Abstract
Torque vectoring control is one of the most interesting techniques applicable to electric vehicles with multiple motors. Essentially it is the possibility to allocate desired amounts of torque to each motor. With an uneven allocation of torque between left and right sides of the vehicle, a direct yaw moment can be generated and exploited to enhance the vehicle handling behaviour. This allows to enhance vehicle safety, stability and cornering performance. Significant energy efficiency benefits are also achievable, either as a main priority or as a secondary objective when the main target is the vehicle handling behaviour. This Chapter explains the underlying principles of each element of a torque vectoring control framework: reference generator, high level controller, and low level controller. Notable applications are also presented and discussed in detail.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Also, sometimes R is confused with the distance between instant centre and centre of mass \(\frac{\sqrt{u^2+v^2}}{r}\) (or simply CG in Fig. 3), this is fine for small values of v.
- 2.
\(S_r\) may be roughly between 12 and 20.
- 3.
Again the sideslip angle is assumed small so that \(V \approx u\).
- 4.
The effect of \(a_x\) on the cornering response can be seen in De Novellis et al. (2015a), Figs. 6 and 7.
- 5.
For instance, the yaw rate controller is designed for dry conditions, \(\mu \approx 0.8 - 1\), but the road is wet. Or, even in dry conditions, \(\mu \) happens to be overestimated.
- 6.
Unless \(m V^2 + C_1 a_1 - C_2 a_2=0\).
- 7.
See Table 1 in Tota et al. (2018).
- 8.
For instance, e.g., Manning and Crolla (2007) suggest that the feedforward contribution “tends to reduce the time lag between steer angle input and vehicle reaction”.
- 9.
In other words, a simple “cruise control” logic.
- 10.
In principle the double-track model above could also be used, with potentially any tyre model—however in case of strong nonlinearities and/or if the tyre model accounts for combined interactions, for computational reasons it would be more appropriate to derive a \(M_{z,FF}\) map, as in De Novellis et al. (2013).
- 11.
The interested reader might find interesting to know how to obtain this result from, e.g., Stanford-University (2020).
- 12.
Note that this is not a Differential Riccati Equation (DRE) because of the infinite horizon used in 56 (otherwise the right-hand-side of this equation would be \( - \dot{P}\) instead of 0).
- 13.
Because the single-track vehicle model assumes constant vehicle speed, a gain scheduling approach is often implemented.
- 14.
- 15.
The reference yaw rate is designed based on the steady-state relationship \(r_{ref}=a_y/V\), but in general \(a_x \ne 0\) is also allowed.
- 16.
It should also be noted that compared to a conventional ESC, the torque vectoring controller interventions can be seamlessly and continuously generated, without necessarily decreasing the vehicle speed.
- 17.
- 18.
In iCOMPOSE a dedicated sideslip angle sensor was used, to ensure a reliable measurement of u and v in any condition, so as to be able to fully focus on the design of the controllers.
- 19.
Another example would be a parking manoeuvre, which entails high steering angles, hence high kinematic sideslip angles, but low tyre slips, hence small dynamic sideslip angles.
- 20.
That is, the wheel steer angle divided by the vehicle wheelbase and multiplied by the distance between the rear axle and the point of interest.
- 21.
Obviously this index makes sense only if \(\beta _{ref}\) is defined. As discussed, concurrent yaw rate and sideslip control is possible even without defining \(\beta _{ref}\), by integrating the sideslip angle in the reference yaw rate formulation, as shown in 42.
- 22.
Note that lateral force contributions, \(F_{y_{ij}}\) do not appear in these equations because they cannot be controlled, as extensively discussed in Sect. 4.2.
- 23.
- 24.
These can be easily obtained imposing that the first order derivative of \(P_{loss,{ij}}\) with respect to \(T_{ij}\) must be positive, and that the second order derivative is zero for a positive value of \(T_{ij}\).
- 25.
Note that the left-hand side can be either \(P_{loss,{1j}}(T_{sw},V)+P_{loss,{2j}}(0,V)\) or \(P_{loss,{1j}}(0,V)+P_{loss,{2j}}(T_{sw},V)\) since, as discussed, \(\sigma =0\) and \(\sigma =1\) yield the same power losses for a vehicle side.
- 26.
While \(\sigma =0\) and \(\sigma =1\) are equivalent in terms of power losses, \(\sigma =1\) is preferred for safety reasons since, from a vehicle dynamics point of view, understeer is better than oversteer.
- 27.
It is worth to note that, hypothetically, assigning more than the overall torque demand on the external vehicle side would imply a negative (regenerative) torque on the inner side, which is far from optimal (Lenzo et al., 2017a).
- 28.
Details are in Lenzo et al. (2017a).
