Adaptive optimal slip ratio estimator for effective braking on a non-uniform condition road

Figures & data

Figure 1. The vehicle single-track geometric parameters.

Figure 2. The variation of the friction coefficient, µ against the slip ratio, λ on different road conditions [1].

Table 1. Constants for different road conditions [24].

Road surface	c1	c2	c3
Dry asphalt	1.28	23.99	0.52
Wet asphalt	0.857	33.82	0.34
Snow	0.194	94.12	0.0646
Ice	0.05	306	0

Figure 3. The ABS control system.

Figure 4. The braking timing.

Table 2. Tyre and vehicle parameters [1].

Pars	Values	Pars	Values
v0	20 m/s	h	0.5 m
m	2045 kg	Lf	1.488 m
R	0.3 m	Lr	1.712 m
J	1.5 kgm^2	σ	1
L	3.2 m	df	0.45
		σω	0.005

Figure 5. The ABS controller performance in tracking the issued arbitrary slip ratio command.

Figure 6. The ABS performance using µ peak detector and the optimal slip ratio reference.

Figure 7. The performance of the speed estimator under various initial braking speed.

Figure 8. The performance of the ABS adaptive sliding mode control using $\hat{v}$.

Figure 9. The rear and front wheels braking torques.

Figure 10. The vehicle speed and its estimation over a non-uniform condition road.

Figure 11. Effective braking on a nonuniform road condition; the varying optimal reference slip ratio reference (λ) and the maximum attainable tire-road friction coefficient (µ).

Table 3. Summary of several conducted tests.

	Speed value		Slip ratio (λ) value			Braking performance
Asphalt condition	Measured	Estimated	Fixed (=0.4)	Optimal	Adaptive optimal	Time (s)	Distance (m)
Dry	*	–	*	–	–	1.807	18.92
Dry	*	–	–	*	–	1.674	17.61
Dry	–	*	–	*	–	1.687	17.87
Wet	–	*	–	*	–	2.548	25.9
DWP^a [1]	–	*	–	*	–	2	19.28
DWP^a	–	*	–		*	1.974	18.93

^aDry & Wet patches.

Zhang X, Yong X, Ming P, et al. A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations. Veh Syst Dyn. 2014;52(4):475–503. doi: 10.1080/00423114.2013.864775

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Sardarmehni T, Rahmani H, Menhaj MB. Robust control of wheel slip in anti-lock brake system of automobiles. Nonlinear Dyn. 2014;76(1):125–138. doi: 10.1007/s11071-013-1115-1

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