤差是可行的，但當(dāng)這指數(shù)地增加和n增加時對模擬時

9、間是不利的。位置速度被廣泛應(yīng)用于描述輸送帶的動力學(xué)方法上。但是這種方法導(dǎo)致一個系統(tǒng)線性時間變化。例如，在時間t輸送帶i段起初應(yīng)用電動機的力。但是, 在時間t+1, 電動機的力不再在i段起作用而i+1段起作用。所以, 當(dāng)帶運行時檢測段的位置必與時間有關(guān)。位置速度方法表達將必根據(jù)時間變化。明顯地這種方法導(dǎo)致一個更加復(fù)雜的模型。在這研究中采取應(yīng)變速度法，它開發(fā)一個線性時間不變式的系統(tǒng)。輸送帶各段的應(yīng)力和速度與地面保持同樣。因此, 這種方法避免

10、時間變化的問題并建立一個簡單模型。</p><p>　　傳送帶的一個離散模型，從帶的n段表示力，公式1-2描述了速度改變率，ε和v分別表示應(yīng)力和速度，是應(yīng)用于電動機的原動力。</p><p><b>　　(1-2)</b></p><p>　　公式1-3應(yīng)力變化率：</p><p><b>　?。?-3）<

11、;/b></p><p>　　不同于剩余的段, 代替重量的重力是一個另外模型。所以, 它必須分開地被對待。在重力上速度和應(yīng)力的變量依靠重量, 如k段，能用公式1-4和1-5分別表示：</p><p><b>　　(1-4)</b></p><p><b>　　(1-5)</b></p><p>

12、;　　上面所有等式可以用公式1-6表示：</p><p>　　，，W= （1-6）</p><p>　　公式1－6的表示形式叫做張力速度模塊，運用一個已知W和u數(shù)字方法解決張力速度模塊，能獲得每段帶的張力和速度。RUNGE-KUTTA 方法就是使用數(shù)字化的一個例子。人們目標(biāo)是為了發(fā)現(xiàn)輸送帶的各段張力或應(yīng)力。通常用表示應(yīng)力，公式1-7為一個固體模塊表達式[3]

13、：</p><p><b>　?。?-7）</b></p><p>　　E是模數(shù)，η是黏度系數(shù)。公式1-7 表示減少張力和速度最大值, 應(yīng)力也減小。</p><p>　　基于這點，創(chuàng)造了一個多輸入多輸出(MIMO) 系統(tǒng)。常用的控制MIMO系統(tǒng)的三個方法是桿連接式、線性二次調(diào)節(jié)器(LQR) [11] 和H無限[12] 。桿連接式方法要求一個準(zhǔn)確

14、模塊, 這樣桿可根據(jù)所用的模塊被安置在需要的地點。否則, 不正確安置桿將會導(dǎo)致能源浪費和控制錯誤。使用分散式張力速度模塊是連續(xù)操作裝置的略計, 因此，許多不確定性總存在。在一些情況下桿連接式方法不會是一種好控制方法。H無限方法是一種好控制方法, 但是對管理者來說會相對地復(fù)雜的并導(dǎo)致一個高動態(tài)指令。選擇LOR 方法取決于處理模塊的錯誤能力和在使用中它的適應(yīng)能力強。但是, 選擇適當(dāng)?shù)目刂茀⒘繉OR是困難的。因為不適當(dāng)?shù)膮⒘咳菀椎匦纬梢粋€振

15、動系統(tǒng), 即過調(diào)節(jié)反應(yīng), 選擇控制參量必須相當(dāng)謹(jǐn)慎。</p><p>　　圖1反饋控制系統(tǒng)的結(jié)構(gòu)圖。W表示帶上裝載物體的重量, e代表速度誤差并且u是原動力。傳送帶通過張力速度模塊描述它的動力性。一個PI 控制器參考速度被用于控制驅(qū)動。如先前提及的, 運用LQR 方法計算比例值。H 矩陣的目的將反饋狀態(tài)數(shù)量從x 降低到x`, x 代表各傳送帶段的張力和速度, x' 只表示速度。這稱遞減狀態(tài)反饋。整個反饋系

