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譯文題目: 基于使用DTFC最優(yōu)滑動(dòng)控制的
新型混合防抱死制動(dòng)系統(tǒng)電動(dòng)汽車
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文獻(xiàn)出處:國(guó)際科學(xué)26.1(Jan-Mar 2014): 197-203.
基于使用DTFC最優(yōu)滑動(dòng)控制的新型混合防抱死制動(dòng)系統(tǒng)電動(dòng)汽車
Sharifian, Mohammad Bagher Bannae;?Yousefi, Babak;?Ebadpour, Mohsen
(伊朗大不里士大學(xué),電氣和計(jì)算機(jī)工程學(xué)院)
摘要:一輛汽車的制動(dòng)性能是汽車安全的一個(gè)重要因素。一個(gè)成功設(shè)計(jì)的制動(dòng)系統(tǒng)的車輛必須滿足不同的需求,迅速減少車速和維護(hù)方向穩(wěn)定性。事實(shí)證明,轉(zhuǎn)速和車速在一定的比例范圍內(nèi),制動(dòng)力最大。當(dāng)代,制動(dòng)系統(tǒng)的主要功能就是防抱死制動(dòng)系統(tǒng)(ABS)。首先是阻止車輪鎖止,第二處于理想滑動(dòng)。在本文中該方法結(jié)合的原則應(yīng)用于ABS、電氣制動(dòng)系統(tǒng)和由兩個(gè)機(jī)械和電氣部分組成。模擬轉(zhuǎn)矩控制和滑移控制系統(tǒng)設(shè)計(jì)利用MATLAB / Simulink軟件已經(jīng)完成。為了證明在可變化性和比較小附著系數(shù)的道路上,提出的制動(dòng)系統(tǒng)的高性能,傳統(tǒng)的剎車所面臨的問(wèn)題。該方法的可靠性已經(jīng)得到證實(shí)。
關(guān)鍵詞:混合動(dòng)力電動(dòng)汽車(HEVs);防抱死制動(dòng)系統(tǒng)(ABS);直接轉(zhuǎn)矩和磁通控制(DTFC);滑動(dòng)控制
引言
近幾十年來(lái),相關(guān)的研究和開(kāi)發(fā)活動(dòng)交通一直強(qiáng)調(diào)發(fā)展高效、清潔、安全的交通工具。通常建議電動(dòng)車((EVs)、混合動(dòng)力電動(dòng)汽車((HEVs)和燃料電池汽車在不久的將來(lái)取代傳統(tǒng)汽車。人們對(duì)混合動(dòng)力電動(dòng)汽車日益增長(zhǎng)興趣是由于這一事實(shí):在低速電動(dòng)汽車和高速柴油機(jī)都可以高性能工作。除了高效的電機(jī)由于發(fā)電機(jī)這些機(jī)器的功能,他們節(jié)約電力的能力 [1-3]。在電動(dòng)汽車或混合動(dòng)力電動(dòng)汽車,都可以使用電機(jī)制動(dòng)。車輪制動(dòng)過(guò)程中,鎖止是對(duì)車輛的穩(wěn)定性造成負(fù)面影響。另一方面,它還危害乘客的生命。那就是為什么今天是很常見(jiàn)的使用汽車防抱死系統(tǒng)[4]。
安裝防抱死制動(dòng)系統(tǒng)(ABS)的車輛的目的是保持在一定范圍內(nèi),以確保車輪滑移最大制動(dòng)力,減小制動(dòng)距離。此外,它直接增加制動(dòng)力和側(cè)向摩擦力,幫助維持車輛穩(wěn)定[5]。在每個(gè)輪子上通過(guò)應(yīng)用傳感器和使用四個(gè)調(diào)節(jié)器石油龍頭來(lái)調(diào)整制動(dòng)力將在ABS獲得最好的制動(dòng)狀態(tài)。在[6],提出了一種方法來(lái)優(yōu)化石油閥門的開(kāi)啟和關(guān)閉來(lái)計(jì)算合適的機(jī)油壓力在每個(gè)輪子上的最少時(shí)間。有另一種類型的電氣制動(dòng)只適合普通事故,稱為再生制動(dòng)。再生制動(dòng)過(guò)程中部分動(dòng)能轉(zhuǎn)化為電能。這種制動(dòng)器使用低可靠性的傳統(tǒng)的制動(dòng)器 [7-9]。在防抱死制動(dòng)系統(tǒng)(ABS)中,由于各種各樣的壓力,制動(dòng)管、變附著系數(shù)的道路及其依賴速度,道路彎曲不同輪滑移值和其他參數(shù),滑移的計(jì)算方法非常重要。在[10],通過(guò)使用一個(gè)反饋,控制循環(huán)已經(jīng)形成衡量動(dòng)態(tài)滑動(dòng)率。通過(guò)李雅普諾夫理論策略開(kāi)啟和關(guān)閉閥門的油壓控制提出了控制滑移。基于智能技術(shù)可以使用算法。
