輸送機(jī)系統(tǒng)反饋控制

1、輸送機(jī)系統(tǒng)反饋控制雷讎鏗空等副嬌份個(gè)涔僅站摘要 當(dāng)輸送帶改變它的現(xiàn)在狀態(tài)時(shí)就會(huì)引起高強(qiáng)度的瞬間壓力，尤其是在它啟動(dòng)和制動(dòng)時(shí)。這些壓力對(duì)系統(tǒng)來說是有害的, 通常會(huì)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(jī)啟動(dòng)和制動(dòng)時(shí)對(duì)輸送帶進(jìn)行控制是十分必要的。禍戤窆俚枘膈陷處砑轟朊諱在這篇文章中，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(gè)非連續(xù)的速度信號(hào)傳遞給反饋系統(tǒng)，并對(duì)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(shí)這是一個(gè)重要的因素。導(dǎo)佬斕遣耒蛄芳罕選躞樘插1 介紹闥濉敗瑋崢誚此

2、桫岢盆縞瘙帶式輸送機(jī)技術(shù)一直是以遠(yuǎn)距離運(yùn)輸大量物體、成本低的方式運(yùn)用的。在現(xiàn)如今，它被廣泛地應(yīng)用于許多領(lǐng)域，例如：礦山運(yùn)輸煤、鐵、石灰石等等。這些技術(shù)在操作時(shí)遇到的困難是在輸送帶上產(chǎn)生的駐波，尤其在啟動(dòng)和制動(dòng)時(shí)。這些駐波通常引起帶子跑偏，帶子和托棍磨損會(huì)影響帶子的壽命，維護(hù)費(fèi)用會(huì)在短期內(nèi)劇增。 吡蔻擢呂淙擾臼諸佾扮里鞫 這項(xiàng)研究是為了使瞬間壓力最小化并降低維護(hù)費(fèi)用?？朔@些壓力的一個(gè)原始的方法是設(shè)計(jì)一個(gè)高度安全的輸送帶(F.O.S)，這對(duì)執(zhí)行預(yù)期的F.O.S標(biāo)準(zhǔn)很有意義。然而，這會(huì)導(dǎo)致系統(tǒng)成本的提高。現(xiàn)在，被廣泛應(yīng)用的方法是通過控制帶子的啟動(dòng)和制動(dòng)來減少帶子加速和減速的變化比率。這常常被認(rèn)為是

3、安全的啟動(dòng)或制動(dòng)。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(jī)械和電學(xué)的帶式運(yùn)輸機(jī)?，F(xiàn)在，被應(yīng)用的平穩(wěn)啟動(dòng)法是打開所有的回路。在系統(tǒng)開始和結(jié)束的時(shí)這些方法通常是不管用的。它們也是要經(jīng)過一段時(shí)間來選擇適當(dāng)?shù)姆椒ㄊ蛊溥_(dá)到一個(gè)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(hù)，這也提高了超載費(fèi)用。 在這篇文章中，介紹了在電動(dòng)機(jī)上的電子反饋控制，這是一個(gè)閉環(huán)式控制方法。一個(gè)相似的方法早已在HARRISON1的文章中被簡短地討論過了, HARRISON1利用硅控整流器控制直流電動(dòng)機(jī)。然而，這個(gè)研究的落實(shí)方法是在交流電動(dòng)機(jī)2上使用矢量控制。直流電動(dòng)機(jī)通常比交流電動(dòng)機(jī)貴，尤其當(dāng)維護(hù)費(fèi)用也考慮

4、時(shí)。所以，交流電動(dòng)機(jī)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統(tǒng)通過測(cè)量輸送帶各段的速度來計(jì)算電動(dòng)機(jī)所需的輸出量，測(cè)量的速度經(jīng)由通信電纜被傳輸?shù)街骺刂普尽?這些主控制站處理從控制器一起獲得的數(shù)據(jù)。然后，這些處理過的數(shù)據(jù)被用在驅(qū)動(dòng)裝置(可變電壓、可變頻率驅(qū)動(dòng)裝置)上，采用矢量空間的觀念控制交流電動(dòng)機(jī)。使用反饋控制方法的好處主要在于人們最關(guān)注的是系統(tǒng)達(dá)到最好的工作狀態(tài)，而不是我們通常使用的開環(huán)系統(tǒng)。通過讓負(fù)載在反饋控制系統(tǒng)中被平分并減少壓力。這個(gè)系統(tǒng)也可以通過限制最小輸出量來避免超負(fù)載。反饋控制系統(tǒng)的應(yīng)用很容易達(dá)到穩(wěn)定的狀態(tài)。利用電子學(xué)控制的優(yōu)點(diǎn)是降低保護(hù)成本和易于

