模塊化智能型雙缸隔膜電動噴霧器的設(shè)計【全套含CAD圖紙】,全套含CAD圖紙,模塊化,智能型,隔膜,電動,噴霧器,設(shè)計,全套,cad,圖紙 一個樹狀多支結(jié)構(gòu)模型式程序的線性運動 ——主動噴霧噴灑機(jī)的設(shè)計 農(nóng)業(yè)工程處，Kardinaal Mercierlaan 92,3001比利時魯汶 摘要——文件的第一部分，一個多體系統(tǒng)的運動線性方程已經(jīng)確立。在這一部分， 這種方法是被用作計算由10個部分組成的噴涂機(jī)的運動計算方程的。吏羅拉式 是輪胎是典型的輪胎。給確定低通濾波品質(zhì)的輪胎長度輪胎接觸地面也被考慮。 通過一個直接承襲于多體模型的更小的示范模型，在一個帶回路恢復(fù)功能的高斯 線性二次法的幫助下懸浮式噴霧設(shè)計出來。液壓驅(qū)動拖拉機(jī)通過在對面旋轉(zhuǎn)噴霧 吊桿來抵消拖拉機(jī)的意外旋轉(zhuǎn)，這樣噴嘴與田間作物間的距離仍然在可接受的范 圍內(nèi)。在模擬實驗中，通過在規(guī)范化軌道上駕駛噴霧機(jī)，有償和無償噴霧吊桿運 動產(chǎn)生，并相應(yīng)壓縮了的部分噴霧產(chǎn)生。 符號 Ac 氣缸凈面積[平方米] Cd 因次流量系數(shù)[-] G 真實植物模型 GO 象征植物模型 △Ga 非確定結(jié)構(gòu)化添加劑 △Gm 非確定結(jié) 構(gòu)化添加劑 HOO 卡爾曼濾波器及被評估的植物輸出的開環(huán)傳遞 矩陣（=環(huán)路 增益,回報率） HOS 卡爾曼濾波的開環(huán)傳遞矩陣 1.引言 農(nóng)業(yè)生產(chǎn)遭受嚴(yán)重的由昆蟲，雜草和病蟲害帶來的損失。由于世界人口的成 倍增長，作物保護(hù)已成為世界上最重要的學(xué)科領(lǐng)域，用以提高生產(chǎn)力和作物產(chǎn) 量。 傳統(tǒng)的植保分類方法分為五類:化學(xué)、生物、農(nóng)藝、機(jī)械、生物物理技術(shù)[1]。 化學(xué)防治方法目前最常使用。因為其特有的高效率，操作的簡單性以及寬廣的范 圍：除草劑、殺蟲劑可使用同一機(jī)器。這些化學(xué)物質(zhì)溶解于液 體載體由拖拉機(jī)帶動的噴霧吊桿進(jìn)行大面積噴灑。 目前傾向于使用濃縮劑噴灑(小噴量技術(shù))，化學(xué)藥劑的成本上升，化學(xué)污 染的日益嚴(yán)重需要更精密的，盡可能在大面積土地均勻噴灑液體的噴灑機(jī)械的出 現(xiàn)。 噴霧方式的不當(dāng)主要是由于不同的水力設(shè)備之間的壓力、噴嘴糟糕的狀況、 駕駛拖拉機(jī)時速度不均、風(fēng)況，最后也是很重要的，噴桿在垂直方向的無用的震 動偏移。由于土地狀況所引起的拖拉機(jī)車身的不平衡導(dǎo)致了噴桿的不良動作，直 接導(dǎo)致農(nóng)作物和噴嘴之間的垂直距離不斷改變，導(dǎo)致了不規(guī)則分布噴霧的現(xiàn)象.。 當(dāng)工作速度較髙，使農(nóng)業(yè)機(jī)械的使用更劇烈、，震蕩現(xiàn)象更加明顯，如果土地狀 況惡劣，拖拉機(jī)的影響更大。所有這些負(fù)面效應(yīng)將加大闡述噴霧模型參數(shù)的難度。[2] 顯然，補償無用的噴桿移動是比以往更加有趣和具有挑戰(zhàn)性的研究領(lǐng)域。此外,，提供穩(wěn)定的噴桿使化學(xué)藥劑更接近于植物，使風(fēng)力的負(fù)面影響大大減少。 拖拉機(jī)的振動能夠由一個被動或主動的懸浮噴桿來相應(yīng)的削減。靜態(tài)懸浮裝置由 不需要電源的液壓缸、聯(lián)通器和阻尼組成。被動[3，4]或主動減振器[4-7]由一個 或多個驅(qū)動器、感應(yīng)器、信號傳感器、濾波器、監(jiān)察人、鐘擺補償組成，為了減 輕拖拉機(jī)上的噴桿不良滾動，這項課題已經(jīng)被認(rèn)知。主動方式是用古典頻域技 術(shù)設(shè)計的典型的單輸入單輸出反饋控制系統(tǒng)。在主動系統(tǒng)中，液壓驅(qū)動電液閥總 是使用的，因為通常液體動力由拖拉機(jī)帶動。紅外線或超聲波檢測裝置，安裝在 噴桿上監(jiān)測噴嘴和地面的垂直距離。托馬斯已經(jīng)詳細(xì)描述了這些傳感器的特點和 動態(tài)特征[8]。 在70年代末和80年代，控制學(xué)專家融合了最佳的古典理論和現(xiàn)代技術(shù)， 研制出新的控制理論。在這個新理論中，健全的補償，必須滿足某些假設(shè)的穩(wěn)定 性和性能標(biāo)準(zhǔn)，將開發(fā)有關(guān)“hydro track”噴灑機(jī)械，在Delano公司工程車間 組裝（圖1)。線性二次高斯法與回路轉(zhuǎn)換復(fù)原法(LQG/LTR方法)將用來作為控 制系統(tǒng)的設(shè)計工具。反饋系統(tǒng)通過一個液壓器使噴桿在相反的方向抵消拖拉機(jī)軋旋的不良運動，這種距離在噴嘴和大田作物間仍然是可接受的范圍。 2.噴灑機(jī)械的運動方程 hydro track噴霧機(jī)，由10個機(jī)構(gòu)組成：焊接構(gòu)架上的駕駛室、一個140L 的油箱，88萬千瓦的電機(jī)，一個噴桿，正在組建的后面的兩個車輪與前軸展開 兩個前輪。固定在上框的滌綸液體儲罐，擁有最大容量為3000L。臂總長度可相 差21和36米。在應(yīng)用中，臂的長度等于27米.。四個輪子的直徑一樣為1.34 米，hydrostatically四個驅(qū)動波克蘭液壓馬達(dá)等。拖拉機(jī)位于輪子上方較高處， 以防止在化學(xué)噴霧期間田間作物因機(jī)械碰觸而損傷。 拖拉機(jī)駕駛室，袖箱和汽車休息橡膠墊保證拖拉機(jī)框架的六個自由度。在前 軸懸架有一個三角結(jié)構(gòu)。球形接頭里的一個側(cè)滑自由度被阻斷，連接一個頂點的 軸與下墊面的拖拉機(jī)幀。其他頂點攜帶前輪。兩個氮加載短跑盆充當(dāng)彈簧-阻尼 系統(tǒng)，均放置在前軸和拖拉機(jī)底盤附近前輪以增加乘坐舒適性。壓力阻尼器會自 動適應(yīng)不斷變化的噴灑機(jī)重量，以保持拖拉機(jī)機(jī)箱關(guān)于領(lǐng)域內(nèi)的一個恒定的水 平。噴射臂是裝在拖拉機(jī)的鋼架的后方擺機(jī)制必須抑制不良的拖拉機(jī)的滾動 (圖2)。主動懸架系統(tǒng)是放置在硬性規(guī)定上的拖拉機(jī)的噴桿和鋼框之間的液壓缸 來獲取的。該機(jī)構(gòu)裝置共計31個自由度(d.O.f.):相對于土壤的拖拉機(jī)底盤有 圖2:噴霧機(jī)臂懸架和驅(qū)動器的背面 6d.o.f；關(guān)于底盤：駕駛室、油箱和發(fā)動機(jī)總計18d.o.f.，噴桿有一個轉(zhuǎn)動自由 度，前軸有一個轉(zhuǎn)動和上下的自由度（d.o.f.)