裝配圖大學(xué)生方程式賽車設(shè)計（整體車架、標(biāo)準(zhǔn)安全系統(tǒng)、座椅及附件設(shè)計）（有cad圖+三維圖+中英文翻譯）,裝配,大學(xué)生,方程式賽車,設(shè)計,整體,總體,車架,標(biāo)準(zhǔn),全系統(tǒng),座椅,附件,cad,三維,中英文,翻譯 設(shè)計和評價一個統(tǒng)一底盤控制系統(tǒng)在虛擬測試軌道上的車輛防側(cè)翻和穩(wěn)定性改進 摘 要 本文介紹的是統(tǒng)一的底盤控制(UCC)系統(tǒng)的發(fā)展和在虛擬測試軌道（VTT）上控制系統(tǒng)的評價。統(tǒng)一底盤控制系統(tǒng)的目的是防止車輛側(cè)翻，并通過集成電子穩(wěn)定性控制（ESC）和主動正轉(zhuǎn)向(AFS)來改善車輛的操縱性和其橫向穩(wěn)定性。防側(cè)翻通過速度控制可以達到，通過偏航速率控制可以改進車輛的穩(wěn)定性。因為統(tǒng)一底盤控制器總是與驅(qū)動程序一同工作，車輛的總體性能不僅依靠控制器工作的好壞而且依靠它和駕駛員的相互作用。通過全面的駕駛模擬器上由組成的實時汽車駕駛模擬器、 視覺動畫引擎、 可視顯示和合適的人車接口的虛擬測試軌道研究了車輛性能和車輛、控制器和人力驅(qū)動程序之間的交互作用。虛擬測試軌道已開發(fā)和用于對統(tǒng)一底盤控制系統(tǒng)在實驗室中的各種現(xiàn)實情況下的評估。并且使在實驗室對底盤控制器的評估中不帶危險和傷害的實地試驗成為了可能。并且值得關(guān)注的是還承諾了可以節(jié)約發(fā)展成本同時也全部循環(huán)利用了整體發(fā)展周期。 1. 簡介 車輛側(cè)翻在地面運輸?shù)膮^(qū)域里是一個嚴重的問題，由國家公路交通安全管理局(NHTSA)出版的一份報告發(fā)現(xiàn)即使側(cè)翻構(gòu)成的所有意外只占有一小部分，但是只要它發(fā)生了，就會造成不成比例地大部分的嚴重和致命的傷害。在2002年，有近 1100 萬輛乘用車、 SUV、 皮卡和輕型客貨車發(fā)生了撞車事故 ，然而只有2.6%的事故與側(cè)翻有關(guān)。但是，由于車輛側(cè)翻而導(dǎo)致的致命的車禍發(fā)生了約 21.1%，其相應(yīng)的百分比明顯高于其他類型的事故(NHTSA，2003年)。為了幫助消費者了解車輛可能發(fā)生的側(cè)翻，NHTSA提出了使用靜態(tài)穩(wěn)定因子（SSF）側(cè)翻抵抗評級程序，這是利用高度重心 (CG) 的半履帶寬度的比率來確定的翻轉(zhuǎn)抵抗評級。SSF 在汽車行業(yè)內(nèi)受到質(zhì)疑，因為它沒有考慮到懸架的偏轉(zhuǎn)、輪胎牽引方面或車輛控制系統(tǒng)的動態(tài)的影響。因此，2002年，NHTSA 發(fā)表了另一個公告就確定了動態(tài)翻轉(zhuǎn)的測試程序 (NHTSA，2001年)。 大多數(shù)現(xiàn)有的側(cè)翻預(yù)防技術(shù)可分為兩類，即 類型(1) 是通過主動懸架、 主動防傾桿或正向穩(wěn)定器直接控制車輛翻轉(zhuǎn)動作(陳 & 許，2008年)，這種類型可以通過提高側(cè)翻最低限值來防止車輛的側(cè)翻； 類型(2) 是通過差動制動和主動前輪轉(zhuǎn)向來控制車輛的偏航運動從而間接影響車輛的側(cè)翻動作的類型(韋蘭加 & 昌西，2000年)。一些有關(guān)側(cè)翻發(fā)現(xiàn)和側(cè)翻的預(yù)防措施的研究已經(jīng)開始做了。?？说热颂岢隽艘环N算法，可以發(fā)現(xiàn)懸置側(cè)翻和一種基本預(yù)估的側(cè)翻指數(shù)(?？?、布朗&馬丁，2004年)。陳和鵬提出一種基于時間過度 (TTR) 公制的抗側(cè)翻算法(陳 & 彭，2001年)。在這個研究中，差動制動被選定為驅(qū)動的方法。安格人和彭為防側(cè)翻評估車輛動力學(xué)控制 (VDC) 系統(tǒng)(安格人 & 彭，2004年)。楊和劉韋防側(cè)翻制定了一個結(jié)實的主動懸架(楊 & 劉，2003年)。 斯科菲爾德和海格隆德為防側(cè)翻制定了一種方法，即采用最佳的輪胎分布力 (斯科菲爾德 & 海格隆德，2008年)。月恩和易提出了一個翻轉(zhuǎn)指數(shù)，指示車輛側(cè)翻的危險，和側(cè)翻緩解控制系統(tǒng)的基本指數(shù)一樣，通過電子穩(wěn)定控制 (ESC)來減少側(cè)翻的指數(shù)(月恩、基姆 & 易，2007年)。由于橫向加速度是車輛側(cè)翻的主導(dǎo)因素，很多研究防側(cè)翻已建議使用偏航運動控制以減少橫向加速度。然而，由于這些翻轉(zhuǎn)預(yù)防計劃只專注于減少橫向加速度，車輛的操縱性和橫向穩(wěn)定性就無法保證了(月恩、稠、酷、易，2009年)。因此，當(dāng)防側(cè)翻控制器工作以減少橫向加速度時，它就會傾向于向計劃相反的方向運動。這可能會導(dǎo)致車輛偏離道路，從而導(dǎo)致事故。喬等人為房側(cè)翻制定了車輛動力控制系統(tǒng)（VDC）來確保車輛的橫向穩(wěn)定性 (喬、尤、杰昂、李 & 易，2008年）。在這個研究中，VDC被設(shè)計出來，以及優(yōu)先考慮了防側(cè)翻、過度側(cè)滑角度和車輛的不足轉(zhuǎn)向和過多轉(zhuǎn)向。然而，這種方法會導(dǎo)致車輛的可操縱性或防側(cè)翻的減少。 出于此原因，統(tǒng)一的底盤控制系統(tǒng)(UCC)被設(shè)計出來用于防止車輛的側(cè)翻。同時，通過結(jié)合各自的底盤控制模型來保證良好的操縱性和橫向穩(wěn)定性。例如，電子固定控制（ESC）和主動前轉(zhuǎn)向（AFS）。設(shè)計了一種車輛速度控制算法以防止車輛側(cè)翻。另外一種用于控制偏航運動的算法旨在提高可操縱性和橫向穩(wěn)定性。擬議的統(tǒng)一底盤控制（UCC）工作以增強可操作性和在沒有側(cè)翻危險的正常駕駛的情況下的橫向穩(wěn)定性。當(dāng)側(cè)翻的風(fēng)險增加，啟動統(tǒng)一底盤控制（UCC）來防止車輛側(cè)翻，同時可以確保車輛通過司機的駕駛可以在小路上不斷移動。為了檢測即將發(fā)生的車輛側(cè)翻，側(cè)翻指數(shù)(RI)，已經(jīng)在事先的研究中被計劃使用了(月恩等人，2007年)。 因為統(tǒng)一底盤（UCC）控制器總是與司機的操縱一起工作，所以全部車輛的動作將不僅僅依靠控制器工作的好壞，而且也依靠和司機的相互作用。因此，一個封閉的循環(huán)評估在（UCC）控制器設(shè)計中比開環(huán)模擬影響更大。所以人們總是規(guī)定了更有效的轉(zhuǎn)向(鐘 & 易，2006年)。此外，主動安全系統(tǒng)，例如統(tǒng)一底盤控制（UCC），主動巡航控制、碰撞預(yù)警、 碰撞躲避系統(tǒng)等，評價嚴重依賴實地測試，需要費時和昂貴的試驗，并往往產(chǎn)生重大的危險(漢 & 易，2006年)?；谀Ｐ偷哪M使成為可能執(zhí)行詳盡設(shè)計試驗和現(xiàn)場試驗前的評價。出于此原因，一個有關(guān)虛擬測試軌道（VTT）的全面的駕駛模擬器已經(jīng)被開發(fā)了。并使用在統(tǒng)一底盤控制的人權(quán)循環(huán)評價中?；诩彼倏刂疲≧CP）的概念，在虛擬軌道（VTT）中已經(jīng)在2004年被李描述過了。 在這篇文章中，統(tǒng)一底盤控制（UCC）算法的控制性能已經(jīng)被研究了。通過一個真實的循環(huán)仿真，并運用在了虛擬測試軌道上（VTT）。在測試中，根據(jù)虛測試擬軌道，通過由十三名司機進行控制和細節(jié)分析及總結(jié)的結(jié)果。 2. 統(tǒng)一底盤控制器設(shè)計 在這個研究中，統(tǒng)一底盤控制（UCC）系統(tǒng)旨在防止車輛側(cè)翻并提高操縱性和橫向穩(wěn)定性，通過結(jié)合獨立底盤控制模型。