16、統(tǒng)會將模塊里的所有狀態(tài)反饋給控制器。由于測量的張力困難, 僅用速度反饋。使用流速計容易得到速度。值得注意的是, 在這個反饋控制系統(tǒng)中速度是主要環(huán)節(jié), 系統(tǒng)會給一個相應(yīng)的遞減狀態(tài)反饋反應(yīng)。</p><p>　　圖1：傳送帶系統(tǒng)反饋控制塊圖</p><p>　　在設(shè)置控制器上必須被強調(diào)獲取一定數(shù)量的技術(shù)?？刂破鞯闹饕繕?biāo)是在系統(tǒng)上達到最宜控制, 產(chǎn)生快速度變化反應(yīng)、低穩(wěn)定狀態(tài)和瞬間應(yīng)變。用比例

17、控制器提高系統(tǒng)的反應(yīng)。但是, 需要高控制作用力產(chǎn)生高比例輸出。另外, 由于使用控制方法, 遞減狀態(tài)反饋會導(dǎo)致高比例輸出并產(chǎn)生過調(diào)節(jié)反應(yīng), 并且導(dǎo)致高瞬應(yīng)變, 好的控制器將對系統(tǒng)給出的零穩(wěn)定狀態(tài)的誤差做成反應(yīng)。一個小的輸出會降低系統(tǒng)響應(yīng), 需要長時間到達零的穩(wěn)定狀態(tài)誤差。但是, 大的輸出量能產(chǎn)生不穩(wěn)定系統(tǒng)。所以, 選擇適當(dāng)?shù)目刂破鬏敵隽磕艿玫揭粋€性能好的系統(tǒng)。當(dāng)驅(qū)動輸出比例總相等時，可達到最小瞬變應(yīng)變,。通過設(shè)置相同驅(qū)動輸出, 可達到極小

18、的穩(wěn)定狀態(tài)應(yīng)變。這歸結(jié)于在驅(qū)動裝置之間均分了負(fù)載。并且, 限制控制裝置輸出力以致從驅(qū)動裝置它不需要不合情理地大功率, 而且在實踐中能防止超載驅(qū)動。</p><p>　　如果電源故障，所有電子控制器和電機將被關(guān)閉并導(dǎo)致輸送帶未管制停止?？朔@個問題方法是使用某種蓄裝置，譬如DC公共汽車整流器電容器，它能為控制器和電動機提供能量。不用太多能量就能完成帶的停滯控制。這表明閉合回路控制能產(chǎn)生一個穩(wěn)定性和性能好系統(tǒng)。大磁極

19、有快速的反應(yīng)即低過調(diào)節(jié)和短增時間。所以,，轉(zhuǎn)移大桿只能浪費能量。然而，轉(zhuǎn)移小桿能產(chǎn)生好的性能，從而元件的頻率和的阻尼率增加。閉合回路系統(tǒng)產(chǎn)生一個平穩(wěn)速度反應(yīng)但是開環(huán)系統(tǒng)不穩(wěn)定達到調(diào)整點時。結(jié)果也表示開環(huán)系統(tǒng)與閉合回路系統(tǒng)比較能獲得更短調(diào)節(jié)時間、低輸出。一個閉合回路系統(tǒng)的短調(diào)節(jié)時間的方式為了增加比例量。高放大系統(tǒng)通過四次增加比例量，但不是整體的量。許多增量導(dǎo)致系統(tǒng)過調(diào)節(jié)或者甚至系統(tǒng)不穩(wěn)定。系統(tǒng)主要目標(biāo)是達到零的穩(wěn)定狀態(tài)誤差。所以，一個好系