在[11],ABS系統(tǒng)提供檢測(cè)路況和滑移控制。為了估計(jì)摩擦和道路外形,LuGre模型已經(jīng)使用。然后,應(yīng)用一種基于模糊神經(jīng)網(wǎng)絡(luò)的估計(jì)量。在一些報(bào)紙中,估計(jì)滑移率是根據(jù)灰色模型和由滑??刂破?SMC)證實(shí)了它們的準(zhǔn)確性。在這些方法中,滑移估計(jì)值要結(jié)合最優(yōu)滑移調(diào)節(jié)器[12]。有一些方法,以提高車輛穩(wěn)定性原理類似于ABS的原則。在[13],基于模糊邏輯的方法來(lái)控制偏航和橫向滑動(dòng)。在這種方法中,在高速車輛的后方馬達(dá)通過(guò)安裝控制器來(lái)控制橫向穩(wěn)定性。
在本文中,獲得最大利用機(jī)械制動(dòng)器制動(dòng)力,在同一時(shí)間利用恒力和電氣制動(dòng)的可能性來(lái)調(diào)整滑移是目的??紤]到制動(dòng)力依賴于道路狀況,提高車輪制動(dòng)力矩導(dǎo)致車輪抱死,從而導(dǎo)致制動(dòng)力降低大約30%和100%的側(cè)向穩(wěn)定性。在提出的方法中,通過(guò)從車輪滑動(dòng)得到反饋,它的數(shù)量是固定在最優(yōu)數(shù)量(通常0.2)獲得最大制動(dòng)力。此外,一些其他問(wèn)題,ABS系統(tǒng)在結(jié)冰或塵土飛揚(yáng)的道路上,一直有影響。
一、制動(dòng)力的原則
當(dāng)車輛勻速前進(jìn),速度正比于車輪速度并且車輪沒(méi)有滑動(dòng)。但當(dāng)司機(jī)按下制動(dòng)踏板降低速度時(shí),車輪速度逐漸減少,車身的比例也被毀壞。應(yīng)該指出,在這種情況下由于慣性力,車身傾向于移動(dòng)。因此,在車輪與路面之間形成一個(gè)小坡度。車輪速度和車速之間的差異表示滑移量?;坡视?jì)算如下:
Λ=(Vv-Vw)/Vv (1)
在等式(1)中,參數(shù)Vv和Vw分別表示車速和車輪速度。0%的滑移率顯示了輪自由滑動(dòng),沒(méi)有任何障礙,100%的滑移率顯示模型在路上完全鎖止和輪下滑。通過(guò)增加車輪速度和車速之間的區(qū)別,車輪和路面之間的滑移太高了。這引起摩擦和制動(dòng)力,進(jìn)而車速降低。制動(dòng)力和滑移率關(guān)系圖1所示。制動(dòng)力并不總是與滑動(dòng)率有關(guān)。然而,當(dāng)10 - 30%之間的滑移率,獲得的最大制動(dòng)力[14]。
圖1 制動(dòng)力和滑移率關(guān)系圖
二、最優(yōu)制動(dòng)力的分配
按下制動(dòng)踏板時(shí),制動(dòng)盤上創(chuàng)建一個(gè)制動(dòng)轉(zhuǎn)矩。這種制動(dòng)力矩在車輪和接觸的地面之間產(chǎn)生一個(gè)力。如果這個(gè)力大于最大制動(dòng)力矩,它將使車輛停止。制動(dòng)力及其最大值可以得到如下:
Fb=Tb/rd (2)
Fbmax=Ub*w (3)
在方程(2)和(3),,Tb、rd、參考轉(zhuǎn)矩、有效半徑分別為輪子的速度。Hb是道路和車輪的附著系數(shù)和滑移率變化。可獲得最大數(shù)值(1520)的比例下滑。制動(dòng)力隨著制動(dòng)力矩的增加而增加。如圖2所示,當(dāng)制動(dòng)功率達(dá)到最大可容忍的路輪,其值仍然幾乎是不變的[14]。在道路和輪子之間最大可實(shí)現(xiàn)的制動(dòng)力是依賴/ ib和車重。