References
Acosta, M., & Kanarachos, S. (2018). Tire lateral force estimation and grip potential identification using neural networks, extended kalman filter, and recursive least squares. Neural Computing and Applications, 30(11), 3445–3465.
Åström, K. J., & Murray, R. M. (2010). Feedback systems: An introduction for scientists and engineers. Princeton University Press.
Bucchi, F., & Frendo, F. (2016). A new formulation of the understeer coefficient to relate yaw torque and vehicle handling. Vehicle System Dynamics, 54(6), 831–847.
Cheli, F., Sabbioni, E., Pesce, M., & Melzi, S. (2007). A methodology for vehicle sideslip angle identification: Comparison with experimental data. Vehicle System Dynamics, 45(6), 549–563.
Chen, L., Chen, T., Xing, X., Cai, Y., Jiang, H., & Sun, X. (2018). Multi-objective coordination control strategy of distributed drive electric vehicle by orientated tire force distribution method. IEEE Access, 6, 69559–69574.
Chindamo, D., Lenzo, B., & Gadola, M. (2018). On the vehicle sideslip angle estimation: A literature review of methods, models, and innovations. Applied Sciences, 8(3), 355.
De Filippis, G., Lenzo, B., Sorniotti, A., Sannen, K., De Smet, J., & Gruber, P. (2016). On the energy efficiency of electric vehicles with multiple motors. In 2016 IEEE Vehicle Power and Propulsion Conference (VPPC) (pp. 1–6). IEEE.
De Filippis, G., Lenzo, B., Sorniotti, A., Gruber, P., & De Nijs, W. (2018). Energy-efficient torque-vectoring control of electric vehicles with multiple drivetrains. IEEE Transactions on Vehicular Technology.
De Novellis, L., Sorniotti, A., & Gruber, P. (2013). Optimal wheel torque distribution for a four-wheel-drive fully electric vehicle. SAE International Journal of Passenger Cars-Mechanical Systems, 6(2013-01-0673), 128–136.
De Novellis, L., Sorniotti, A., & Gruber, P. (2014a). Design and comparison of the handling performance of different electric vehicle layouts. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 228(2), 218–232.
De Novellis, L., Sorniotti, A., & Gruber, P. (2014b). Wheel torque distribution criteria for electric vehicles with torque-vectoring differentials. IEEE Transactions on Vehicular Technology, 63(4), 1593–1602.
De Novellis, L., Sorniotti, A., Gruber, P., & Pennycott, A. (2014c). Comparison of feedback control techniques for torque-vectoring control of fully electric vehicles. IEEE Transactions on Vehicular Technology, 63(8), 3612–3623.
De Novellis, L., Sorniotti, A., & Gruber, P. (2015a). Driving modes for designing the cornering response of fully electric vehicles with multiple motors. Mechanical Systems and Signal Processing, 64, 1–15.
De Novellis, L., Sorniotti, A., Gruber, P., Orus, J., Rodriguez Fortun, J.-M., Theunissen, J., & De Smet, J. (2015b). Theoretical design and experimental assessment. Direct yaw moment control actuated through electric drivetrains and friction brakes. Mechatronics, 26, 1–15.
Ding, S., Liu, L., & Zheng, W. X. (2017). Sliding mode direct yaw-moment control design for in-wheel electric vehicles. IEEE Transactions on Industrial Electronics, 64(8), 6752–6762.
Dizqah, A. M., Lenzo, B., Sorniotti, A., Gruber, P., Fallah, S., & De Smet, J. (2016). A fast and parametric torque distribution strategy for four-wheel-drive energy-efficient electric vehicles. IEEE Transactions on Industrial Electronics, 63(7), 4367–4376.
Esmailzadeh, E., Goodarzi, A., & Vossoughi, G. R. (2003). Optimal yaw moment control law for improved vehicle handling. Mechatronics, 13(7), 659–675.
Frendo, F., Greco, G., Guiggiani, M., & Sponziello, A. (2007). The handling surface: A new perspective in vehicle dynamics. Vehicle System Dynamics, 45(11), 1001–1016.
Gasmi, A., Boudali, M.-T., Orjuela, R., & Basset, M. (2019). Multi-criteria stability combination for yaw stability control of autonomous vehicles. IFAC-PapersOnLine, 52(5), 465–470.
Genta, G. (1997). Motor vehicle dynamics: Modeling and simulation (Vol. 43). World Scientific.
Goggia, T., Sorniotti, A., De Novellis, L., Ferrara, A., Gruber, P., Theunissen, J., et al. (2015). Integral sliding mode for the torque-vectoring control of fully electric vehicles: Theoretical design and experimental assessment. IEEE Transactions on Vehicular Technology, 64(5), 1701–1715.
Gruber, P., Sorniotti, A., Lenzo, B., De Filippis, G., & Fallah, S. (2016). Energy efficient torque vectoring control. Advanced vehicle control AVEC (pp. 17–22). CRC Press.
