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Chen et al. Complex Eng Syst 2023;3:8 I http://dx.doi.org/10.20517/ces.2022.50 Page 7 of 15
= [ , Δ ] . The output variables of this system are the same as the state variables, that is, = [ , , ] .
The two control variables can be expressed approximately in terms of the longitudinal force of each tire, as
follows:
= + + +
(13)
Δ = − + − /2
According to Eq. (5), the state-space representation of this control system is as follows:
¤ = ( , ) (14)
To reduce computational cost, the system state-space equation is linearized as follows:
¤ = + (15)
=
h i 1/ 0 0
where = ( , ) = , = ( , ) = 0 0 1/ , = diag(1, 1, 1)
h i
+ 1 + cos + + − + sin ;
h i
1
+ sin + + cos + +
1
= − 2 + sin + + cos + + ; (16a)
h h i i
1
+ sin + − cos + −
2
h i
1
+ + cos + − sin − +
2
h i
1
+ + cos + + − + sin ;
h i
1
+ sin + + cos + + ; (16b)
= h h i i
1
+ sin + − cos + − 2
h i
1
+ + cos + − 2 sin − +
h i
1
+ + cos + + − + sin ;
h i
1
−1 + + sin + + cos + + ; (16c)
= h h i i
1
+ sin + − cos + − 2
h i
1
+ + cos + − 2 sin − +
