Dynamic Understeer Control Using Active Rear Toe
Abstract
Active rear toe is the ability to control the angle of the rear wheels around the vertical axis, allowing the carβs turning radius to change. By changing this radius, the lateral acceleration can be controlled, therefore the understeer of the vehicle can be controlled. The controls scheme is a sliding mode control, specifically a hyperbolic tangent boundary layer and a type 1 zeno controller. The system shows effectiveness to control the understeer of the vehicle up until limit grip on the tire. Once this level is achieved, lateral acceleration can only be removed, not added. It is recommended that ART should supplement controls through the brakes of the car, allowing for the car to be controlled over a larger range of performance.
What is Understeer?
If πΎππ=0, the car is considered a neutral steer configuration. This is a marginally stable condition where both the front and rear tires loose have equivalent slip angle. A car has understeer when πΎππ>0 and occurs when the front slip angle is greater than the rear. For the driver, this feels like the car is pushing through the corner and more steering then neutral steer is needed to achieve the same turning radius. Oversteer occurs when the rear slip angle is higher than the front slip angle, πΎππ<0. When the car is in an oversteering condition, less steering angle is needed then a neutral car. This is also an unstable condition where a controller must actively actuate the steering and/or throttle to maintain stability
How Rear Steer can control Understeer
Understeer can be effected by many different things. One of the main items is the CG (center of gravity) positions in the car. This changes the weight distribution and the lateral force generated by the tire. For example, if a company has a model of car with 2 variants with different CG and/or mass, this will influence the understeer behavior of the car and thus change the feel. By modifying the turning radius (R_kinematic) the understeer is also effected. Therefore, rear steer can be applied to control the cars to have the same understeer gradient by effectively canceling the effects of the different mass/CG position.
There are three main conclusions that can be drawn from this thesis. First, Active Rear Toe is a viable method for dynamically changing the handling characteristics of a vehicle in real time. Second, a nonlinear controls approach, such as sliding mode control is necessary for effective ART control. The simulations showed a non-gain scheduled PID approach was not effective. Third, the understeer gradient is commonly used to discuss handling characteristics but was a very sensitive parameter to control directly. Lateral acceleration was found to be a much easier parameter to control, and because of its direct effect on the understeer gradient, it was still able to control Kus.
Interested in further reading? Feel free to download a copy of my thesis.