Road vehicle yaw stability control systems like electronic stability program (ESP) are important active safety systems used for maintaining lateral stability of the vehicle. Vehicle yaw rate is the key parameter that needs to be known by a yaw stability control system. In this paper, yaw rate is estimated using a virtual sensor which contains kinematic relations and a velocity-scheduled Kalman filter. Kinematic estimation is carried out using wheel speeds, dynamic tire radius, and front wheel steering angle. In addition, a velocity-scheduled Kalman filter utilizing the linearized single-track model of the road vehicle is used in the dynamic estimation part of the virtual sensor. The designed virtual sensor is successfully tested offline using a validated, high degrees of freedom, and high fidelity vehicle model and using hardware-in-the-loop simulations. Moreover, actual road testing is carried out and the estimated yaw rate from the virtual sensor is compared with the actual yaw rate obtained from the commercial yaw rate sensor to demonstrate the effectiveness of the virtual yaw rate sensor in practical use. 1. Introduction Lateral stability of a road vehicle is very important for the safety of the driver and passengers during extreme lateral maneuvers or during lateral maneuvers under adverse environmental conditions like driving on snow or ice, sudden tire pressure loss, or sudden side wind. Vehicle stability control systems called ESP, vehicle dynamics control (VDC), yaw stability control (YSC), and so forth are used to improve the lateral stability of vehicles under such adverse conditions. Yaw stability control systems will become mandatory for new vehicles in Europe after 2011 (see [1]). Yaw rate is the most vital vehicle variable that needs to be known by a road vehicle stability system. The current state-of-the-art is that yaw rate is measured by yaw rate sensors in the form of microelectromechanical Sensor (MEMS) units. These sensors are commercially available, and they are used in vehicle stability systems, but like every other component inside a road vehicle, their price is a concern for manufacturers who try to lower costs [2, 3]. Some hard and expensive to measure vehicle variables like yaw rate can be estimated using other on-vehicle sensors such as lateral accelerometers and wheel speed sensors. There have been several attempts to estimate yaw rate using lateral accelerometers [2–6]. In [2], the vehicle yaw rate estimation was performed using two lateral accelerometers that are placed at the right and left sides of the vehicle. Yaw rate
References
[1]
UNECE—United Nations Economic Commission for Europe, Transport Programme, Electronic Stability Control Systems Regulation, Annex. 9, E/ECE/324, E/ECE/TRANS/505, Regulation no.13-H, p. 3, November 2009.
[2]
N. Sivashankar and A. G. Ulsoy, “Yaw rate estimation for vehicle control applications,” Journal of Dynamic Systems, Measurement and Control, vol. 120, no. 2, pp. 267–274, 1998.
[3]
W. Chee, “Yaw rate estimation using two 1-axis accelerometers,” in Proceedings of the IEEE American Control Conference (ACC '05), pp. 423–428, Portland, Ore, USA, June 2005.
[4]
A. Hac and M. D. Simpson, “Estimation of vehicle side slip angle and yaw rate,” SAE Paper 2000-01-0696, 2000.
[5]
G. Zenhai, “Soft sensor application yaw rate measurement based on Kalman filter and vehicle dynamics,” in Proceedings of the IEEE Intelligent Transportation Systems, October 2003.
[6]
C. Novara, F. Ruiz, and M. Milanese, “Direct identification of optimal SM-LPV filters and application to vehicle yaw rate estimation,” IEEE Transactions on Control Systems Technology, vol. 19, no. 1, pp. 5–17, 2011.
[7]
Y. A. Ghoneim and Y. K. Chin, “Active brake control having yaw rate estimation,” US Patent 6 169 951 B1, 2001.
[8]
P. J. T. Venhovens and K. Naab, “Vehicle dynamics estimation using Kalman filters,” Vehicle System Dynamics, vol. 32, no. 2, pp. 171–184, 1999.
[9]
H. Cherouat, M. Braci, and S. Diop, “Vehicle velocity, side slip angles and yaw rate estimation,” in Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE '05), pp. 349–354, June 2005.
[10]
M. T. Emirler, K. Kahraman, M. ？entürk, B. A. Güven？, L. Güven？, and B. Efendio？lu, “Estimation of vehicle yaw rate using a virtual sensor,” in Proceedings of the IFAC National Member Organization Conference (TOK '09), Y？ld？z Technical University, Turkey, 2009.
[11]
M. T. Emirler, K. Kahraman, B. A. Güven？, L. Güven？, and B. Efendio？lu, “Estimation of road vehicle yaw rate using a virtual sensor and an observer,” in Proceedings of the European Control Conference (ECC '09), Budapest, Hungary, 2009.
[12]
M. T. Emirler, Vehicle yaw rate estimation using virtual sensor and vehicle lateral dynamics control [M.S. thesis], Istanbul Technical University, Istanbul, Turkey, 2010, Turkish.
[13]
L. Imsland, T. A. Johansen, T. I. Fossen, H. F. Grip, J. C. Kalkkuhl, and A. Suissa, “Vehicle velocity estimation using nonlinear observers,” Automatica, vol. 42, no. 12, pp. 2091–2103, 2006.
[14]
U. Kiencke and A. Dai？, “Observation of lateral vehicle dynamics,” Control Engineering Practice, vol. 5, no. 8, pp. 1145–1150, 1997.
[15]
B. Samadi, R. Kazemi, K. Y. Nikravesh, and M. Kabganian, “Real-time estimation of vehicle state and tire-road friction forces,” in Proceedings of the IEEE American Control Conference (ACC '01), pp. 3318–3323, Arlington, Va, USA, June 2001.
[16]
B. A. Güven？, L. Güven？, E. S. ？ztürk, and T. Yi？it, “Model regulator based individual wheel braking control,” in Proceedings of the IEEE Conference on Control Applications, Istanbul, Turkey, 2003.
[17]
D. Simon, Optimal State Estimation, Wiley, Hoboken, NJ, USA, 2006.
[18]
J. Ackermann, P. Blue, T. Bünte, et al., Robust Control: The Parameter Space Approach, Springer, London, UK, 2002.