圖2 a)制動(dòng)時(shí)車輪受力圖 b)轉(zhuǎn)矩和制動(dòng)力關(guān)系圖
三、制動(dòng)力之間的前后軸
在平坦道路上車力如圖3所示。轉(zhuǎn)向盤和氣動(dòng)抗性被忽視,是由于他們與制動(dòng)力相比其值小。負(fù)加速度的車輛,制動(dòng)模式定義為j可以容易得到:
j=(Fbf+Fbr)/Mv (4)
Fbr和Fbf分別表示制動(dòng)力作用于前后車輛的輪軸。最大制動(dòng)力被限制是由于輪路間的粘附系數(shù)和每個(gè)輪子的機(jī)械負(fù)載荷。因此,從制動(dòng)力矩獲得的制動(dòng)力應(yīng)正比前后輪軸的負(fù)載。結(jié)果,前后輪軸同時(shí)實(shí)現(xiàn)他們的最大制動(dòng)力。忽視了在制動(dòng)期間從后軸到前軸的整體移動(dòng),輪子的重量在前后輪軸接觸點(diǎn)圖3 A和B可以計(jì)算(5)和(6)[4]。
Wf=Mv*g*(Lb+hg*j/g)/L (5) Wr=Mv*g*﹙La-hg*j/g﹚/L (6)
圖3 前后輪軸受力分布圖
此外,在前、后軸制動(dòng)力的值應(yīng)該等于重量的名義值。所以:
Fbf/Fbr=Wf/Wr=(Lb+hg*j/g)/(La-hg*j/g) (7)
(7)(4)相比,在理想的制動(dòng),前后輪軸的制動(dòng)力圖4所示,j是車輛在道路上的最大負(fù)加速度。
圖4 理想制動(dòng)力分配圖(I-curve)
根據(jù)圖4,理想制動(dòng)力分配曲線命名I-curve是非線性雙曲線。同時(shí)鎖定前輪和后輪,前后輪軸的制動(dòng)力應(yīng)遵循I-curve。在實(shí)際設(shè)計(jì)中,這些力和他們的比率被認(rèn)為是線性和定義前軸的制動(dòng)力與總制動(dòng)力的比例。根據(jù)(8)。
β=Fbf/Fbr (8)
圖5顯示了理想和實(shí)際制動(dòng)曲線[14]。圖5表明,這些曲線相交與一點(diǎn),在這一點(diǎn)上前輪和后輪同時(shí)被鎖止。這一點(diǎn)似乎為一定值的附著系數(shù)Ho,可以從以下公式計(jì)算:
Fbf/Fbr=β/(1-β) (9)
β/(1-β)=(Lb+hg*j/g)/(La-hg*j/g) (10)
u0=(L*β-Lb)/hg (11)
制動(dòng)時(shí),ia小于Ho(一個(gè)地區(qū)?曲線在I-curve之下),前輪比后輪提前鎖止,反之亦然。當(dāng)后輪首先鎖止時(shí),車輛失去方向穩(wěn)定性和后輪的橫向穩(wěn)定性降低為零。在這種情況下,一個(gè)小側(cè)向力像風(fēng)力或離心力等將會(huì)導(dǎo)致側(cè)向不穩(wěn)定。車輛將旋轉(zhuǎn)90,然后180度脫離道路。另一方面,制動(dòng)時(shí)前輪被鎖止,司機(jī)將失去控制車輛前進(jìn)方向,將無(wú)法有效控制車輛。然而,這并不意味著不穩(wěn)定是完全發(fā)生。因此,前軸自控力從而防止側(cè)向不穩(wěn)定[14]。
圖5 理想—實(shí)際制動(dòng)曲線圖
根據(jù)這些討論,似乎后輪的鎖止更危險(xiǎn),尤其是在小道路。因?yàn)樵谶@樣的道路上,制動(dòng)力逐漸減少,動(dòng)能逐漸降低。所以,狀況不穩(wěn)定、車輛本身變得更遠(yuǎn)。因此,汽車設(shè)計(jì)必須首先保證后輪不鎖止。由于限制,產(chǎn)生的轉(zhuǎn)矩和牽引電機(jī)的供應(yīng)用于電動(dòng)汽車和很多不同ja0。圖6所示,電氣和機(jī)械轉(zhuǎn)矩比根據(jù)路滑條件可以調(diào)整。如圖6所示,例如在冷凍條件下,扭矩為200 N.m和有關(guān)電氣制動(dòng)電機(jī)功率值的定義。Ho越?電氣部分總比,其值會(huì)越高[14]。
圖6 u在不同條件下的分布圖
四、直接轉(zhuǎn)矩和磁通控制(DTFC)
