This paper presents reduced-order models of brake system dynamics derived from a physical modeling perspective. The vacuum booster model combines a static control valve with dynamic air flows, resulting in the ability to easily reproduce both static hysteresis effects and rapid transients. Following the assumption of incompressible flow, a four-state model of the brake hydraulics is presented and, subsequently, reduced to one or two states for certain applications. Experimental results support the simplifying assumptions made during the modeling process by demonstrating better agreement with the response from pedal force to brake pressure than previously displayed in the literature. These models are intended for use in the design and analysis of vehicle control systems and the evaluation of driver/vehicle interactions through dynamic simulation.

1.
Antoniotti, M., and A. Gollu, 1997, “SHIFT and Smart AHS: A language for hybrid systems engineering, modeling, and simulation,” Proceedings of the USENIX Conference of Domain Specific Languages, Santa Barbara, CA.
2.
Buschmann, G., M. Roth and K. Saalbach, 1993, “Tandem master cylinder in change—due to specific requirements of Anti Lock and Traction Control Systems,” SAE Paper #930504.
3.
Connolly, T. R., and J. K. Hedrick, 1996, “Longitudinal transition maneuvers in an automated highway system,” Proceedings of the ASME Dynamic Systems and Control Division, 1996 IMECE, Atlanta, GA. Vol. DSC-58.
4.
Fisher, D. K., 1970, “Brake system component dynamic performance measurement and analysis,” SAE Paper #700373.
5.
Gerdes, J. C., and J. K. Hedrick, 1996, “Vehicle speed and spacing control via coordinated throttle and brake actuation,” Proceedings of the 13th Triennial World Congress, International Federation of Automatic Control, San Francisco, CA, Vol. Q, pp. 183–188.
6.
Gerdes, J. C., D. B. Maciuca, J. K. Hedrick and P. E. Devlin, 1993, “Brake system modeling for IVHS longitudinal control,” Advances in Robust and Nonlinear Control Systems, ASME Winter Annual Meeting, pp. 119–126.
7.
Gillespie, Thomas D., 1992, Fundamentals of Vehicle Dynamics, Society of Automotive Engineers. Warrendale, PA.
8.
Ioannou
P.
, and
Xu
Z.
,
1994
, “
Throttle and brake control systems for automatic vehicle following
,”
IVHS Journal
,
1
(
4
),
345
377
.
9.
Khan
Y.
,
Kulkarni
P.
, and
Youcef-Toumi
K.
,
1994
, “
Modeling, experimentation and simulation of a brake apply system
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
116
(
1
), pp.
111
122
.
10.
Limpert, Rudolf, 1992, Brake Design and Safety. Society of Automotive Engineers. Warrendale, PA.
11.
McMahon, D. H., J. K. Hedrick, and S. E. Shladover, 1990, “Vehicle modelling and control for automated highway systems,” Proceedings of the 1990 American Control Conference, San Diego, CA, pp. 297–303.
12.
McMahon, D. H., V. K. Narendran, D. Swaroop, J. K. Hedrick, K. S. Chang, and P. E. Devlin, 1992, “Longitudinal vehicle controllers for IVHS: Theory and experiment,” Proceedings of the 1992 American Control Conference, Chicago, IL, pp. 1753–1757.
13.
Nash, R., 1983, “Brake integrated hydraulic actuation system master cylinder,” SAE Paper #830412.
14.
Puhn, Fred, 1985, Brake Handbook, HP Books. Los Angeles, CA.
15.
Radlinski, R. W., 1991, “The effect of aftermarket linings on light vehicle braking performance,” Final Report DOT HS 807 835. U.S. Department of Transportation, NHTSA.
16.
Raza
H.
,
Xu
Z.
,
Ioannou
P.
, and
Yang
B.
,
1997
, “
Modeling and control design for a computer-controlled brake system
,”
IEEE Transactions on Control System Technology
, Vol.
5
(
3
), pp.
279
296
.
17.
van Zanten, Anton T., Rainer, Erhardt and Georg Pfaff, 1995, “VDC, the vehicle dynamics control system of Bosch,” SAE Paper #950759.
18.
Xu, Z., and P. Ioannou, 1992, “Modeling of the brake line pressure to tire brake force subsystem,” Technical Report 92-09-01. California PATH Program.
This content is only available via PDF.
You do not currently have access to this content.