例如，電子固定控制（ESC）和主動前轉(zhuǎn)向（AFS）?？偣灿腥N控制模式，分別是ROM、 ESC-γ和ESC-β。分別表示防側(cè)翻、可操縱性和橫向穩(wěn)定性。統(tǒng)一底盤控制（UCC）的工作是以增強可操作性和橫向穩(wěn)定性，這是在正常的沒有側(cè)翻危險的情況下?？刹倏v性和橫向穩(wěn)定性的改善是通過在實際偏航比率和期望偏航比率之間減少偏航比率的誤差來實現(xiàn)的。該驅(qū)動程序是建立在司機轉(zhuǎn)向輸入和車輛的側(cè)滑角的基礎(chǔ)上的。當(dāng)有高度側(cè)翻危險時，啟動統(tǒng)一底盤控制（UCC）工作，來減少車輛的側(cè)翻，同時，提高車輛的可操縱性和橫向穩(wěn)定性。如在上一節(jié)中所述，因為之前的研究考慮到了減少側(cè)翻的控制(ROM)，即基于 RI 的 ROM 控制(月恩等人，2007年)。只著眼于預(yù)防車輛的側(cè)翻，因此就不能保證車輛的操縱性和橫向穩(wěn)定性。由于車輛側(cè)翻確實會存在較大的橫向加速度，先前的側(cè)翻基本指數(shù)RI基于ROM的控制器就起作用了，從而減少了橫向加速度。此控制器的策略會傾向于司機控制車輛的相反的方向，可能會引起車輛偏離路面，從而導(dǎo)致交通事故。為此，側(cè)翻指數(shù) / 車輛基本底盤控制器就被設(shè)計出來，旨在防止車輛側(cè)翻并同時確保車輛可以在司機的控制下在小路上連續(xù)移動。 圖1顯示的是一種側(cè)翻指數(shù)RI/車輛橫向基本統(tǒng)一底盤控制策略的概念算法。實施的統(tǒng)一底盤控制系統(tǒng)由高低級別的控制器組成。其中高級控制器確定控制模式，如防側(cè)翻、操縱性和橫向穩(wěn)定性 ；它也計算的所需的剎車力和為其目標(biāo)所需的偏航力矩。每個控制模式都控制一個偏航力矩和縱向輪胎力，在其軌道上帶著它一致的目標(biāo)。在低級別控制器中輸入控制模型時，它就計算出縱向及橫向輪胎力。如電子固定控制（ESC）和主動前轉(zhuǎn)向（AFS）。 11 2.1 高級控制器：決定所需制動力和所需的偏航力矩 高級控制器包括三種控制模式和一個邏輯開關(guān)。一種控制偏航力矩和縱向輪胎力由在軌道上的一致控制模型決定。所以，開關(guān)控制決定了它的基本起點。在司機的驅(qū)動程序的輸入和傳感器信號的基礎(chǔ)上，高級控制器控制的模型就被選擇了出來，如圖2所示。 在此研究中，側(cè)翻指數(shù)RI被用于檢測即將發(fā)生的車輛側(cè)翻上。其中側(cè)翻指數(shù)RI是無量綱的數(shù)，它可以指明的車輛側(cè)翻風(fēng)險。它是通過以下式子計算的： （1） 精確的橫向加速度，預(yù)估的翻轉(zhuǎn)角度Φ，估計的翻轉(zhuǎn)比率θ，和依靠車輛幾何學(xué)所得出的嚴謹?shù)慕Y(jié)果(月恩等人，2007年)。 在公式(1)中，、和都是正常數(shù)（0<<1,0<<1）。和是重量參數(shù)。與車輛的側(cè)翻情況和橫向加速度有關(guān)。是設(shè)計參數(shù)，由翻轉(zhuǎn)角度比率的幾何分析決定。公式（1）中的這些參數(shù)都是由在不同駕駛環(huán)境下的模擬研究所決定的。并調(diào)整出了這樣一個側(cè)翻指數(shù)RI以防止車輛側(cè)翻。一個由側(cè)翻指數(shù)所決定的細節(jié)描述在以前的研究中被發(fā)現(xiàn)了(月恩等人，2007 年)。橫向加速度可以輕松從傳感器中確定，并且已經(jīng)存在于車輛配備的電子固定系統(tǒng)（ESC）。但是一些傳感器需要確定翻轉(zhuǎn)角和翻轉(zhuǎn)比率，盡管它直接測量這些非常困難且代價也高(舒伯特、 尼科爾斯、沃爾納、空、斯基夫曼，2004年）。 由于這個原因，翻轉(zhuǎn)角度和翻轉(zhuǎn)比率總是被一個類似翻轉(zhuǎn)狀態(tài)預(yù)測器的基本模型所預(yù)測(帕克、月恩、易 & 基姆，2008年)。 制定側(cè)翻指數(shù)RI的預(yù)估應(yīng)用在車輛試驗的數(shù)據(jù)是從曼多公司（MANDO）獲得的。記錄的實驗數(shù)據(jù)應(yīng)用在這個評估中并不是出自統(tǒng)一底盤控制系統(tǒng)（UCC）。換句話說，曼多（MANDO）控制算法是不同于本文所描述的。所以測試得到的結(jié)果與預(yù)期結(jié)果相比較會顯示一些不同。圖4顯示的是車輛測試數(shù)據(jù)和翻轉(zhuǎn)指數(shù)，這是由國家公路交通安全管理局（NHTSA）發(fā)明的魚鉤實驗。作為一個為動態(tài)側(cè)翻傾向預(yù)測的動態(tài)實驗，實驗的結(jié)果用于整車質(zhì)量評估上。魚鉤實驗的操作步驟在圖3中所示。 圖4(a)中所示的是在兩種實驗案例下車輛轉(zhuǎn)向角的時間歷程。其輸入速度分別是43.2和45.6英里/小時，但車輛橫向穩(wěn)定性控制輸入僅適用于45.6英里/小時的案例。在這兩種情況下，一個或兩個輪子被抬升了約 4.2 s，但是側(cè)翻趨勢卻一致增加了。因此，一旦選擇控制輸入，翻轉(zhuǎn)角度和橫向加速度均會下降，側(cè)翻指數(shù)也就一起隨著下降了，如圖4(b)–(d)中所示。與控制情況相比較，側(cè)翻角度、 橫向加速度和側(cè)翻指數(shù)在非控制情況中一同的增加了。因此得出，車輛 的側(cè)翻持續(xù)了大約6s的時間。 如果側(cè)翻指數(shù)（RI）超過特定的閾值，防止側(cè)翻的模型ROM就被激活了。另外，控制器既是可操縱性得模型也是橫向穩(wěn)定性的模型。在一個很小的側(cè)滑角下，可操縱性模式中的控制器，也就是ESC-γ就起作用了。如果實際偏航比率和所需的偏航比率之間的差值超過了特定的閾值，處于激活狀態(tài)下的橫向穩(wěn)定模型就由車輛的側(cè)滑角決定。如果側(cè)滑角超過它的臨界值，在橫向穩(wěn)定性模型中的控制器，也就是ESC-β，和側(cè)滑角就能被存在于車輛中的傳感器在有限的時內(nèi)成功的檢測到（尤、哈恩、李，2009年）。 可操縱性和橫向穩(wěn)定性由偏航力矩控制方法所保證。而防止側(cè)翻通過偏航力矩/速度控制來實現(xiàn)。高級控制器計算出所需要的制動力，，為防側(cè)翻和所需的偏航的力矩，的可操縱性和橫向穩(wěn)定性。在高級控制器中，所需的控制模式切換的狀態(tài)轉(zhuǎn)換圖見圖5。 用于狀態(tài)轉(zhuǎn)換的信號是偏航比率的誤差，側(cè)滑角β 以及側(cè)翻指數(shù)RI。以致于圖5中的每一項都代表了一個轉(zhuǎn)換器。并在表 1 中描述了其激活的條件。當(dāng)車輛的狀態(tài)是處于ESC-γ 或ESC-β時，正如圖5中所示的一樣，偏航力矩控制就被應(yīng)用到了，并生成所需的偏航力矩來跟蹤目標(biāo)偏航率。在ESC-γ中，目標(biāo)的偏航比率在司機的轉(zhuǎn)向輸入的基礎(chǔ)上生成了，目的是為了提高操縱性。在ESC-β中，目標(biāo)偏航比率的產(chǎn)生是為了減少過多的側(cè)滑角β。為實現(xiàn)車輛的橫向穩(wěn)定性。當(dāng)車輛狀態(tài)是ROM時，偏航力矩和速度控制被應(yīng)用了，并分別為車輛穩(wěn)定性生成所需的偏航力矩和防側(cè)翻的制動力。 在表1中，側(cè)翻指數(shù)的起始值（）被設(shè)置為0.7，這是比較重要的數(shù)值。因為所有車輛的車輪都是與地面直接相接處的。的起始值（）被選定為0.06rad，這是在假定文章中的μ=0.3的前提下的。（拉賈瑪尼，2006年）。偏航比率誤差的起始值（）設(shè)定為0.08rad/s，是為了給出最大的偏航比率誤差。當(dāng)車輛從小路上以60km/h的速度行駛到干燥的柏油路上。 2.1.1.