直接轉(zhuǎn)矩控制來(lái)源于重構(gòu)磁通量的直接控制,而且比磁通量矢量控制其實(shí)現(xiàn)容易。磁通和轉(zhuǎn)矩通常由磁滯控制器控制。由PWM調(diào)制器造成的延誤在這個(gè)方法可以削減并且PWM調(diào)制器可以進(jìn)行替換為一個(gè)最優(yōu)切換技術(shù)。傳統(tǒng)轉(zhuǎn)矩控制方法的總結(jié)在表中提出了。
本文提出的方法是一個(gè)商業(yè)名稱叫做DTFC技術(shù)使?fàn)恳姍C(jī)自我控制。該方法首先提出了感應(yīng)電動(dòng)機(jī)由PWM電壓源控制,開(kāi)發(fā)成一個(gè)控制扭矩的矢量,應(yīng)用于交流電機(jī)由電壓或電流源逆變器提供的。事實(shí)上,基于定子磁通矢量的大小、轉(zhuǎn)矩誤差及其數(shù)量和矢量的定子磁通在每6個(gè)活躍狀態(tài) (或12個(gè)狀態(tài)),某一電壓向量 (或電壓向量的組合) 直接或有特定的時(shí)間表適用于逆變器。為了計(jì)算磁通、定子轉(zhuǎn)矩的大小和相位誤差對(duì)應(yīng)的值應(yīng)該估計(jì)。因此,一個(gè)合適的轉(zhuǎn)矩和磁通估計(jì)量或者速度傳感器直接控制的磁通量向量和DTFC(磁通控制)是必要的。DTFC法和直接矢量控制的基本框圖圖7所示。
圖7 a)直接磁通量控制圖 b)直接轉(zhuǎn)矩控制圖
圖7所示,DTFC是一種直接電流矢量控制。兩種控制策略,圖7所示需要磁通和轉(zhuǎn)矩的觀察器。然而,直接轉(zhuǎn)矩控制和定子磁通控制具有良好的精度。因此用直流電流設(shè)計(jì)PI控制器不是必需的。以及開(kāi)環(huán)PWM用于該方法被一個(gè)最佳的轉(zhuǎn)換表代替了。這些簡(jiǎn)化意味著DTFC只使用磁通、扭矩和速度觀測(cè)器控制電機(jī)。此外,定子磁通作用的DTFC和不需要轉(zhuǎn)子磁通從而導(dǎo)致控制系統(tǒng)更簡(jiǎn)單。雖然動(dòng)態(tài)特性圖7所示的方法都是一樣的,直接矢量控制一般緩慢是由于轉(zhuǎn)子磁通分析的必要。
id=(L+sr)*λr/Lm (12)
等式 (12)顯示,對(duì)于轉(zhuǎn)子通過(guò)其適應(yīng)機(jī)制工作,有一個(gè)時(shí)間常數(shù)(rr)。所以很明顯,DTFC間接充當(dāng)直接矢量對(duì)噪聲控制更簡(jiǎn)單和更強(qiáng)大。此外,它具有更好的動(dòng)態(tài)轉(zhuǎn)矩響應(yīng)速度范圍。
五、模擬結(jié)果
模擬是由兩部分組成:第一部分包括動(dòng)態(tài)響應(yīng)的模擬車輛制動(dòng)模式和基于p和道路情況的滑移變化。在第二部分,獲得值與預(yù)期值、速度參考和計(jì)算電機(jī)轉(zhuǎn)矩值比較,這些值應(yīng)用于DTFC。電機(jī)轉(zhuǎn)矩模擬控制系統(tǒng)的電氣防抱死制動(dòng)系(EABS)統(tǒng)圖8所示。模擬中使用的電機(jī)是一個(gè)三相感應(yīng)電動(dòng)機(jī),其參數(shù)表II所示
圖8 EABS電機(jī)轉(zhuǎn)矩控制系統(tǒng)圖
表Ⅱ 模擬電機(jī)參數(shù)
在實(shí)踐中,考慮到應(yīng)用制動(dòng)力和最大可持續(xù)車輪力之間的差異,滑移變化。涉及這些變化相關(guān)的方程可以計(jì)算。在提到的控制系統(tǒng)中,滑動(dòng)選擇參考0.2。重要的是要注意,滑移曲線分為兩個(gè)部分:滑移率大于0.2的曲線和小于0.2的曲線。輸入這些方程的制動(dòng)轉(zhuǎn)矩比率和最大可持續(xù)車輪扭矩比率并且輸出就是滑移值。計(jì)算滑移后,它的值與0.2相比。如果是大于0.2,它將減去0.2。如果是小于0.2,它將被增加到0.2。這些值的變化可以依賴或獨(dú)立于滑移值。這些計(jì)算的步驟框圖如圖9所示。
為了使模擬更真實(shí),最大可持續(xù)車輪轉(zhuǎn)矩和機(jī)械轉(zhuǎn)矩是在230 Nm和400 Nm分別在1和3的規(guī)定,隨意波動(dòng)?;?轉(zhuǎn)矩-速度子系統(tǒng)在車輛制動(dòng)模式下的相關(guān)結(jié)果,如圖10—17所示。