Guiggiani, M. (2018). The science of vehicle dynamics. Springer.
Guo, H., Cao, D., Chen, H., Lv, C., Wang, H., & Yang, S. (2018). Vehicle dynamic state estimation: State of the art schemes and perspectives. IEEE/CAA Journal of Automatica Sinica, 5(2), 418–431.
Guo, N., Lenzo, B., Zhang, X., Zou, Y., Zhai, R., & Zhang, T. (2020). A real-time nonlinear model predictive controller for yaw motion optimization of distributed drive electric vehicles. IEEE Transactions on Vehicular Technology, 69(5), 4935–4946.
He, J.-B., Wang, Q.-G., & Lee, T.-H. (2000). PI/PID controller tuning via LQR approach. Chemical Engineering Science, 55(13), 2429–2439.
Isermann, R. (2012). Digital control systems: Volume 2: Stochastic control, multivariable control, adaptive control, applications. Springer Science & Business Media.
Kaiser, G. (2015). Torque vectoring-linear parameter-varying control for an electric vehicle. Technische Universität Hamburg.
Kiencke, U., & Nielsen, L. (2000). Automotive control systems: For engine, driveline, and vehicle.
Koehler, S., Viehl, A., Bringmann, O., & Rosenstiel, W. (2015). Improved energy efficiency and vehicle dynamics for battery electric vehicles through torque vectoring control. In 2015 IEEE Intelligent Vehicles Symposium (IV) (pp. 749–754). IEEE.
Lenzo, B., & De Castro, R. (2019). Vehicle sideslip estimation for four-wheel-steering vehicles using a particle filter.
Lenzo, B., Sorniotti, A., De Filippis, G., Gruber, P., & Sannen, K. (2016). Understeer characteristics for energy-efficient fully electric vehicles with multiple motors. In EVS29 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium Proceedings.
Lenzo, B., De Filippis, G., Moradinegade Dizqah, A., Sorniotti, A., Gruber, P., Fallah, S., & De Nijs, W. (2017a). Torque distribution strategies for energy-efficient electric vehicles with multiple drivetrains. Journal of Dynamic Systems, Measurement, and Control, 139(12).
Lenzo, B., Sorniotti, A., Gruber, P., & Sannen, K. (2017b). On the experimental analysis of single input single output control of yaw rate and sideslip angle. International Journal of Automotive Technology, 18(5), 799–811.
Lenzo, B., Bucchi, F., Sorniotti, A., & Frendo, F. (2019a). On the handling performance of a vehicle with different front-to-rear wheel torque distributions. Vehicle System Dynamics, 57(11), 1685–1704.
Lenzo, B., Gruber, P., & Sorniotti, A. (2019b). On the enhancement of vehicle handling and energy efficiency of electric vehicles with multiple motors: The icompose project. In The IAVSD International Symposium on Dynamics of Vehicles on Roads and Tracks (pp. 1342–1349). Springer.
Lenzo, B., Zanchetta, M., Sorniotti, A., Gruber, P., & De Nijs, W. (2020). Yaw rate and sideslip angle control through single input single output direct yaw moment control. IEEE Transactions on Control Systems Technology.
Lin, C., & Zhifeng, X. (2015). Wheel torque distribution of four-wheel-drive electric vehicles based on multi-objective optimization. Energies, 8(5), 3815–3831.
Qian, L., Sorniotti, A., Gruber, P., Theunissen, J., & De Smet, J. (2016). H-infinity loop shaping for the torque-vectoring control of electric vehicles: Theoretical design and experimental assessment. Mechatronics, 35, 32–43.
Mahmoudi, A., Soong, W. L., Pellegrino, G., & Armando, E. (2015). Efficiency maps of electrical machines. In 2015 IEEE Energy Conversion Congress and Exposition (ECCE) (pp. 2791–2799). IEEE.
Mangia, A., Lenzo, B., & Sabbioni, E. (2021). An integrated torque-vectoring control framework for electric vehicles featuring multiple handling and energy-efficiency modes selectable by the driver. Meccanica, 1–20.
Manning, W. J., & Crolla, D. A. (2007). A review of yaw rate and sideslip controllers for passenger vehicles. Transactions of the Institute of Measurement and Control, 29(2), 117–135.
Pacejka, H. (2006). Tire and vehicle dynamics. Butterworth-Heinemann.
Parra, A., Zubizarreta, A., Pérez, J., & Dendaluce, M. (2018). Intelligent torque vectoring approach for electric vehicles with per-wheel motors. Complexity, 2018.
Pennycott, A., De Novellis, L., Gruber, P., & Sorniotti, A. (2015). Sources of power loss during torque-vectoring for fully electric vehicles. International Journal of Vehicle Design, 67(2), 157–177.