，每一個車輪有一個上下的d.o.f.。 上述四個液壓驅(qū)動車輪受制于一個引進(jìn)的虛構(gòu)扭傳動剛度與每個輪子的傳動阻 尼。輪胎與地面的接觸長度決定了輪胎上的低通濾波器品質(zhì)，這取決于輪胎所要 承受的重量，這些已經(jīng)被考慮在內(nèi)。兩個位移傳感器(紅外線或超聲波)固定在噴 桿的嘴部用來測量噴嘴和土壤或田間作物之間的垂直距離。 各個噴灑機(jī)器的零件已經(jīng)在工廠地板上在機(jī)器組裝期間被測量了。實測數(shù)據(jù) 已經(jīng)輸入Lexigraphic，一款三維的CAD-CAM-CAE操作軟件系統(tǒng)。機(jī)器的10 個機(jī)構(gòu)部件的機(jī)械參數(shù)(尺寸、重心、質(zhì)量慣性矩和產(chǎn)品的惰性)已經(jīng)被匯集到 UNIGRAPHICS里面。其他的型號參數(shù)(彈簧剛度、阻尼常數(shù))由實驗室測量或提 供貨物的廠商直接給出。由于拖拉機(jī)的全部質(zhì)量大大下降，在室外的土地上噴灑 操作，一個充滿液體的把罐、一個半滿的液體儲_及一個空儲罐底盤的模型參數(shù) 已經(jīng)計算出。與地面接觸的輪胎長度已經(jīng)適應(yīng)這三種情形。 計算公式分別解釋了文章中的關(guān)于三個不同容量罐體的一部分線性運動方 程。狀態(tài)空間的轉(zhuǎn)換，它們所代表系統(tǒng)的70個狀態(tài)：62個狀態(tài)來自于矢量二階 模式和當(dāng)使用Crowell輪胎模型時的8個代表輪胎動態(tài)時縱向和橫向狀態(tài)的。這種 狀態(tài)，是用來在物理結(jié)構(gòu)設(shè)計過程中'，并在模擬階段評價真實模型，取代機(jī)電液 補償?shù)摹? 噴霧機(jī)的一個半滿罐系統(tǒng)矩陣詳載于附錄。讀者也許為便于標(biāo)記這個矩陣， 會將拖拉機(jī)駕駛室、汽車的油箱的18個d.o.f.移取不予考慮，因為它們是無關(guān)的 自由度問題。在這種情況下，代表噴桿的轉(zhuǎn)動的自由度是廣義拉格朗日坐標(biāo)Q7。 設(shè)計參數(shù)和必要的測量數(shù)據(jù)，在文檔中詳細(xì)描述了 [9]。 3.動態(tài)的液壓裝置 忽視伺服驅(qū)動器和動態(tài)反饋系統(tǒng)的破壞。其系統(tǒng)方程應(yīng)該把噴灑機(jī)的狀態(tài) 方程的。 由兩個輔助狀態(tài)與狀態(tài)的變量和Pb可得到[10] 19 汽缸的油容積Ac已經(jīng)增加了一倍，這是考慮到油在液壓管道中的可壓縮性 和泄露情況。 4.LQG/LTR方法的總結(jié) 用LQGL/LTR方法設(shè)計的這種補償器，要求一個具有代表性的空間狀態(tài)的標(biāo)稱模型。 一臺基于LQG的補償器包括一個卡爾曼過濾器和一個調(diào)節(jié)器。測量信號通 過估計未知狀態(tài)的卡爾曼過濾器傳送出去。被估計的和直接地測量的狀態(tài)通過傳 動器由調(diào)節(jié)器產(chǎn)生驅(qū)動信號(s)。 在無限(舊)時間不變的情況下，雙重性原則和分離原則允許我們計算調(diào)節(jié)增益矩 陣K和卡爾曼增益矩陣K，獨立地彼此又相似的規(guī)程[11]，只要等式4是可以 成立和計算求解的。這意味著無法控制和/或不可預(yù)見的模式邏輯(4)應(yīng)漸近趨于 穩(wěn)定。因為只有測量，此應(yīng)用可以被視為一種輸出反饋系統(tǒng)過濾器(相反的狀態(tài) 反饋系統(tǒng)的所有狀態(tài)測量和反饋，而不用直接觀察)。由于這個原因，應(yīng)該在調(diào)節(jié) 之前設(shè)計卡爾曼濾波器的邏輯。 全狀態(tài)反饋LQ控制器的相位幅度至少為60° (純相位變動的60°可能同時被容 忍在各種沒有疏松的穩(wěn)定輸入渠道里)增益幅度無限大(增益在每個輸入通道可 以增加無限大在不考慮疏松的穩(wěn)定前提下)[15];壞處增益邊緣反增益在每個頻道 的投入至少可以減少1/2或8分貝[16]。然而，這些令人印象深刻的穩(wěn)定性不太 容易保證，尤其在實施最佳觀測時。^幸的是，存在著已設(shè)計的調(diào)整程序能充分恢復(fù)穩(wěn)定性差的全狀態(tài)反饋系統(tǒng)[17]。 5.標(biāo)稱模型 在復(fù)雜的機(jī)制中所描述的大型模型和眾多的狀態(tài)下設(shè)計補償器期間，設(shè)計者 常常釆用如下兩種模型：一種詳細(xì)的評估模型或真實的模型代替真實的物理過程 的階段進(jìn)行模擬，另外一種是一個較小的設(shè)計模型或象征模型通常是從評價模 型，即使用綜合補償器。這個做法是根本的基于模型的補償器開發(fā)的當(dāng)控制系統(tǒng) 設(shè)計技術(shù)被運用，為了保持卡爾曼過濾器的維度可接受。LQG/LTR方法屬于那 個小組，因為植物的標(biāo)稱模型將被合并在估計缺掉狀態(tài)的植物在控制活動期間的 卡爾曼過濾器。 一個標(biāo)稱模式應(yīng)該從評估的模式中導(dǎo)出來，以一貫的方式，即設(shè)計模型必須盡可 能小，以維護(hù)盡可能多的信息。真正的模型，從一個半滿罐的hydro track，看起 來似乎是最可行的選擇減少的模型中導(dǎo)出。在這項研究中，減少模型可以遵循的 結(jié)構(gòu)輸出分布矩陣C(附錄)，這表明，只有拖拉機(jī)的旋轉(zhuǎn)運動和噴桿，代表廣義拉格朗日坐標(biāo)仏和扔，都屬于實測輸出。因此聽起來邏輯保留^而必及其衍生物，連同仏和巧，作為狀態(tài)的設(shè)計模型。被減少的標(biāo)稱模型的準(zhǔn)確性與六個狀 態(tài)(附錄）由確認(rèn)它的輸入-輸出頁與原物的輸入-輸出頁評估模型進(jìn)行比較。圖3 顯示PG在整個頻率范圍內(nèi)，均表現(xiàn)出完美的雷同，唯一的例外是由截短拖拉機(jī) 模式所導(dǎo)致的約20 rad 1的小偏差。 6.結(jié)論 一個詳細(xì)的線性化的模型操作在由典型的Crowell模型代表的噴灑機(jī)器，由 multiband方法在第本文的的第一部分的概述中導(dǎo)出。雖然標(biāo)稱模型的6個狀態(tài) 直接地從大拖拉機(jī)模型中推論出來，而不是使用被提煉的平衡的減少技術(shù)，但它 依然顯示擁有一個充足的精確度。 以這些模型，由于LQG/LTR方法的內(nèi)在質(zhì)量，噴桿的活躍懸浮成功地被設(shè)想了。嚴(yán)格的性能指標(biāo)都容易得到滿足，而不釆用成型濾波器，補償器保留慢響 應(yīng)對大型拖拉機(jī)大量變動和恢復(fù)的穩(wěn)定邊際創(chuàng)造對非模型動搖的有些免疫能輸 入系統(tǒng)的動態(tài)現(xiàn)象作動器輸入。