為可操縱性和橫向穩(wěn)定性預(yù)設(shè)偏航力矩（ESC-γ/ESC-β模式） 如果側(cè)翻指數(shù)RI很小，ESC-γ和ESC-β模型就被激活了。目的是為了分別實現(xiàn)所需的可操縱性或橫向穩(wěn)定性。在這種控制模式中，所需的偏航力矩被確定出來其目的是通過使用一個自行車模型計算目標(biāo)車輛響應(yīng)來減少偏航率誤差。這種線性模型在特定的區(qū)域內(nèi)可以表示線性輪胎特性，并且在許多出版的刊物中已經(jīng)被證實了(例如，納蓋、斯諾及高，2002年）。另外，因為車輛主動安全控制應(yīng)該在車輛進入任何危險的情況之前被啟動，此時，輪胎處于極限附著狀態(tài)附近，輪胎的特性已經(jīng)超出了線性區(qū)域之外，此時，控制就開始起作用了。因此，線性自行車模型能足夠設(shè)計出一個控制器，來確保車輛的穩(wěn)定性。 采用直接橫擺力矩控制的方法來確定所需的偏航力矩，圖6中顯示了2-D自行車模型，包括了直接偏航力矩。 2-D自行車模型的動態(tài)方程表示如下所示： 一般情況下，通過公式(2)，所需的偏航比率，在司機的轉(zhuǎn)向輸入的基礎(chǔ)上，理論上根據(jù)線性輪胎力的2-D自行車模型確定。自行車模型的穩(wěn)態(tài)偏航比率已經(jīng)介紹過了。車輛的可操縱性又由司機的目的所反映，這就表示出了車輛的縱向速度和驅(qū)動程序的轉(zhuǎn)向輸入功能，如下所示： 所需的偏航比率，如公式(3)中提到的，被作為參考ESC-γ控制模式的偏航比率。 一般情況下，如果側(cè)滑角超過了3°的話，橫向穩(wěn)定性就無法保證了。過度的車身側(cè)滑會引起車輛偏航動作的延遲，從而使司機的轉(zhuǎn)向輸入增大，并威脅到了車輛的橫向穩(wěn)定性。如車輛的側(cè)滑角增加，穩(wěn)定偏航力矩就取決于轉(zhuǎn)向輸入的減少，因此，該車輛的橫向動作就變得不穩(wěn)定。所以，控制就介入進來以保持車身的側(cè)滑角在小于3°的范圍之內(nèi)合理的變動，這樣就會按照需求提高車輛的橫向穩(wěn)定性(喬等人，2008年）。 is Rollover mitigation control Unified chassis control velopmen rabili ed perfo controller, and the human driver are investigated through a full-scale driving simulator on the VTT which consists of a real-time vehicle simulator, a visual animation engine, a visual display, and suitable by a small a disproportionately the vehicle control system. Accordingly, in 2002, NHTSA time- and method for rollover prevention that employs an optimal tire force ARTICLE IN PRESS Contents lists available at ScienceDirect Control Engineering Control Engineering Practice 18 (2010) 585–597 (Yoon, Kim, fax: +82 2 882 0561. automotive industry as it does not consider the effects of suspension deflection, tire traction aspects, or the dynamics of Liu proposed a robust active suspension for rollover prevention (Yang and (2) the type which indirectly influences roll motions by controlling the yaw Vehicle stability Virtual test track Design and evaluation of a unified chass prevention and vehicle stability improvement Jangyeol Yoon a , Wanki Cho a , Juyong Kang a , Bongyeong a School of Mechanical and Aerospace Engineering, Seoul National University, 599 Gwanangno, b Mando Corporation Central R it also calculates the desired braking force and the desired yaw moment for its objectives. Each control mode generates a control yaw moment and a longitudinal tire force in line with its coherent objective. The lower-level controller calculates the longitudinal and lateral tire forces as inputs of the control modules, such as the ESC and the AFS. 2.1. The upper-level controller: decision, desired braking force, and desired yaw moment The upper-level controller consists of three control modes and a switching logic. A control yaw moment and the longitudinal tire force are determined in line with its coherent control mode so that the switching across control modes is performed on the basis of the threshold. Based on the driver’s input and sensor signals, the upper-level controller determines which control mode is to be selected, as shown in Fig. 2. In this study, RI is used to detect an impending vehicle rollover where the RI is a dimensionless number that can indicate the risk of vehicle rollover and it is calculated through: the measured lateral acceleration, a y , the estimated roll angle, ^ f, the estimated roll rate, ^ _ f, and their critical values which depend on the vehicle geometry in the following manner (Yoon et al., 2007): In (1), C 1 , C 2 , and k 1 are positive constants (0oC 1 o1, 0oC 2 o1), C 1 and C 2 are weighting factors, which