20、統(tǒng)在瞬時狀態(tài)期間不影響綜合化，但仍然能達到零的穩(wěn)定狀態(tài)誤差。小復(fù)雜桿開始控制造成一個振動反應(yīng)。但是，期望快速的反應(yīng)因為系統(tǒng)由高頻率元件控制。這些是在桿的定位件和反應(yīng)的之間關(guān)系[11] 。開環(huán)系統(tǒng)與閉合回路系統(tǒng)相比產(chǎn)生高瞬間應(yīng)變。并且, 高輸出閉合回路系統(tǒng)產(chǎn)生高瞬間應(yīng)變。這是許多高速度變化率造成的。開環(huán)系統(tǒng)比閉合</p><p>　　當(dāng)應(yīng)用反饋控制時，在研究中一個重要問題是系統(tǒng)的可控性。一個無法控制的系統(tǒng)通過控制器

21、也不能影響的其狀態(tài)，換句話說，系統(tǒng)無法影響模塊的所有桿。這導(dǎo)致系統(tǒng)不能充分地控制反應(yīng)。未控制的大桿對系統(tǒng)無影響，因為他們不能由控制器移動。但是, 按LOR 方法要求將有一個完全地可控制的系統(tǒng)。完成第一情況的完全地可控制的系統(tǒng)至少有二驅(qū)動裝置控制傳送帶。第二，把傳送帶以一個好的和簡單的方式劃分成有限段，但這也許會產(chǎn)生一個無法控制的系統(tǒng)。可調(diào)性由傳送帶驅(qū)動裝置的位置確定。由于帶的緊線的重量，會產(chǎn)生移動的波形。這導(dǎo)致一個無法控制的系統(tǒng)變得可控

22、制。但是, 因為緊線器重量與傳送帶長度比較相對地小，波形不會轉(zhuǎn)移。這產(chǎn)生一個微弱地可控制的系統(tǒng)。所以，使用傳送帶段的質(zhì)數(shù)可避免無法控制的問題，即達到一個完全地可控系統(tǒng)。從可控性模塊數(shù)尋找可控性度的方法。</p><p>　　在此文，介紹的反饋控制系統(tǒng)在傳送帶上使駐波減到最小。反饋控制系統(tǒng)比常用的開環(huán)控制系統(tǒng)有更好的性能。閉合回路系統(tǒng)能均分電機之間負(fù)載使應(yīng)變減到最小，但是在開環(huán)系統(tǒng)中均分驅(qū)動裝置之間的載荷是困難的。

23、在電機之間一個輕微的差距會對負(fù)載產(chǎn)生不同的滑移和扭矩。閉合回路系統(tǒng)能容易地限制輸出量避免超載驅(qū)動。這個反饋控制系統(tǒng)缺點是招致額外成本，它取決于需要的額外驅(qū)動裝置。但是，衡量其價值和性能，發(fā)現(xiàn)該系統(tǒng)值得實施?？刂撇呗允窃谔岣呦到y(tǒng)的性能上進一步研究。</p><p>　　Feedback control of convey systems</p><p><b>　　Summary&

24、lt;/b></p><p>　　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 usually shorte

25、n 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.<

26、;/p><p>　　In this paper, a feedback control method is introduced to reduce these transient stresses. A discrete strain-velocity model was developed which allows the analysis of the feedback control system to be

27、 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 controllability of the system, which is an important factor when t

28、he closed loop system is implemented.</p><p>　　1.Introduction</p><p>　　Belt conveyor technology is still the most cost-effective way of transporting bulk solids continuously over a long distance

29、. In the present day, it is widely used 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 operat

30、ions, especially at starting and stopping. These standing waves induce stresses to the belt life span, by causing belt splice or even belt and pulley structu</p><p>　　Research is conducted to minimize the tr

31、ansient stresses and to lower the cost of maintenance. An initial method to overcome these stresses is to design the belt with a very high factor of safety (F.O.S), which typically has a value of ten to the desired opera