同時，也表明強壯性測試針對非結(jié)構(gòu)化模型的不 確定性是必要的，它們的成功應(yīng)用是堅決通過提供可靠的評價模型得到的。 噴灑應(yīng)用機(jī)械 噴霧器的基本單位和心臟是液體泵。因此，首先需要研究和確定液體泵的一 些運行參數(shù)。正如所有霧化技術(shù)一樣，都需要外加的能源進(jìn)行對液體的解體作用， 以完成霧化。航空股和旋轉(zhuǎn)式霧化在能源供應(yīng)乘飛機(jī)或離心力實現(xiàn)了霧化。水栗 是常用這些技術(shù)已獲得均勻效果的。但對于液壓噴嘴壓力的氣溶膠液體霧滴由泵 (或壓縮天然氣）作為能量來源。 栗的類型 泵機(jī)可以分為正面位移和非正面的類型。第一種形式來取代具體的液體體積 (空氣）的革命。這意味著一些壓力從閥釋放，或者壓力控制裝置使用未被利用 的回水缸進(jìn)行噴霧操作。容積式泵還將借助低真空，因此，也不會要求充填泵或 將它與下面的液體為首，然后開始抽水。非正面的泵(主要是離心），不需繞道閥， 不需要自己抽空氣，但一般有更長的壽命比正面水泵，需要裝修接近旋轉(zhuǎn)部件 和受到快速磨損尤其磨料懸浮或濕粒子。 A MODELLING PROCEDURE FOR LINEARIZED MOTIONS OF TREE STRUCTURED MULTIBODIES—2: DESIGN OF AN ACTIVE SPRAY BOOM SUSPENSION ON A SPRAYING-MACHINE H.Ramon and J. De Baedeker K.U.Juvenilia, Department of Agricultural Engineering, Kardinaal Mercierlaan 92.3001 Leuven, Belgium (Received 26 August 1994) Abstract--In part 1 of the paper, the linearized equations of motion of a multiband system have been established. In this part, the method is used to compute the equations of motion of a spraying-machine consisting of 10 bodies. Ayres are represented by the Tyre model of Arolla. The contact length Tyre-ground which determines the low-pass filtering quality for the Ayres, is also taken into account. Through a smaller nominal model that has been derived directly from the multiband model, an active spray boom suspension is designed with the aid of the linear quadratic Gaussian method with loop transfer recovery. A hydraulic actuator counteracts undesired rolling of the tractor by rotating the spray boom in the opposite direction, such that the distance between the spray nozzles and the field crops remains within an acceptable range. In the simulations, compensated and uncompensated spray boom motions are generated by driving the machine over some incompressible standardized tracks and corresponding spray deposit distributions are generated. NOTATION Ac net area of the cylinder [m2] Cd dimensionless discharge coefficient [—] G true plant model GO nominal plant model △Ga additive unstructured uncertainties △Gm additive unstructured uncertainties HOO open loop transfer matrix of the Kalgan filter and plant evaluated al the output (=loop gain,return ratio) HOS open loop transfer matrix of the Kalgan filter n*n-identity matrix 1.INTRODUCTION Agricultural production suffers severe losses from insects, plan diseases and weeds. Owing to an exponentially growing world population, crop proProtection has become one of the most important field operations to increase productivity and crop yield. Current methods of plant protection are classified in five categories: chemical, biological, agronomical, mechanical and biophysical techniques [1]. Chemical control methods are Stilton most frequently utilized. Their efficiency is large, they are easy to employ and they-have a broad spectrum of applications: herbicides, pesticides, insecticides,… which can be delivered by the same machinery. These chemicals are dissolved in a carrier liquid which is distributed over the field crops through tractors equipped with a spray boom. New tendencies