圖9 滑移—轉(zhuǎn)矩—速度控制及計(jì)算子系統(tǒng)圖
圖10 電子轉(zhuǎn)矩圖
圖11 最大可持續(xù)道路—車輪轉(zhuǎn)矩圖
圖12 可應(yīng)用轉(zhuǎn)矩減圖及可持續(xù)道路—車輪轉(zhuǎn)矩圖
圖13 滑移率圖
圖14 沒(méi)有控制器的滑移圖
圖15 每個(gè)車輪上的轉(zhuǎn)矩圖
圖16 汽車加速度變化圖
圖17 汽車速度變化圖
在顯示的數(shù)據(jù),注意到轉(zhuǎn)矩跟隨最大轉(zhuǎn)矩和車輪滑移被控制在可接受的波動(dòng)0.2。第二部分是與DTC和感應(yīng)電動(dòng)機(jī)有關(guān)圖18所示。
圖18 DTC子系統(tǒng)圖
感應(yīng)電動(dòng)機(jī)由PWM電壓源逆變器所控制。在速度控制回路,PI控制器是用于生成參考磁通和轉(zhuǎn)矩值。在DTC塊中,計(jì)算電機(jī)轉(zhuǎn)矩和估計(jì)磁通,然后與參考值比較??紤]到特殊的情況,輸出脈沖比較器應(yīng)用于切換到逆變器開(kāi)關(guān)。這個(gè)子系統(tǒng)產(chǎn)生和遵循所需的扭矩高速度和準(zhǔn)確度。
六、結(jié)論
電力和混合動(dòng)力汽車可以使用電氣制動(dòng)。然而,考慮到這種想法的限制,它用于機(jī)械制動(dòng)。在嚴(yán)重和突然剎車時(shí),再生制動(dòng)是不可能的。因?yàn)樵谶@種制動(dòng)車輛停止是最快的。另外,電機(jī)本身不能產(chǎn)生制動(dòng)轉(zhuǎn)矩。甚至如果電機(jī)有這種能力,電源和效率問(wèn)題阻止這種情況。所以,最好的方式似乎是使用帶有ABS特色的并行制動(dòng)。然而,應(yīng)該探索更好的方法,因?yàn)锳BS方法不減少制動(dòng)距離。該方法是結(jié)合ABS和電氣制動(dòng),而ABS系統(tǒng)在汽車輪子上負(fù)責(zé)控制油壓,涉及電氣車輛特征。在實(shí)際情況下,赤潮的控制系統(tǒng)比ABS系統(tǒng)更簡(jiǎn)單、更便宜,由于控制4泵減少到2泵。關(guān)于制動(dòng)的性能質(zhì)量的適當(dāng)?shù)姆椒?,從模擬結(jié)果來(lái)看,滑移控制及其根據(jù)期望的值是顯而易見(jiàn)的。這種方法的唯一缺陷可能是,在電氣制動(dòng)使用能量,降低車輛的效率。然而,用于制動(dòng)、增加制動(dòng)和車輛安全的能量是微不足道的小值。
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附件:外文資料原文
A NEW HYBRID ANTI-LOCK BRAKING SYSTEM FOR HEVS BASED ON OPTIMAL SLIP CONTROL USING DTFC
Sharifian, Mohammad Bagher Bannae;?Yousefi, Babak;?Ebadpour, Mohsen.?Science International26.1?(Jan-Mar 2014): 197-203.
Headnote
ABSTRACT: The?braking?performance of a?vehicle?is an important factor in?vehicle?safety. A successfully designed?braking system?for a?vehicle?must always meet the distinct demand of quickly reducing?vehicle speed and maintaining?vehicle?direction controllable by the?steering?wheel. It has been proved that for a certain ratio of wheel rotation and?vehicle?speed,?braking?force is maximum. The main function of nowadays braking systems?which is known as anti-lock?braking system?