Piyabongkarn, D., Lew, J. Y., Rajamani, R., & Grogg, J. A. (2010). Active driveline torque-management systems. IEEE Control Systems Magazine, 30(4), 86–102.
Preda, I., Covaciu, D., & Ciolan, G. (2010). Coast down test–theoretical and experimental approach.
Rajamani, R. (2011). Vehicle dynamics and control. Springer Science & Business Media.
Sforza, A., Lenzo, B., & Timpone, F. (2019). A state-of-the-art review on torque distribution strategies aimed at enhancing energy efficiency for fully electric vehicles with independently actuated drivetrains. International Journal of Mechanics and Control, 20(2), 3–15.
Siampis, E., Velenis, E., & Longo, S. (2016). Front-to-rear torque vectoring model predictive control for terminal understeer mitigation. In The Dynamics of Vehicles on Roads and Tracks: Proceedings of the 24th Symposium of the International Association for Vehicle System Dynamics (IAVSD 2015), Graz, Austria, 17–21 August 2015 (p. 153). CRC Press.
Skogestad, S., & Postlethwaite, I. (2007). Multivariable feedback control: Analysis and design (Vol. 2). New York: Wiley.
Stanford-University (2020). Linear quadratic regulator. Retrieved June 09, 2020, from https://stanford.edu/class/ee363/lectures/dlqr.pdf
Tota, A., Lenzo, B., Qian, L., Sorniotti, A., Gruber, P., Fallah, S., et al. (2018). On the experimental analysis of integral sliding modes for yaw rate and sideslip control of an electric vehicle with multiple motors. International Journal of Automotive Technology, 19(5), 811–823.
Tuncay, R. N., Ustun, O., Yilmaz, M., Gokce, C., & Karakaya, U. (2011). Design and implementation of an electric drive system for in-wheel motor electric vehicle applications. In 2011 IEEE Vehicle Power and Propulsion Conference (pp. 1–6). IEEE.
Utkin, V., & Shi, J. (1996). Integral sliding mode in systems operating under uncertainty conditions. In Proceedings of 35th IEEE Conference on Decision and Control (Vol. 4, pp. 4591–4596). IEEE.
Utkin, V., Guldner, J., & Shi, J. (2017). Sliding mode control in electro-mechanical systems. CRC Press.
Vantsevich, V. V., Barz, D., Kubler, J., & Schumacher, A. (2005). Tire longitudinal elasticity and effective rolling radii: Experimental method and data. Technical report, SAE Technical Paper.
Vantsevich, V. V., Paldan, J., & Verma, M. (2017). Instantaneous compression-based tyre rolling radius. In Dynamics of Vehicles on Roads and Tracks Vol 1: Proceedings of the 25th International Symposium on Dynamics of Vehicles on Roads and Tracks (IAVSD 2017), 14–18 August 2017, Rockhampton, Queensland, Australia (p. 259). CRC Press.
Vignati, M., Sabbioni, E., & Tarsitano, D. (2016). Torque vectoring control for IWM vehicles. International Journal of Vehicle Performance, 2(3), 302–324.
Wang, J., Gao, S., Wang, K., Wang, Y., & Wang, Q. (2021). Wheel torque distribution optimization of four-wheel independent-drive electric vehicle for energy efficient driving. Control Engineering Practice, 110, 104779.
White, R. A., & Korst, H. H. (1972). The determination of vehicle drag contributions from coast-down tests. SAE Transactions, 354–359.
Wong, A., Kasinathan, D., Khajepour, A., Chen, S.-K., & Litkouhi, B. (2016). Integrated torque vectoring and power management framework for electric vehicles. Control Engineering Practice, 48, 22–36.
Zanchetta, M., Tavernini, D., Sorniotti, A., Gruber, P., Lenzo, B., Ferrara, A., Sannen, K., De Smet, J., & De Nijs, W. (2019). Trailer control through vehicle yaw moment control: Theoretical analysis and experimental assessment. Mechatronics,64, 102282.
Zhou, H., & Liu, Z. (2009). Design of vehicle yaw stability controller based on model predictive control. In 2009 IEEE Intelligent Vehicles Symposium (pp. 802–807). IEEE.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 CISM International Centre for Mechanical Sciences
About this chapter
Cite this chapter
Lenzo, B. (2022). Torque Vectoring Control for Enhancing Vehicle Safety and Energy Efficiency. In: Lenzo, B. (eds) Vehicle Dynamics. CISM International Centre for Mechanical Sciences, vol 603. Springer, Cham. https://doi.org/10.1007/978-3-030-75884-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-75884-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-75882-0
Online ISBN: 978-3-030-75884-4
eBook Packages: EngineeringEngineering (R0)