towards the use of concentrated spraying agents (small volume spraying techniques), the rising cost of chemicals and increasing concern over pollution pressure on the environment moresque sophisticated spraying-machines which have to be able to spray the liquid as uniformly as possible across the field. Irregularities in the spray pattern are mainly acreacted by pressure variations in the hydraulic equipment, badly set (tuned) spray nozzles, a varying driving speed of the tractor, wind and last, but not least, by unwanted rolling and to a lesser degree by vertical translations of the spray boom. Both boom motions are caused by undesired movements of the tractor body that arc mainly effected by soil roughnesses. As a consequence, the vertical distances between crops and nozzles are changed continuously which results in an irregular spray deposit coistrilablution. Higher work velocities, made possible by the use of more powerful agricultural machines, even magnify vibrations, effected by soil irregularities, on tractor and implement- All these negative effects on Che spray pattern are more thoroughly explained in Ref. [2]. Obviously, compensation of unwanted spray boom motions become more than ever an interesting and challenging research area. Besides, stabilized spray booms offer the possibility of dispersing the chemicals closer to the plants so that negative wind, effects are strongly reduced. Attenuation of the boom response to tractor vibrations can be accomplished by passive or active boom suspensions. Passive suspensions are a combination of springs, links and dampers and do not require a power supply. Active suspensions consist of a power source, one or more actuators, sensors, signal transducers, filters and controllers. Pendulum compensators with passive [3,4], or active dampers [4-7], in order to attenuate undesirable rolling movements of a spray boom on a tractor, have already been studied. The active versions are typical examples of single-input single-output feedback conrotl systems which are designed with classical arc- frequency-domain techniques. In an active system, hydraulic actuators with electro-hydraulic valves are always used, because fluid power is normally available on tractors. Ultrasonic or infrared measurement devices, mounted on the boom tips monitor the vertical distances between the tips and the ground. The characteristics and dynamics of these sensors are fully described by Thomas [8]. At the end of the 1970s and during the 1980s, control specialists developed a new control theory that blends the best features of classical and modern techniques. In this respect, a robust compensator that Muslim satisfy some postulated robustness and perconformance criteria, will be developed on the spray- archine “Hydro track”，assembled at the engineering workshop of the company Delano (Fig. 1). The linear quadratic Gaussian method with loop transfer recovery (LQG/LTR method) will be used as a control system design tool. The feedback system should counteract undesigned tractor rolling by RotaING the spray boom in the opposite direction through a hydraulic actuator, such that the distance between the spray nozzles and the field crops remains within an acceptable range. 