對未來研究之建議

本論文中，利用QFT/H∞理論，設計一可避免IPM 傾斜動作受到負載干擾(來 自地面干擾或不完全傾斜命令)所影響之控制器，此控制器被經由一已驗證之 IPM 多體系統模型所驗證，而此IPM 多體模型被藉由與實車曲行測試比較，驗證其具 有高度準確性，此一模型可以幫助傾斜動作控制器之設計。對於未來研究有以下 建議：

(1) 利用此多體系統模型分析更多 IPM 的共振模態。

(2) 在 IPM 實車中，實現此本論文中所提出之強健雙迴路 PID 控制器。

(3) 利用不同的控制理論設計 IPM 傾斜動作控制器，以適應不同的駕駛習慣或提 高控制傾斜動作之性能。

(4) 考慮本文已設計的控制器之特性，改善傾斜動作控制策略，使其更能提高 IPM 之過彎穩定性。

附錄一

m m =

b

+ m

_c

If rollover just happened F then

a g x y

l car tilt l half car tilt l non tilting

If tilts to the left side and Then

a g a g

_θ

a g

_{θ θ}

θ π θ π

= = =

< < < <

> >

(A.11)

附錄二

mb6 圖10 中體 5。

約束方程數(number of constraint equations)和其連接之體(connecting bodies)如 表4所示。

J5 r 2 [mb3, mb4]

J6 r 2 [mb3, mb6]

J7 r-r 1 [mb4, mb5]

J8 r-r 1 [mb4, mb5]

J9 r-r 1 [mb6, mb7]

J10 r-r 1 [mb6, mb7]

J11 t 2 [mb2, mb8]

備註： r, revolute joints; t, transitional joints; r-r, revolute-revolute composite joints;

r-t, revolute-translational composite joints (各接接頭之描述請見附錄三與[15])

附錄三

圖12中說明多體系統之座標定義如下：

xy coord. 固定在參考點的整體座標(global coordinate)。

ξiηi coord. 在body i 上的體固定座標(Body-fixed coordinate) ，其 ξiηi座標軸

x i y i

T

有了上述座標定義，接下來對於本文中所使用之接頭作精要敘述：

相對旋轉驅動約束(relative revolute driving constraint)

相對旋轉驅動約束是旋轉接頭限制的兩個剛體，在有驅動動器的作用下限制

r (revolute) joint 旋轉接頭

ηi r-r (revolute-revolute) joint 旋轉-旋轉接頭

如圖72 所示，旋轉-旋轉接頭之約束為在 body i 上 P 點與在 body j 上 P 點之

η

i r-t (revolute-translational) joint 旋轉-平移接頭

如圖 73 所示，旋轉-平移接頭之約束為在平移接頭上移除其對兩物體間的相

Ψ

j

η

j

ξ

j

η

i

ξ

i

Ψ

i

圖73 旋轉-平移接頭示意圖

附錄四

Fj,ys 由彈簧作用在body j 的力。

Fj,yd 由阻尼作用在body j 的力。

yj,c 點Cj對y 軸的分量。

Ct 阻尼係數(Damping coefficient)。

Kt 彈簧常數(Spring constant)。

lo Pj與Cj.的原始距離。

, , ,

附錄五

圖16-18與式(3.1)-(3.8)之符號：

θsl 左側輪之外傾角(Camber angle)。

θsr 右側輪之外傾角。

φ 底盤翻滾角(roll angle)

θd mb2垂直軸與mb1水平軸之夾角。

θm 由M 至接頭 J1(圖 11)之線與地面鉛直方向夾角。

Lcj,x M 對於接頭 J1之向量在x 方向上之分量。

Lcj,y M 對於接頭 J1之向量在y 方向上之分量。

lb Mb與接頭J1之距離。

lch Mc與接頭J1之距離。

lmo M 與接頭 J1之距離。

附錄六

Fxsr 右側輪所受x 方向地

f,v (vertical spring constant)。

r,v

圖74說明了假設在一平坦路面上穩態轉向時，作用在IPM(此時彈簧未變形)

/( cos )

,

sr v sr tsr tsr sr sr

k = k k k + k θ

(F.4)

¹

k

_,

( Δz l ) /(cos cos )

sin cos sin cos cos

zf f xf f b yf f

sin cos sin cos cos

zr r xr r b yr r

xr yr x

/

F = F a a

_y (F.17)

xsl ysl x

/

y

F = F a a

(F.18)

xsr ysr x

/

y

F = F a a

(F.19)

圖74 地面施加於 IPM 之力

圖75 輪胎 v-axis 之定義

θ

m

θ

b

θ

b

θ

sl

θ

sr

ϕ + Δ ϕ ψ

θ

b

F3 4

F2

F1

F

ψ O

2

圖76 地面力作用與運定學運動所造成之彈簧變形

附錄七

表8 圖 11 中，懸吊系統對應其連接之體的初始相對位置

矩陣中，其

Q矩陣

其為24×1之矩陣，會依系統狀態而變，此矩陣中包括作用各個物體質量中心 的重力、連接至彈簧的物體之彈簧力與其造成之力矩、連接至阻尼器的物體之阻 尼力與其造成之力矩、連接至輪胎的物體之輪胎力與其造成之力矩，置於其相對 應物體之位置。

γ矩陣

依J1、J2、J3、J4、J5、J6、J7、J8、J9、J10、J11、Jrd(Jrd僅在驗證時有用到，

在傾斜動作控制器作用下，其移除)的順序，擺入18×1(在傾斜動作控制器作用下 為17×17)矩陣中，其將依系統狀態而改變。

將依系統狀態而改變。

附錄八

圖77 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，8.0m/s 曲行測試之 傾斜動作(1)

time (sec)

8.0 m/s, L=0.3m, 13.33Hz

time (sec)

8.0 m/s, L=0.4m, 10Hz

圖78 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，8.0m/s 曲行測試之 傾斜動作(2)

圖79 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，8.0m/s 曲行測試之 傾斜動作(3)

圖80 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，13.0m/s 曲行測試之 傾斜動作(1)

圖81 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，13.0m/s 曲行測試之 傾斜動作(2)

圖82 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，13.0m/s 曲行測試之 傾斜動作(3)

圖83 完全傾斜命令，在不同波長之路面干擾下(A=0.02m)，13.0m/s 曲行測試之 傾斜動作(4)

圖84 完全傾斜命令，在不同振幅之路面干擾下(L=0.2m)，8.0m/s 曲行測試之傾 斜動作(1)

圖85 完全傾斜命令，在不同振幅之路面干擾下(L=0.2m)，8.0m/s 曲行測試之傾 斜動作(2)

time (sec)

8.0 m/s, A=0.05m

圖86 完全傾斜命令，在不同振幅之路面干擾下(L=0.2m)，8.0m/s 曲行測試之傾 斜動作(3)

time (sec)

13.0 m/s, A=0.01m

圖87 完全傾斜命令，在不同振幅之路面干擾下(L=0.2m)，13.0m/s 曲行測試之 傾斜動作(1)

圖88 完全傾斜命令，在不同振幅之路面干擾下(L=0.2m)，13.0m/s 曲行測試之 傾斜動作(2)

圖89 完全傾斜命令，在不同振幅之路面干擾下(L=0.2m)，13.0m/s 曲行測試之 傾斜動作(3)

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1

法與驗

志良，簡 ，邱俊誠，鍾鵬文， “菱形四輪可傾窄車之建模、模擬與分析”，

在文檔中 一款菱形四輪可傾窄車之多體系統建模與使用QFT/H∞方法之強健雙迴路PID傾斜動作控制器設計 (頁 86-128)