5、遠(yuǎn)程控制。由于系統(tǒng)裝置的需要，系統(tǒng)欠缺也會(huì)增加設(shè)備成本，如測(cè)量輸送帶速度傳送器，傳遞信息和用于信息處理的微處理機(jī)的通信設(shè)備。由于維護(hù)費(fèi)用低，你需要長期付維修費(fèi)用。笆荒鵜脧杭耗緗夸覘頹卞覬控制的第一步是為工廠創(chuàng)造一個(gè)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(diǎn)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(dá)的，包含著非常復(fù)雜的關(guān)系。 同時(shí)，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。晉掠痖硭惰鹱蕘朗垡摧杌朕一個(gè)不連續(xù)模型把連續(xù)的帶子分成一個(gè)有有限數(shù)字的片段而且假設(shè)相同的片段里面的

6、原動(dòng)力基本相同，例如，在帶子的一段里有相近的持續(xù)速度，伸度，壓力等。這個(gè)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。詫形訃崍嫉駁鈾按烤焯癸靨用一個(gè)恰當(dāng)?shù)臄?shù)學(xué)模型, 一個(gè)合理的控制策略能有利于得到有效的模擬結(jié)果。一個(gè)大的模擬誤差總能導(dǎo)致錯(cuò)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(dòng)態(tài)屬性，凱爾文固體模型是一個(gè)彈簧與平行的一個(gè)黏彈性元件，它是對(duì)大多數(shù)帶式輸送機(jī)分析簡單和相對(duì)地準(zhǔn)確。當(dāng)一個(gè)分散模型代表一條連續(xù)的傳送帶時(shí)引用量子化誤差。對(duì)于使用的模型, 傳送帶的固有頻率的相對(duì)誤差與帶被分段的數(shù)量成反比，依照由公式1-1：陵賚舌薇竦賡茯郎園不

7、焙扌 （1-1）鈑漩蚓孫怊漉壓勞嘿要癀蹋是連續(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(shí)現(xiàn)一個(gè)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(shí)對(duì)模擬時(shí)間是不利的。位置速度被廣泛應(yīng)用于描述輸送帶的動(dòng)力學(xué)方法上。但是這種方法導(dǎo)致一個(gè)系統(tǒng)線性時(shí)間變化。例如，在時(shí)間t輸送帶i段起初應(yīng)用電動(dòng)機(jī)的力。但是, 在時(shí)間t+1, 電動(dòng)機(jī)的力不再在i段起作用而i+1段起作用。所以, 當(dāng)帶運(yùn)行時(shí)檢測(cè)段的位置必與時(shí)間有關(guān)。位置速度方法表達(dá)將必根據(jù)時(shí)間變化。明顯地這種方法導(dǎo)致一個(gè)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(gè)線性時(shí)間不變式的系統(tǒng)。輸送帶各段的應(yīng)力和速

8、度與地面保持同樣。因此, 這種方法避免時(shí)間變化的問題并建立一個(gè)簡單模型。沉召斯沽壢婺酵嶧召夂確撼傳送帶的一個(gè)離散模型，從帶的n段表示力，公式1-2描述了速度改變率，和v分別表示應(yīng)力和速度，是應(yīng)用于電動(dòng)機(jī)的原動(dòng)力。潑坯雌腹砝鈰甫秣印舌壇么 (1-2)君漏寄部樾泮溘釹篋物姬菊公式1-3應(yīng)力變化率：踏琺竅陡趵戀埃妾絲伽兮聚 （1-3）繒剃崖辰服哏棗丁飯骨葡達(dá)不同于剩余的段, 代替重量的重力是一個(gè)另外模型。所以, 它必須分開地被對(duì)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：政盲芳居芥吻癍彰鈦捱砧挽 (1-4)松租甭冖氮撙勝藍(lán)裟拍匹蟶 (1-5)靈適掛彘猴鎊券損掃髓茺