(ABS) first is to prevent wheels from locking, second bringing the?vehicles?slip to the ideal slip. The proposed method in this paper is a combination of the principles which are used in ABS and electrical?braking systems?and consists of two mechanical and electrical parts. Simulation of torque?control?and slip?control system?design has been performed with MATLAB/Simulink software. To prove the high performance of proposed?braking system?a road with variable and rather small adhesive coefficient, which conventional brakes face with problem on it, has been considered. The reliability of proposed method has been proved.
Keywords: hybrid electric?vehicles?(HEVs), anti-lock?braking system?(ABS), direct torque and flux?control(DTFC), slip?control
(ProQuest: ... denotes formulae omitted.)
INTRODUCTON
In recent decades, the research and development activities related to transportation have emphasized the development of high-efficiency, clean, and safe transportation. Electric?vehicles?(EVs), hybrid electric?vehicles(HEVs), and fuel cell?vehicles?have been typically proposed to replace conventional?vehicles?in the near future. Growing interest in HEVs is due to this fact that, in low speeds electrical motors and in high speeds diesel engines have high performance. In addition to high-efficiency of electrical motors due to generator behavior of these machines, they are capable of saving part of their electrical powers [1-3]In EVs or HEVs, it is possible to use electrical motors for?braking. Wheels' locking during?braking?process is causing a negative impact on the stability of the?vehicle. On the other hand, it also endangers the lives of passengers. That's why today is very common to use?vehicles?with anti-locking?system?[4].
