Vehicle Torque
Vectoring
Control
ECE 1635
April 6, 2015
Christopher Au Moeed Siddiqui Yujie Guo
Agenda
Background
Plant
Controller
Simulation Results
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Background
● Two types of undesirable vehicle steering dynamics
○ Understeer
○ Oversteer
● TV Advantages:
○ Improved handling
○ Traction when turning
○ Better overall performance in
poor road conditions
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Plant Model
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Plant: Mathematical Models
Reference Model：
Vehicle Motion Model：
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Plant: Simulation Parameters
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Controller - State Feedback
Full State Feedback Controller
With Integral Action:
● Controllable system
● Pole placement using Matlab
Controllability Matrix:
Control Law:
Closed Loop System:
Block Diagram for Full State
Feedback Controller /with
Integral Action
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Controller - State Feedback
Tuning Full State Feedback Controller
With Integral Action:
Tuning Parameters:
Step Response: Close Loop Bode Diagram:
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Controller - Sliding Mode
Sliding Mode Controller
● Discontinuous control signal
● Adds robustness to the closed-loop system
Smoothed Error:
Control Law:
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Controller - Sliding Mode
Consider the Lyapunov candidate function:
Choose design parameter:
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Simulation - HIL Setup
● HIL DEMO
Steering Input Vehicle Yaw Rate
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Simulation - HIL Problems
● To resolve controller instability when using HIL:
○ Increased sampling period in Labview
○ Eliminated dead zone when motor changes direction
○ Added scaling to PD controller to replicate gearing
○ More aggressive LPF
Motor speed PD controller
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Simulation Results - State Feedback
● State Feedback Controller Performance
○ approximate 0 steady state error
○ 1 sec delay during transients
○ maximum torque range -400N/m to +400N/m
Steering Input Yaw Rate Torque Transfer
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Simulation Results - Sliding Mode Control
● 0% ss error
● 0.5 second delay
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Controller Comparison
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Controller Simulation Video
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3DOF Bicycle Model
Distance and Angle Matrix:
Velocity Matrix:
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Conclusion
● Two controllers were design to implement torque
vectoring
○ State feedback based on an augmented plant
○ Nonlinear sliding mode controller
● HIL simulation in Labview
○ Results show that sliding mode performs better
● Recommendations
○ Kalman Filter
○ Feedforward controller
○ Adaptive controller
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Thank You
Questions?
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References
[1] DSC CONTROL. (2012). Retrieved March 30, 2015, from
http://madstyle1972.com/MAZDA6_2014/servicehighlights/books/n6w04/html/id041500103900.html
[2] Burgess, M. Torque vectoring. Retrieved March 17, 2015, from
http://www.vehicledynamicsinternational.com/downloads/VDI_Lotus_Vector.pdf
[3] NAGAI, M., HIRANO, Y., & YAMANAKA, S. (2007). Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment
Control. Retrieved March 17, 2015, from
http://www.tandfonline.com/doi/abs/10.1080/00423119708969336#.VRlpCpPF8WU
[4] Aircraft Pitch: State-Space Methods for Controller Design. (2012). Retrieved March 17, 2015, from
http://ctms.engin.umich.edu/CTMS/index.php?example=AircraftPitch§ion=ControlStateSpace
[5] Slotine, J., & Li, W. (1990). Applied Nonlinear Control Paperback. Prentice Hall; 1 edition. Retrieved March 17, 2015, from
ftp://222.18.54.49/xiaomagecc/Applied%20Nonliear%20control%20[Slotin%201991--Prentice%20Hall].pdf
[6] Thang Truong, D., Meywerk, M., & Tomaske, W. (2013). Torque Vectoring for Rear Axle using Adaptive Sliding Mode Control.
Retrieved March 17, 2015, from
https://www.deepdyve.com/lp/institute-of-electrical-and-electronics-engineers/torque-vectoring-for-rear-axle-using-adaptive-sliding-
mode-control-4RQOOh9G9i
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