9、賄上面所有等式可以用公式1-6表示：吸趴尜印宿佟截殆甏詬妍纓 ，W= （1-6）容兩腐孌蝎婺灞爽藤假幣笙公式16的表示形式叫做張力速度模塊，運(yùn)用一個(gè)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(gè)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(gè)固體模塊表達(dá)式3：坍抽崾悱袍掉酊忝苤副隋馭 （1-7）廷饌嬙箋沸喝蝕樓圓倍妻群E是模數(shù)，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。唾綿濂袋艾櫛腎佛荀舀禮銘基于這點(diǎn)，創(chuàng)造了一個(gè)多輸入多輸出(MIMO) 系統(tǒng)。常用的控制MIMO系統(tǒng)的三個(gè)方法是

10、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(gè)準(zhǔn)確模塊, 這樣桿可根據(jù)所用的模塊被安置在需要的地點(diǎn)。否則, 不正確安置桿將會(huì)導(dǎo)致能源浪費(fèi)和控制錯(cuò)誤。使用分散式張力速度模塊是連續(xù)操作裝置的略計(jì), 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(huì)是一種好控制方法。H無限方法是一種好控制方法, 但是對(duì)管理者來說會(huì)相對(duì)地復(fù)雜的并導(dǎo)致一個(gè)高動(dòng)態(tài)指令。選擇LOR 方法取決于處理模塊的錯(cuò)誤能力和在使用中它的適應(yīng)能力強(qiáng)。但是, 選擇適當(dāng)?shù)目刂茀⒘繉?duì)LOR是困難的。因?yàn)椴贿m當(dāng)?shù)膮⒘咳菀椎匦纬梢粋€(gè)振動(dòng)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。培矜痢溧恨全抗撞處溺痿墉圖

11、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(dòng)力。傳送帶通過張力速度模塊描述它的動(dòng)力性。一個(gè)PI 控制器參考速度被用于控制驅(qū)動(dòng)。如先前提及的, 運(yùn)用LQR 方法計(jì)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(gè)反饋系統(tǒng)會(huì)將模塊里的所有狀態(tài)反饋給控制器。由于測(cè)量的張力困難, 僅用速度反饋。使用流速計(jì)容易得到速度。值得注意的是, 在這個(gè)反饋控制系統(tǒng)中速度是主要環(huán)節(jié), 系統(tǒng)會(huì)給一個(gè)相應(yīng)的遞減狀態(tài)反饋反應(yīng)。潦戍唾綬敬翰胺夏憑萏腑啦圖1：傳送帶系統(tǒng)反饋控制塊圖膚叟廨燾歡蠃擔(dān)糠侖敏窳蛉郛柔枉煸鋰

12、起摳鬃懨誹跫阝在設(shè)置控制器上必須被強(qiáng)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(dá)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(huì)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(duì)系統(tǒng)給出的零穩(wěn)定狀態(tài)的誤差做成反應(yīng)。一個(gè)小的輸出會(huì)降低系統(tǒng)響應(yīng), 需要長時(shí)間到達(dá)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€(gè)性能好的系統(tǒng)。當(dāng)驅(qū)動(dòng)輸出比例總相等時(shí)，可達(dá)到最小瞬變應(yīng)變,。通過設(shè)置相同驅(qū)動(dòng)輸出, 可達(dá)到極小的穩(wěn)定狀態(tài)應(yīng)

13、變。這歸結(jié)于在驅(qū)動(dòng)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(dòng)裝置它不需要不合情理地大功率, 而且在實(shí)踐中能防止超載驅(qū)動(dòng)。郗贍狁駐聾恁橡塞雖戟鋇必如果電源故障，所有電子控制器和電機(jī)將被關(guān)閉并導(dǎo)致輸送帶未管制停止?？朔@個(gè)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(dòng)機(jī)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(gè)穩(wěn)定性和性能好系統(tǒng)。大磁極有快速的反應(yīng)即低過調(diào)節(jié)和短增時(shí)間。所以,，轉(zhuǎn)移大桿只能浪費(fèi)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(gè)平穩(wěn)速度反應(yīng)但是開環(huán)系統(tǒng)不穩(wěn)定達(dá)到調(diào)整點(diǎn)時(shí)。結(jié)果也

14、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(shí)間、低輸出。一個(gè)閉合回路系統(tǒng)的短調(diào)節(jié)時(shí)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(dá)到零的穩(wěn)定狀態(tài)誤差。所以，一個(gè)好系統(tǒng)在瞬時(shí)狀態(tài)期間不影響綜合化，但仍然能達(dá)到零的穩(wěn)定狀態(tài)誤差。小復(fù)雜桿開始控制造成一個(gè)振動(dòng)反應(yīng)。但是，期望快速的反應(yīng)因?yàn)橄到y(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)比閉合回路有更高的平穩(wěn)性，在閉合回路系統(tǒng)中，兩驅(qū)動(dòng)裝

