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Page 384 Zhang et al. Intell Robot 2022;2(4):371­90 I http://dx.doi.org/10.20517/ir.2022.26

Figure 5. Structure of the car-following systems in Carsim/Simulink joint simulation environment.

. As ∈ (0.01, 0.04), is sufficiently small to be neglected in this study. The following exist:

, , . (48)
2 2 2
eff eff eff
Then, can be rewritten as = . Therefore, Equation (47) can be rewritten as follows:
2
2
eff
e,des = eff ( + ). (49)
Thus, the corresponding expected throttle opening des can be obtained from the inverse dynamic relation.

4.2. Braking control
During vehicle braking, the desired acceleration and the yaw moment given by the upper controller
can be used to determine the longitudinal tire force from the following equation [40] :

 − = + + +

 ( )

 = + − −

+ 2 ℎ , (50)
=
 − 2 ℎ

 + 2 ℎ

 =
 − 2 ℎ
where is the distance between the right and left wheels and ℎ is the height of the centre of mass of the vehicle.
Equation (50) can be solved for the longitudinal force on the four wheels. Then, we can calculate the hydraulic
pressure wheel cylinder from the following equation:

, = , (51)

where denotes the efficient wheel radius and represents the pressure constant of a single wheel.

5. SIMULATION VALIDATIONS
CarSim/Simulink joint simulations are conducted to verify the effectiveness of the proposed predictive control
based on the T-S fuzzy model. The structure of the car-following system is shown inFigure 5. The proposed
controller is derived by solving the optimization problem in Equation (41) with the YALMIP toolbox intro-
duced in [41] within the MATLAB/Simulink environment, where the vehicle model and road conditions are
provided by the CarSim platform. We simulate a severe riding condition by considering a road with snow
cover on the left-hand side of the vehicle. The test scenario is shown in Figure 6.