are related to the roll states and the lateral acceleration of the vehicle, and k 1 is a design parameter which is determined by the roll angle-rate phase plane analysis. These parameters in (1) are determined through a simulation study undertaken under various driving situations and tuned such that an RI of 1 indicates wheel-lift-off. A detailed description for the determination of the RI is provided in previous research (Yoon et al., 2007). The lateral acceleration can easily be measured from sensors that already exist on a vehicle equipped with an ESC system. However, additional sensors are needed to measure the roll angle and the roll rate, although it is difficult and costly to directly measure these (Schubert, Nichols, Fig. 1. RI/VS-based UCC strategy. RI?C 1 fetT C12 C12 C12 C12_ f th t _ fetT C12 C12 C12 C12 C12 C12f th f th _ f th 0 @ 1 A tC 2 a y C12 C12 C12 C12 a y,c C18C19 te1C0C 1 C0C 2 T fetT C12 C12 C12 C12 ???????????????????????????????????? fetTeT 2 t _ fetT C16C17 2 r 0 B B @ 1 C C A , f _ fC0k 1 f C16C17 40 RI?0, f _ fC0k 1 f C16C17 r0 8 > > > > > : e1T J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597 587 Fig. 2. Control modes for the proposed UCC system. ARTICLE IN PRESS 012345678 Time [sec] No control @43.2mph Control @45.6mph Roll angle 012345678 Time [sec] No control @43.2mph Contro l@45.6mph Lateral acceleration No control @43.2mph Control @45.6mph -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 1 1.5 Roll angle [deg/sec] ay [m/s] J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597588 Wallner, Kong, in this the sliding surface and the sliding condition are defined as follows: s 1 ?gC0g des , 1 2 d dt s 1 2 ?s 1 _ s 1 rC0Z 1 s 1 jj e9T where Z 1 is a positive constant. The equivalent control input that would achieve _s 1 ?0 is calculated as follows: M z,eq ?C0I z 2eC0a ^ C f tb ^ C r T I z bC0 2ea 2 ^ C f tb 2 ^ C r T I z v x gt 2a ^ C f I z D f ! e10T Finally, the desired yaw moment for satisfying the sliding condition regardless of the model uncertainty is determined as follows: M z ?M z,eq C0K 2 sat gC0g des F 1 C18C19 e11T where F 1 is a control boundary, and the gain, K 2 , which satisfies the sliding condition, is calculated as follows: K 2 ?I z F yf I z C0abC0a 2 gtaD f C12 C12 C12 C12 t F yr I z bbC0b 2 g C12 C12 C12 C12 t _g des C12 C12 C12 C12 tZ 2 C26C27 e12T 2.1.2. Desired braking force for rollover prevention (the ROM mode) If the RI increases to a predefined RI threshold value, which can predict an impending rollover, the ROM control input should be applied to the vehicle in order to prevent rollover. Rollover prevention control can be achieved through vehicle speed control and the desired braking force is determined in this section to control the speed. In addition, the desired yaw moment, as determined in the previous section, is also applied to the vehicle to improve the maneuverability and the lateral stability. As mentioned previously, since vehicle rollovers occur at large lateral accelerations, the desired lateral acceleration should be defined and can be determined from the RI (cf. Eq. (1)) as follows: a y,des ? 1 C 2 RI tar C0C 1 fetT C12 C12 C12 C12_ f th t _ fetT C12 C12 C12 C12 C12 C12f th f th _ f th 0 @ 1 A C0e1C0C 1 C0C 2 T fetT C12 C12 C12 C12 ???????????????????????????????????? fetTeT 2 t _ fetT C16C17 2 r 0 B B @ 1 C C A 8 > : 9 > = > ; a y,c e13T In (2), the target RI value, RI tar , is set to 0.6. The desired vehicle speed for obtaining the desired lateral acceleration is calculated from the lateral vehicle dynamics as follows (Yoon et al., 2009): v x,des ? 