The purpose of installing of anti-lock?braking system?(ABS) on the?vehicle?is to keep the wheels slip in a certain range to ensure maximum?braking?force and reduce?braking?distance. Furthermore, it increases?braking?force in direct and lateral friction force that helps to maintain?vehicle?stability [5]. By applying sensors on each wheel and using four regulator oil taps to adjust the?braking?force the best?braking?state will be obtained on ABS system. In [6], a method is presented to optimize the opening and closing oil valves to calculate the appropriate oil pressure on each wheel in least time. There is another type of electric brake that is suitable only for commonplace accidents, called, regenerative?braking. In the process of regenerative?braking?a part of kinetic energy is converted into electrical energy. This brake is used with conventional ones due to low reliability of it [7-9]. In ABS?braking systems, due to the variety of pressure in?braking?pipes, variable adhesive coefficient of roads and its dependence to speed, different wheel slips on road bends, and other parameters, the calculation method of slip has great importance. In [10], by using a feedback, a?control?loop has been formed which measures slip rates dynamically. By means of Lyapunov theory a strategy for opening and closing valves of oil pressure?control?has been presented to?control?slip. The algorithms, based on?intelligent techniques can be used.
In [11], an ABS?system?is provided to detect the road conditions and slip?control. To estimate the friction and road profile, LuGre model has been used. Then, an estimator based on fuzzy-neural network is applied. In some papers, the slip rate is estimated based on Gray model and the accuracy of them is confirmed by sliding-mode controller (SMC). In these methods slip estimation is combined with optimal slip regulator [12]. There are some methods in order to increase the?vehicle?stability which has principles analogous to the principles of ABS. In [13], a method based on fuzzy logic to?control?yaw and lateral slip has been presented. In this method by installing controllers on rear motors lateral stability of?vehicles?at high speed has been controlled.
In this paper, obtaining maximum brake force by using mechanical brake with constant force and electrical brake with the probability of adjusting slip at the same time is aimed. Considering the?braking?force is depend to the road profiles, increasing?braking?torque on the wheel causes wheel lock and consequently leads to approximately 30% reduction in?braking?force and 100% lateral stability. In proposed method, by getting feedback from wheels slip, the quantity of it is fixed at optimal amount (normally 0.2) to obtain maximum braking?force. In addition, some other problems which ABS?systems?on icy or dusty roads have, has been obviated to somewhat.
PRINCIPLES OF?BRAKING?FORCE
When the?vehicle?is moving with constant velocity, its velocity is proportional to its wheels speed, and wheels have not slip. But when the driver presses on the brake pedal to reduce speed, wheels speed gradually decreases and theirs proportion with?vehicle's body is destroyed. It should be noted that, in this case due to the force of inertia, the?vehicle's body is tendency to move. Thus, a small slip between the wheels and the road surface is created. The difference between wheel speed and?vehicle?speed indicates the amount of slip. Slip rate is calculated as follows:
Λ=(Vv-Vw)/Vv (1)
In Eq. (1), parameters Vv and Vw are indicates?vehicle?velocity and wheel speed, respectively. Zero percent of the slip rate shows the wheel moves freely and is not facing with any obstacles. One hundred percent of the slip rate shows the mode in which the wheel completely locks and wheel slipping extremely on the road. By increasing the difference between the wheel speed and?vehicle?velocity, the slip between the wheels and road surface is too high. This is lead to cause friction and?braking?force. Then, the?vehicle?velocity is reduced. Relation between the?braking?force and the slip rate is shown in Fig. 1. Brake force is not always associated with slip rate. However, when the slip rate is between 10 to 30 percent, the maximum?braking?force is obtained [14].