15、置之間均分載荷。在整體傳送帶過程中它產(chǎn)生極小的穩(wěn)定狀態(tài)應(yīng)變區(qū)別。拗力吁檁崞儺掀珉轄珊呈袖當(dāng)應(yīng)用反饋控制時(shí)，在研究中一個(gè)重要問題是系統(tǒng)的可控性。一個(gè)無法控制的系統(tǒng)通過控制器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(duì)系統(tǒng)無影響，因?yàn)樗麄儾荒苡煽刂破饕苿?dòng)。但是, 按LOR 方法要求將有一個(gè)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(dòng)裝置控制傳送帶。第二，把傳送帶以一個(gè)好的和簡單的方式劃分成有限段，但這也許會(huì)產(chǎn)生一個(gè)無法控制的系統(tǒng)。可調(diào)性由傳送帶驅(qū)動(dòng)裝置的位置確定。由于帶的緊線的重量，會(huì)產(chǎn)生移動(dòng)的波形。這導(dǎo)致一個(gè)無法控制的系

16、統(tǒng)變得可控制。但是, 因?yàn)榫o線器重量與傳送帶長度比較相對(duì)地小，波形不會(huì)轉(zhuǎn)移。這產(chǎn)生一個(gè)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(dá)到一個(gè)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。哺臨洪捌抽鰻馗永蜀蜞捂膠在此文，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(jī)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(dòng)裝置之間的載荷是困難的。在電機(jī)之間一個(gè)輕微的差距會(huì)對(duì)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(dòng)。這個(gè)反饋控制系統(tǒng)缺點(diǎn)是招致額外成本，它取決于需要的額外驅(qū)動(dòng)裝置。但是，衡量

17、其價(jià)值和性能，發(fā)現(xiàn)該系統(tǒng)值得實(shí)施?？刂撇呗允窃谔岣呦到y(tǒng)的性能上進(jìn)一步研究。艫飯醮冀踞薅閭膨攛鑰淆鯨蠱付射艋瘦歟巹飽囑鲇愉厶Feedback control of convey systems兼簧寺貪妹化簡唱稅硨氵切Summary甕韙槔征駭罵酣扮轟寇以燔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.尤聰艽怖蕕哄佟嚇?biāo)徙U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.罱逃蔞陬病電原啡藥宜材癤1.Introduction粑嗪胤緯屹莉婭藺愣卵查饕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.滅茁坻邇娟餡绔捐皂縉杰吞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.醬籌瓦庭既蟻雇貽捷博侈髀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.萃惹偶揮翌糖鑼害窘舁晁亠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.銓影啪舷藕袈鬧躉珙錦梳樸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.史雋麂邈魚菅喋株驤鑫啪迤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.仲廂妲玨鄖潞氣蓄邐攆累舔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.囚螽榍鏤弳慘溱露刖屹忱柑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.萇役騾報(bào)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父薛幢蟒合悱韓卷惑睇鵜臼 (1)鋦茭妙醅坡錠曰仉焐磺京絲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.贓隴腡鄔夕莓逃氨痊舂冒粕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.漁趿媵墜崩淶投圮媚固墮笙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.裊浠珉忿蹁倨譖萄縈檀芻笛 (2)惑姊纈旱扭涿糌泥鷺篷拯巍The rate of change of strain is expres

45、s in Eq.(3)能盎蹈失悌柁拶挨鋒鉭粱孿 (3)狡竺燦猝瀏報(bào)劑饃仨鉗蜞返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;榷孜繕離撈妍卅蟆鲞鏢竣爾 (4)蛀碰當(dāng)呵菊鋁白蚧悲搗坎儂 (5)趺侖鉦游爐儆璨趟閉蚶窀炅All the equations above can be presented in a form equivalent to a standard statespace representation, as in Eq. (6):聱肓仵塵糜恒呻資颯玳證釜 W= (6)粳酲慪菰殼肥忠錈等岱仿紜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;滅瘁邵搖鈣懈猹滟澄愕堂鮮 (7)欣潴勇倫涵業(yè)瀾握蕉榀莊呢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.攔齏脅湓璧鱟遄鉦貳熔漢匹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.若燹園摑副鎦軍悚鲅硤怠扃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.咸粲炻等權(quán)鼽狠鎊鵂貌呢僬Fig3: Block diagram of feedback control of a conveyor system 後乏馳芟旄瑰妾柵愛鶉砌使 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