1 g a y,des C0 a y,m C0v x g C0C1C8C9 e14T The desired braking force to yield the desired vehicle speed is calculated through a planar model, as shown in Fig. 7, and through the sliding mode control law. Fig. 7 shows a planar vehicle model including the desired braking force, DF x and the dynamic equation for the x-axis is described as follows: m _ v x ?F xr tF xf cosD f C0F yf sinD f tmv y gC0DF x e15T By the assumption of having small steering angles, Eq. (15) can be rewritten in terms of the derivative of the vehicle speed as follows: _ v x ? 1 m eF xr tF xf C0F yf D f Ttv y gC0 1 m DF x e16T Fig. 7. Planar model including the desired braking force. the use of braking because the ESC module has some negative ARTICLE IN PRESS effects as the simple distribution scheme determines only the differential braking input for the ESC module. These two schemes are switched in accordance with the protocol for switching across control modes in the upper-level controller and the only ESC module is used in the ROM mode since the optimized distribution scheme for the AFS and ESC modules provides a very small braking to each wheel, which cannot decrease the vehicle speed which is essential for preventing rollover. Moreover, the slip angle of the tire is proportionally increased with the lateral acceleration as shown in Fig. 8. Since vehicle rollovers generally occurs at large lateral acceleration, the slip angle of the tire is also very large in the ROM mode situation. The AFS module cannot generate the lateral tire force in large slip angle situations as shown in Fig. 9; therefore the AFS module is not used in the ROM mode, that is, the ESC is the most effective for the ROM mode. For this reason, only the ESC control module is used for the ROM mode. 2.2.1. Tire-force distribution in vehicle stability situations (ESC-g/ ESC-b mode) In vehicle stability situations that do not have risk of rollover, the control interventions for maneuverability, ESC-c, and for lateral stability, ESC-b, are activated. When the lateral accelera- tion is small enough so that the slip angle is small, the characteristics of the lateral tire force lie within the linear region, as shown in Fig. 9. In these situations, only the AFS control module is applied and the AFS control input is determined through the consideration of the 2-D bicycle model as follows: Slip angle [deg] ESCAFS + ESC AFS Lateral tire force [N] 0 36 Fig. 9. Characteristics of the lateral tire force. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -8 -6 -4 -2 0 Lateral acceleration [g] Slip angle [deg] Vehicle Stability Rollover Prevention Fig. 8. Relation between the lateral acceleration and the slip angle. J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597 591 Fig. 10. Coordinate system corresponding Dd f ? M z 2aC f e19T When the lateral acceleration increases greatly, the combined control inputs that are based on the ESC and AFS modules are applied. Since the ESC module has some negative effects, such as the degradation of ride comfort and the wear of tires and brakes, the optimized coordination of tire forces is focused on minimizing the use of braking. An optimal coordination of the lateral and longitudinal tire forces for the desired yaw moment is determined through the Karush–Kuhn–Tucker (KKT) conditions (Cho, Yoon, two of these constraints are determined as