2.EQUATIONS OF MOTION OF THE SRRAVIN&MACHINE The spraying-machine, Hydro track, consists of 10 bodies: a welded frame on which the cab, a fuel tank of 140 ], a motor of 88 kW, a spray boom, two rear wheels and a front axle with two mounted from wheels, are built. A polyester liquid tank, fixed onto the frame* has a maximum content of 30001. The total boom length can vary between 21 and 36 RA. In this application, the length of the boom equals 27 m. The four identical wheels have a diameter of 1.34 m and are hydrostatically driven by four McClain hydraulic motors. The tractor stands high on its wheels to prevent field crops from mechanical damage during the chemical treatment, The tractor cab，the fuel tank and the motor rest on rubber cushions which preserve six degrees of freedom with regard to the tractor frame. The front axle suspension has a triangular structure. A Hesperidcal joint in which the yawing degree of freedom is blocked, connects one vertex of the axle with the underside of the tractor frame. The other invertins carry the front wheels. Two nitrogen-loaded dash pots that serve as spring-damper systems’ are placed between the from axle and Che tractor chassis near the front wheels to increase ride comfort. The pressure in the dampers is automatically adapted to the changing weight of the spraying-machine in order to retain the tractor chassis on a constant level with regard to the field. The spray boom is mounted on a steel frame at the backside of the tractor with a pendulum machanism which must attenuate undesired rolling of the tractor (Fig. 2). An active suspension system is obtained by placing a hydraulic cylinder between the spray boom and the steel frame that is rigidly fixed onto the tractor. The mechanism has in total 31 degrees of freedom (d.o.f.)： 6 d.o.f. of the tractor chassis with regard to the soil; with regard to the chassis: in sum IS d.o.f. for the cab, the fuel tank and the motor, a rolling d.o.f. of the spray boom, a rolling and pitching calo.f, of the front axle and for every wheel 1 pitching d.o.f. The rotational d.o.f. of the Linearized motions for tree structured embodiers. Part 2 four hydrostatically driven wheels are restricted by the introduction of a fictitious torsional driveline stiffness and driveline damping for each wheel. The contact length Tyre-ground which determines the outpass filtering quality of Che Ayres and which depends on the weight the Ayres has to bear, is taken into account. Two displacement sensors (infrared or ultrasonic) arc fixed onto the boom tips and register the vertical distance to the soil, or the field crops. Each part of the spraying-machine has been measured on Che factory floor during the assemblage process of the machine. The measured data have been imported in UNIGRAPHICS, a three-dimensional CAE-CAD-CAM