32、ting 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

33、drives to the belt.</p><p>　　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 startin

34、g stopping of the conveyor belts. Currently, the soft starting methods used are all open loop approaches. These approaches normally do not give a good performance on starting and stopping of the system. They are also tim

35、e consuming to set up properly to achieve a satisfactory performance. Some of these methods might not </p><p>　　In this paper, a power electronic feedback control on the drive motors, which is a closed loop

36、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 implementation approach in this research uses the vect

37、or 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 o</p><p>　　The feedback

38、 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 maste

39、r stations. These master stations process 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

40、 vector space to control the AC motors. The adva</p><p>　　The first step towards control is to create a good mathematical model for the plant. A number of approaches have been studied in the past [3-9]. Most

41、 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

42、 of partial differential equations, contains very complex relationships. Also, it is very difficult to express the transient chara</p><p>　　A discrete model divides the continuous belt into a finite number

43、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

44、error in the discrete model, which depends on the number of belt segments and the model used.</p><p>　　With a good mathematical model, a satisfactory control strategy can be applied to give valid simulation

45、results. A large modeling error could always result in wrong simulation outputs and incorrect control parameters used.</p><p>　　The rheological models used for describing the longitudinal dynamic propertie

46、s 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 rel

47、atively 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 o</p><p&

48、gt;<b>　　(1)</b></p><p>　　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 lar

49、ge number of belt segments in order to achieve a small quantization error, the simulation time is a drawback as this increases exponentially as n increases.</p><p>　　Position-velocity is the most widely used

50、 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 segment of a moving conveyor belt vary from time to time. F

51、or 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’

52、position must be mo</p><p>　　A discrete model of the conveyor belt. From the forces which act on the segment n of the belt, an equation for the rate of change of velocity can be described by Eq. (2), in term

53、s of strain and velocity which are commonly denoted as ε and v respectively. is the motor force applied to the conveyor belt.</p><p><b>　　(2)</b></p><p>　　The rate of change of stra

54、in is express in Eq.(3)</p><p><b>　　(3)</b></p><p>　　Unlike the rest of the segments, the gravity take up weight has a different model. Therefore, it has to be treated separately. Th

55、e derivative of velocity and derivative of strain on the gravity take up weight, say segment k, can be described by Eqs. (4) and (5) respectively;</p><p><b>　　(4)</b></p><p><b>

56、;　　(5)</b></p><p>　　All the equations above can be presented in a form equivalent to a standard statespace representation, as in Eq. (6):</p><p>　　W= (6)</p><p>　　

57、This expression, Eq. (6), is called the Strain-Velocity model. By solving the Strain-Velocity model using a numerical method a given W and u, the strains and velocities for each segment the belt can be obtained. An examp

58、le 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 σ, for a solid model can be expressed by Eq. (7) [3];&l

59、t;/p><p><b>　　(7)</b></p><p>　　where E is YOUNG’S modulus and η is the viscosity coefficient. Eq. (7) shows that by reducing the maximum strains and velocities, the stresses can be min

60、imized.</p><p>　　In this point, a Multiple Input-Multiple Output (MIMO) system has been created. The three methods that are commonly used to control a MIMO system are pole placement, Linear Quadratic Regulat

61、or (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. Otherwise, incorrect placing of poles would result

62、in a waste of energy and controlling errors. The discrete Strain-Velocity model used is a</p><p>　　Fig.1; illustrates the block diagram of a feedback control system. W represents the weight of the load on

63、the belt, e represents the velocities’ errors and u is the motor’s force. The plant, i.e. the conveyor belt, has its dynamics described by the Strain Velocity model. A P1 (proportional and integral) controller with spee

64、d reference, V is used to control the drives. As mentioned previously, the LQR method is applied to calculate the proportional and integral gain. The purpose of H matrix is</p><p>　　Fig3: Block diagram of f