follows: fexT?C0 t 2 D 1 DF x1 taD 2 DF y1 C0M Z ?0 e23T gexT?eDF x1 tF x1 T 2 teDF y1 tF y1 T 2 C0m 2 F z1 2 r0 e24T In the above, D 1 ?1teF z3 =F z1 T, D 2 ?1teF z2 =F z1 T. The equality constraint in (23) means that the sum of the yaw moment generated by the longitudinal and the lateral tire forces should be equal to the desired yaw moment. The inequality constraint in (24) means that the sum of the long- itudinal and the lateral tire forces should be less than the friction forces on the tire. From (22)–(24), the Hamiltonian is defined as follows: H?DF x1 2 tl C0 t 2 D 1 DF x1 taD 2 DF y1 C0M Z C18C19 tr eDF x1 tF x1 T 2 teDF y1 tF y1 T 2 C0m 2 UF z1 2 tc 2 C16C17 e25T where l is the Lagrange multiplier, c the slack variable, and r the semi-positive number. First-order necessary conditions about the Hamiltonian are determined by the Karush–Kuhn–Tucker condition theory as follows: @H @DF x1 ?2DF x1 C0 t 2 D 1 lt2reDF x1 tF x1 T?0 e26T @H @DF y1 ?aD 2 lt2reDF y1 tF y1 T?0 e27T @H @l ?C0 t 2 D 1 DF x1 taD 2 DF y1 C0DM Z ?0 e28T rgexT?r eDF x1 tF x1 T 2 teDF y1 tF y1 T 2 C0m 2 F z1 2 C16C17 ?0 e29T J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597592 F xF,max xR,max F F xF F xR F zF μ μF zR Δ Fig. 11. Friction circles of the front and rear tires. Fig. 12. Hardware configuration of the driving From (29), two cases are derived with respect to r and g(x)as follows: Case 1. r?0, gexTo0. Case 2. r40, g(x)?0. Case 1 means that the sum of longitudinal and lateral tire forces is smaller than the friction of the tire. On the other hand, Case 2 means that the sum of the longitudinal and lateral tire forces is equal to the friction of the tire. The solutions of the optimization problem represented in (3.41) can be obtained for both cases. If the desire yaw moment is positive, M z 40, the solutions are obtained as follows: Case 1 : DF x1 ?0 DF y1 ? M Z aD 2 0 B @ e30T Case 2 : DF x1 ? C0eF x1 tkzTt ??????????????????????????????????????????????????????? e1tk 2 Tm 2 F z1 2 C0ekF x1 C0zT 2 q e1tk 2 T DF y1 ? tD 1 2aD 2 DF x1 t 1 aD 2 M Z e31T where k?(tD 1 /2aD 2 ) and z?(1/aD 2 )M Z +F y1 . The brake pressure for the ESC module and the additional steering angle for the AFS module are determined from (32) simulator with a human in-the-loop. ARTICLE IN PRESS as follows: DD f ? DF yi C f P Bi ? r wf DF xi K Bi ei?1,2T 0 B B B @ e32T In (32), K Bi is the brake gain, and r wf the radius of the wheel. When the desired yaw moment is negative, M z o0, the tire forces can be obtained in a manner similar to (30) and (31). 2.2.2. Tire-force distribution in rollover situations (ROM mode) In the previous sections, the desired braking force, which should be subjected to the vehicle for rollover prevention, and the desired yaw moment for reducing the error in the yaw rate have been determined. By utilizing the above two values, a braking- force distribution is accomplished simply to help prevent vehicle rollover, while ensuring that the vehicle follows the intended path of the driver. The forces of the vehicle can be determined kinematically, as follows: DF x,left ? 1 2 DF x t M z t 1 M z 8 > e33T 0 2 4 6 8 1012141618 Time [sec] Yaw rate 024681012141618 Time [sec] Lateral acceleration 0 2 4 6 8 10 12 14 16 18 -20 -10 0 10 20 -6 -4 -2 0 2 4 6 0 2 4 -50 0 50 Time [sec] Yaw rate [deg/s] Lateral acceleration [m/s 2 ] Steering wheel angle [deg] Vehicle test Simulator Vehicle test Simulator Vehicle test Simulator Steering wheel angle J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597 593 0 2 4 6 8 10 12 14 16 18 Time [sec] Vehicle test Simulator Roll angle -4 -2 Roll angle [deg] Fig. 13. Comparison between actual vehicle test data and the driving simulator (for the slalom test). DF x,right ? 