system. The mechanical parPetersham of the 10 bodies in the machine (masses’ Centre of gravity, mass moments of inertia and products of inertia) have been generated within UNIGRAPHICS. The other model parameters (spring stiffness, damping constants) were measured at the laboratory or were disposed by kind permission of the manufacturers* Since the total tractor mass decreases considerably during Che spraying operation in the field, the model parameters of the chassis have been calculated for a full liquid tank, a half-full liquid tank and an empty liquid tank. The contact length Tyre-ground is adapted to these three aituNations. The linearized equations of motion are computed with the formula explained in part one of the paper for the three different tank contents. Transformed into the state-space, they are parented by a system of 70 states: 62 states derived from the vector second-order model and 8 states that represent the longitudinal and lateral Tyre dynamics when using the Tyre model of Arolla. This state equation is used as an evaluation or true model that replaces the physical structure during the design of the ectropic-hydraulic compensator, and in the simulation phase. The system matrices of the spraying-machine with a half-full tank are given in the Appendix. The reader should remark that for the ease of prepdenting the matrices, the 18 d.o.f. of the tractor cab, the motor and the fuel tank are removed because they are irrelevant to the problem. In this situation, the rolling degree of freedom of the spray boom is represented by the generalized Granola運an coordinate q1. The design parameters and the ne cessary measured data are thoroughly described in Ref, [9], 3.DYNAMICS OF THE HYDRAULIC DEVICES Neglected overvalue and actuator dynamics can destabilize the feedback system. Their system equations should therefore be incorporated in the state equations of the spraying-machine. Two supplementary states with state variables pa and Pb are obtained [10] In which The oil volume in the cylinder has been doubled in order to take into account the compressible oil in the hydraulic conduits and hoses. 4. SUMMARY OF THE LQG/LTE METHOD The compensator is designed with the LQG/LTR method that asks for a state space representation of the nominal model An LQG-based compensator consists of a Kalgan filter and a regulator. Measurement signals are sent through a Kalgan. filter which estimates the unknown states. The estimated and direct measured states arc used by the regulator that generates the actuator signal(s). In the infinite horizon〔IH) time-invariant aituNation, the duality principle and the separation pinSiple permit us to calculate the regulator gain matrix K,. and the Kalgan filter gain matrix Ef Independencedecently of each other with similar procedures [11], as long as ean (4) is stabilization and detectable. This means that the uncontrollable and/or unobservable modes of ean (4) should be asymptotically stable. Since only the output is measured, this application can be