65、eedback control of a conveyor system </p><p>　　A number of techniques on setting the controller gains have to be emphasized. The main aim of the controller is to achieve an optimum control on the system, whi

66、ch 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 produ

67、ce high proportional gains. In addition, due to the control method used, reduced-state feedback would cause the high pro</p><p>　　If there is a complete power failure, all the electronic controllers and moto

68、rs will be shut down and result in an uncontrolled stopping of the conveyor belt. A method to overcome this problem is to have some form of energy storage, such as DC bus rectifier capacitors. To regenerate and supply p

69、ower for both controllers and motors. This will then achieve a controlled stopping of the belt without using too much energy been shifted directly to the left compared to open loop pole. This implies th</p><p

70、>　　An important issue in this research is the controllability of the system when feedback control is applied. An uncontrollable system has one or more states that are unaffected by the controller, in other words, the

71、 system cannot influence all the poles of the model. This results in the system not being able to fully control the response. Uncontrollable large poles do not seem to have any effect on the system, since they are not b

72、eing shifted by the controller. However, a requirement for using </p><p>　　In this paper, a feedback control system is introduced minimize the longitudinal waves in a conveyor belt. The feedback control sys

73、tem produces a better performance compared to the commonly used open loop control system. The closed loop system can achieve equal load sharing among motors to minimize the stress, whereas it is difficult to have load eq

74、ually shared among drives in the open loop system. A slight difference in motors will result in different slip producing different torque to the load</p><p>　　References</p><p>　　[1]HARRISON, A

75、.:Oritera form minizing transient stresses in conveyor belts; Int. Conf. on Materials Handling, Beltcon 2, May 1983. Republic of South Africa.</p><p>　　[2]BOSE, BK.: Power Electronics and Variable Frequency

76、 Drives — Technology and Applications; IEEE Press, US 1997.</p><p>　　[3]NORDELL, L.K. and CIOZDA, Z.P.: Transient belt stress during starting and stopping: elastic response simulated by finite element metho

77、ds; bulk solids handing Vol. 4 (1984) No. 1, pp. 93-98.</p><p>　　[4]ZUR, T.W.: Viscoelastic properties of conveyor belts; bulk solids handling No. 6 (1986) No. 3, pp. 1163-1168.</p><p>　　[5]SC

78、HULZ, G.: Analysis of the belt dynamics in horizontal curves of the long belt conveyers; bulk solids handling Vol. 15, (1995) No. 1, pp. 25-30.</p><p>　　[6] HAN, H.S., PARK, T.W. and PARK, T.G..: Analysis of

79、 a long belt conveyor system using the multibody dynamics program; bulk solids handling Vol. 16(1996) No. 4, pp. 543-549.</p><p>　　[7]KIM, W.J., PARK, T.G. and LEE, S.S : Transient dynamics analysis of belt

80、 conveyor system using the lumped parameter method; bulk solids handling Vol. 15 (1995); No.4, pp. 573-577.</p><p>　　[8]HARRISON, A.: Simulation of conveyor dynamics: in. solids handling Vol. 16 (1996) No.

81、1, pp. 33-36.</p><p>　　[9]LOOEWLIKS,G .: On the application of beam elements in the finite element models of belt conveyors - part I; bulk solids handling Vol. 14 (1994) No. 4. pp. 729-737.</p><p

82、>　　[10]BISHOP, R.E.D., GLANWELL, G.M.L. and MICHAESON,Sn. The Matrix Analysis of Vibration: Cambridge University Press, U.K., pp, 212-218</p><p>　　[11]FRANKLN, G.F., POWELL, J.D. and EMAM I-NAEINI, A.:

83、Feedback Control of Dynamic Systems; 3rd Edition. Addison Wesley, USA, pp. 118-137, pp. 505-514.</p><p>　　[12]SKOCESTED, S. and POSTLETHWAITE ,I.: Multivariable Feedback Control-Analysis and Design: John Wi