2 DF x C0 t : The braking forces of the left and right sides are obtained by substituting (18) and (11) into (33). Fig. 11 shows the friction circles of the front and rear tires and the traction force, determined through the shaft torque, is applied at the front tire, and the drag force is applied at the rear tire. The maximum braking forces of the front and rear tires can be determined as follows: DF xf,max ?F xf C0 ?????????????????????????????? emF zf T 2 C0eF yf T 2 q e34T DF xr,max ?C0F xr C0 ?????????????????????????????? emF zr T 2 C0eF yr T 2 q e35T The braking-force distributions of the front and rear tires are achieved by using equations from (33) through to (35) as follows: DF xr,left ? DF xr,left,max C12 C12 C12 C12 DF xf,left,max C12 C12 C12 C12 DF xf,left e36T DF xr,right ? DF xr,right,max C12 C12 C12 C12 DF xf,right,max C12 C12 C12 C12 DF xf,right e37T In the above, DF xf,left tDF xr,left ?DF x,left and DF xf,right t DF xr,right ?DF x,right . 80km/h Obstacle Fig. 14. The test scenario: obstacle avoidance. ARTICLE IN PRESS The braking pressure of the front-left wheel can be determined as follows: P Bf,left ? r wf eDF xf,left T K Bf if DF xf,left oDF xf,max r wf eDF xf,max T K Bf if DF xf,left ZDF xf,max 8 > > > : e38T The other tire forces can be obtained in a manner similar to (38). 3. Full-scale driving simulator The configuration of the full-scale driving simulator for the human-in-the-loop system is shown in Fig. 12, consisting of four parts: a real-time (RT) simulation hardware, a visual graphical engine, a human-vehicle interface, and a motion platform. The host computer in Fig. 12 is utilized to modify the vehicle simulation program and to display the current vehicle status. The RT simulation hardware calculates the variables of the vehicle model represented using a CARSIM model controlled by the UCC controller with measured driver reactions. By the use of the vehicle-behavior information obtained using RT simulation hardware, the visual graphical engine projects a visual representation of the driving conditions to the human driver via a beam projector with a 100-in screen who interacts with the 3-D virtual simulation and the kinesthetic cues of the simulator body. The driver’s responses are acquired through the steering wheel angle, brake pressure, and throttle positioning sensors, as shown in Fig. 12. The motion platform provides kinesthetic cues, which are related to the behavior of the vehicle with regard to the human driver. An actual full-sized braking system, including a vacuum booster, master cylinder, calipers, etc., is implemented in the simulator so that the feel of the braking action is similar to that of an actual vehicular brake pedal. In the case of the steering wheel, a spring and damper are used to produce the reactive forces of the steering wheel where the spring and damper characteristics are adjusted to make the feel of the steering wheel similar to that of an actual vehicle being driven in the high-speed range. 