considered as an output feedback system with filter (contrary to a state feedback system where all the states are measured and fed back directly without observer). For that reason, it sounds logical to design the Kalgan filter before the regulator. Fig. 4. Input~output PG of the evaluation model with full tank (solid line) and empty tank (dashed line). To modify Kc or the PG of H00 by manipulation of the state weighting and control weighting matrices Q and R, equivalence loop shape techniques can be used [13]. A full-state feedback LQ-controller has a phase margin of at least 60° (pure phase changes of 60° can be tolerated in each input channel simultaneously without loosing stability) and a gain margin of infinitely (the gain in each input channel can be increased infinitely without loosing stability) [15]; the downside gain margin against gain reductions in each input channel is at least 1/2 or 8 dB However, these impressive stability margins arc not guaranteed any more In an optimum observer-based implementation. Fortunately，there exists a design adjustment procedure to recover the stability margins of the full state feedback system [17]. 5. NOMINAL MODEJL During the design of compensators on complex mechanisms which arc described by large models with numerous states, the designer often employs two types of models: a detailed evaluation model or true remains within the boundary of 士 L5V, which is only 13% of its total range (Fig. 10)，the pressure in chamber a of the actuator fluctuates between 26 bar and 236 bar (Fig. 1 i). This represents more than 70% of the acceptable pressure range which argues for the chosen safety mar^n of 士 20，000從 How the cultimate target of reducing irregularities in the spray deposit distribution is reached, is shown in Table 3 and Fig. 12. The over application is decreased from 350 to 105% (ideal 100%) and the under Applingcation, which is worst in the middle between the spray nozzles,, is increased from 0 to 96%. 10. CONCLUSIONS A detailed linearized model of an operational spraying-machine in which the Ayres are represented by the Tyre model of Arolla, has been derived with the multiband method outlined in Pan 1 of the paper. Although the normalize model of 6 states was directly deduced from the large tractor model, instead of using more refined balanced reduction techniques, it is shown to possess a sufficient precision. With these models* an active suspension of a spray boom has been conceived successfully* owing to the intrinsic qualities of the LQG/LTR method. Citringent performance specifications are easily fulfilled without the introduction of shaping fillers, the comdispensator remains insensitive to large tractor mass variations and the recovered stability margins create a certain immunity to modeled destabilizing dynamic phenomena which could enter the system at the actuator input. It is also demonstrated that model which replaces the real physical process Turin the simulation phase^ and a smaller design model c nominal model that is norma