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Cui et al. Complex Eng Syst 2023;3:3 I http://dx.doi.org/10.20517/ces.2022.57 Page 5 of 15

where

2 2
= −2 1 + 2 = −2 1 + 2 2

= −2 1 1 + 2 2 2 = 2 1
1 − 2
= −2 = −2 ( 1 + 2 )
= −2 1 1 − 2 2 2 = 2 1
1 + 2 2
= −[2 1 1 ℎ + 2 2 2 ℎ + 2( 21 + 23 + ) − ℎ]
2
= −2 ( 21 + 23 ) 2
The following formula can be obtained by Laplace transformation of the above formula
3 2
 ( ) 3 + 2 + 1 + 0
 =
 ( ) 4 3 2
 4 + 3 + 2 + 1 + 0

  3 2
( ) 3 + 2 + 1 + 0 (8)
=
4
3
2
( ) 4 + 3 + 2 + 1 + 0


 2
 ( ) 2 + 1 + 0
 =
2
4
3
 ( ) 4 + 3 + 2 + 1 + 0
where
2 2
3 = − + ℎ − ℎ

2 = + −
1 = − + − hum + ℎ
0 = − +
2
2
4 = − + ℎ 2

2 2 2
3 = + − ℎ + ℎ + ℎ − +

2 2
2 = − − + ℎ + + −

−ℎ − + ℎ
1 = − + − + ℎ ℎ − + −
− hum +
0 = − + − hum + hum
2
3 = −ℎ + −

2 2
2 = − ℎ − + + ℎ +

1 = − + + − + −
0 = − + − + ℎ − ℎ
2 = − − ℎ
1 = − hum + + hum −
0 = hum − hum
According to Formula (1) and (8), the transfer function from the rotation angle of steering wheel ( ) to the
rotation angle of front wheel ( ) can be expressed as
( ) +
= (9)
( ) 2 2 1 ( ) ( ) ( )
2 + 2 + 2 + + + 1 ( )
2 ( ) ( )
where
 2
 X 2 = m 1 + 1 2





2 2
2
 2
2 = + 2 + 2 2 1

 2 1



 2 1
 2 = + 1 −
 1