OPTIMUM DISTRIBUTION OF?BRAKING?FORCE
When the brake pedal is pressed, a?braking?torque is created on the brake disc. This?braking?torque makes a force in the contact area of wheel and ground. If this force exceeds the maximum?braking?torque, it will stop the?vehicle.?Braking?force and its maximum values can be obtained as follows:
Fb=Tb/rd (2)
Fbmax=Ub*w (3)
In equation (2) and (3), Tb, rd , and co refer to torque, effective radius of wheels and wheels speed, respectively. Hb is the adhesion coefficient of road and wheel and it varies by slip rate. Its maximum value can be obtained in the (1520) percentage of slip.?Braking?force increases with the increase in brake torque. As shown in Fig. 2, when?braking?force reaches to maximum tolerable road wheels amount, its value remains almost constant [14]. Maximum achievable?braking?force between the road and wheels is depended to /ib and vehicle's weight.
BRAKING?FORCE BETWEEN FRONT AN REAR AXLES
The forces into the?vehicle?on a flat road shown in Fig. 3.?Steering?wheel and aerodynamic resistances are neglected due to their small value in comparison with?braking?force. Negative acceleration of?vehicle?in braking?mode is defined as j which can be easily obtained as follow:
j=(Fbf+Fbr)/Mv (4)
Where, Fbr and Fbf are the?braking?forces which act on front and rear axles of?vehicle. The maximum?braking force is limited by the adhesion coefficient of wheel-road and mechanical load of each wheel. Therefore, the braking?force obtained from?braking?torque should be proportional to the loads of front and rear axles. In a result, front and rear axles achieve their maximum?braking?force at the same time. Neglecting the mass movement from rear axle to front axle during the?braking, wheels' weight in front and rear axles on the contact points A and B of Fig. 3 can be calculated as (5) and (6)[4].
Wf=Mv*g*(Lb+hg*j/g)/L (5) Wr= Mv*g*(La-hg*j/g)/L (6)
Moreover, the value of?braking?force in front and rear axles should be equal to nominal value of weight. So:
Fbf/Fbr= Wf/ Wr=(Lb+hg*j/g)/ (La-hg*j/g) (7) Comparing (7) to (4), in ideal?braking,?braking?forces in front and rear axles are shown in Fig. 4, where, j is the maximum negative acceleration of?vehicle?on road.
According to Fig. 4, ideal?braking?force distribution curve which is named I-curve is a non-linear hyperbolic curve. For locking the front and rear wheels simultaneously,?braking?forces in front and rear axles should follow the I-curve. In a real design, these forces and their ratio are considered linear and defined the ratio of?braking force of front axle to the total?braking?force, according to (8).
β=Fbf/Fbr (8)
Fig. 5 shows the ideal and actual?braking?curves[14]. In Fig. 5 clear that these curves meet together only in one point and in this point, front and rear wheels are locked in the same time. This point appears for a certain value of adhesion coefficient Ho and can be computed from the following equations:
Fbf/Fbr=β/(1-β) (9) β/(1-β)= (Lb+hg*j/g)/ (La-hg*j/g) (10)
u0=(L*β-Lb)/hg (11)
With?braking?in a road which it's ia is less than Ho (A region that the ? -curve is under I-curve), front wheels are locked before rear wheels and vice versa. When the rear wheels lock first, the?vehicle?loses its directional stability and lateral stability of rear wheels decreases to zero. In this condition, a small lateral force such as wind or centrifugal forces in road turns can cause lateral instability and?vehicle?will tum 90 and then 180 degrees around itself and will be taken out of the road. On the other hand, when the front wheels are locked due to?braking, the driver will lose the?vehicle control?on forward direction and will not be able to effective control?of?vehicle. However, it does not mean that the instability is completely happened. Since, there is a self correcting force in the front axle which prevents the lateral instability [14].
According to these discussions, it seems that the locking of rear wheels are more perilous, especially in the roads with small /a , because in such kind of roads?braking?force is less and kinetic energy of?vehicle decreases gradually and so, in instability condition,?vehicle?turns more distances around itself. Therefore, in vehicle?design, it must be ensured that the rear wheels do not lock first. Due to restrictions in the amount of generated torque and the supply of traction motors which used in electric?vehicles?and large differences of ja0 that shown in Fig. 6, electrical and mechanical torque ratios can be adjust by applying the slippery road condition. As shown in