3.1. Configurations of the driving simulator The most important feature of the driving simulator is to guarantee real-time performance and so all the subsystems are 8 0 -200 -100 100 200 100 120 10 Steering wheel angle [deg] w/o control RI-based ROM RI/VS-based UCC RI-based ROM 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 Time [sec] Time [sec] Steering wheel angle. Lateral acceleration. -1 -0.5 0 0.5 1 0 1.5 2 Lateral acceleration [g] w/o control RI-based ROM RI/VS-based UCC w/o control RI-based ROM RI/VS-based UCC J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597594 -10 -5 0 5 Roll angle [deg] RI/VS-based UCC 0 2 4 6 8 10 12 14 16 18 Time [sec] Roll angle. 0 2 4 6 8 101214161 0 20 40 60 80 Velocity [km/h] w/o control RI-based ROM RI/VS-based UCC w/o control Time [sec] Velocity. Fig. 15. Driving tests results using the full-scale 024681012141618 Time [sec] Rollover index. 0 2 4 6 8 10 12 14 16 18 -0.5 0 0.5 Time [sec] Yawrate error [deg/sec] w/o control RI-based ROM RI/VS-based UCC Yaw rate error. 0.5 1 Rollover index simulator based on the VTT. ARTICLE IN PRESS to the simulator body, as shown in Fig. 12 and the motion trajectories. If the UCC control input is not applied, the vehicle rolls over in this situation. It is clear from Fig. 15(e) that the RI increases over unity in the absence of control. Further, the roll angle and lateral acceleration also increase to large values, as shown in Fig. 15(c) and (d). In addition, because this situation is very severe, the vehicle deviates from the lane, as shown in Fig. 17. It can be seen that the driver’s detects the dropped obstacle at about five seconds and immediately tries to avoid the obstacle by changing lane. The vehicle velocities at about five seconds of three cases, viz., NON-control, RI-based ROM, and RI/VS-based UCC, are similar to each other, as shown in Fig. 15(b). When the UCC control is activated, two of the control systems yield good resistance to rollover, as shown in Fig. 15(c) and (e). As the RI-based ROM system intends to control the vehicle in a direction that is opposite to the driver’s intention, the yaw rate 0 2 4 6 8 1012141618 Time [sec] Brake pressures [MPa] Front-left Front-right Rear-left Rear-right RI-based ROM system. 0 2 4 6 8 1012141618 0 5 10 15 20 0 2 4 6 8 10 Time [sec] Brake pressures [MPa] Front-left Front-right Rear-left Rear-right RI/VS-based UCC system. Fig. 16. Brake pressures. J. Yoon et al. / Control Engineering Practice 18 (2010) 585–597 595 platform allows displacements up to a maximum of about 710 cm (heave) and 7101 (roll and pitch). The motion platform renders the linear and angular accelerations of the simulated vehicle model, as computed by the RT simulation hardware so that the human driver gets an impression that s/he is driving an actual vehicle by means of the kinesthetic cues generated by the motion platform, and from the visual representation of the driving situation provided by the visual graphical engine. 3.2. Validation of the vehicle simulator The driving simulator used in this paper is evaluated via actual vehicle test data and Fig. 13 shows the results of a slalom test in which the driver maintains an approximately constant vehicle speed of about 60 km/h. The cone width is 30 m. The magnitude and frequency of the driver’s steering inputs are almost identical in both the vehicle test results and the driving simulator, as shown in Fig. 13(a). The vehicle responses in terms of the yaw rate, the lateral acceleration and the roll angle are also quite similar to the actual test results as shown in Fig. 13(b)–(d). The comparison between the driving simulator and actual vehicle test results shows that the proposed driving simulator is feasi